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Systems. SIAM J. Computing 25(1): 169“192, 1996.
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Completeness Theorem for Protocols with Honest Majority. 19th ACM Symposium
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with Applications to Round-Efficient Secure Computation. 41st IEEE Symposium
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with a Dishonest Majority. Adv. in Cryptology “ Eurocrypt 2003, LNCS vol. 2656,
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171“189, 2001.

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38. Y. Lindell. Personal communication, 2001.
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dations of Computer Science (FOCS), IEEE, pp. 162“167, 1986.


A Black-Box Simulation
Typical definitions of security for two-party computation only require that for
every pair of admissible real-world adversaries there exists a pair of ideal-world
adversaries satisfying some relevant criterion (namely, indistinguishability of
the resulting output distributions). Most work in this area, however, (and espe-
cially prior to the work of Barak [1]) proves the existence of such a via what
is known as a black-box simulation; this means that the ideal-model adversary
corresponding to the dishonest real-model adversary is constructed using
only oracle access to
More formally, a black-box simulation for party 1 (with a completely anal-
ogous definition for black-box simulation for party 2) implies the existence of
a simulator for which the following holds: For any real-model adversary
let (where are the inputs of and are the
random coins of be defined by where de-
notes the next-message function of on the given inputs and random coins
(we stress that is not explicitly given the auxiliary input nor the random
coins Then and (where are just the hon-
est algorithms) satisfy the relevant criterion. Furthermore, runs in expected
polynomial-time, where each oracle call to is counted as a single
step. Finally (although this is not essential to our results), it is typical to as-
sume that is a uniform algorithm. Note that if runs in strict polynomial
time, the above implies that the entire algorithm runs in expected polynomial
time; furthermore, if is uniform then so is (on the other hand, if is
a non-uniform machine, then will be too). We say that a protocol is proven
secure via black-box simulation if the simulations for both parties are black-box.
We stress a crucial point about the above: when we say runs in expected
polynomial-time, we mean that there is a fixed polynomial such that the
expected running time of on input when interacting with any (and
counting queries to as a single step), is On the other hand, the expected
running time of (including the steps of and no longer counting each query
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Round-Optimal Secure Two-Party Computation 353

to as a single step) cannot be bounded a priori by any fixed polynomial, as
the running time of will of course depend on the running time of Of
course, as noted above, if runs in strict polynomial time then runs in
expected time (at most) which is polynomial. (Note that this definition
of black-box simulation avoids the technical problem of, e.g., [28] regarding the
need for to feed coins whose length depends on and is not bounded
a priori by any polynomial.)


B Proof Systems Used in This Work
We provide here a laconic sketch of the proof systems claimed in Section 4;
further details and proofs will appear in the full version. We first describe the
WI proof of knowledge of [36] (as described in [18]).
We will be working with the NP-complete language HC of graph Hamil-
tonicity, and thus assume statements to be proved take the form of graphs,
while witnesses correspond to Hamilton cycles. If thm is a graph, we abuse no-
tation and also let thm denote the statement “thm HC”. We show how the
proof system can be used to prove the following statement: where
thm will be included as part of the first message, while is only included in
the last round (indeed, it will not be fixed until the third round begins). The
proof system runs parallel executions of the following 3-round protocol:
1. The prover commits to two adjacency matrices for two randomly-chosen cycle
graphs C, The commitment is done bit-by-bit using a perfectly-binding
commitment scheme.
2. The verifier responds with a single bit chosen at random.
3. If the prover opens all commitments. If the prover sends two
permutations mapping the cycle in thm (resp., to C (resp., For
each non-edge in thm (resp., the prover opens the commitment at the
corresponding position in C (resp.,
4. The verifier checks that all commitments were opened correctly. If the
verifier additionally checks whether both decommitted graphs are indeed
the verifier checks whether each non-edge in thm
cycle graphs. If
(resp., corresponds to a non-edge in C (resp.,
Note that the prover does not need to know either thm or (or the corre-
sponding witnesses) until the beginning of the third round. However, we assume
thm is fixed as part of the first-round message because this will enable us to
claim stronger properties about the above proof system.
Very informally, we claim that the proof system above satisfies the following:
It is complete and sound. In particular, the probability that an all-powerful
prover can cause a verifier to accept when either thm or are not true
is at most We stress that this holds even if the prover can adaptively
choose after viewing the second-round message of the verifier.
It is witness indistinguishable.
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354 Jonathan Katz and Rafail Ostrovsky

It is a proof of knowledge for thm. (More formally, we can achieve a notion
similar to that of witness-extended emulation [37] for thm.) We do not know
whether such a claim holds for
Note also that the first round of the above proof system (as well as the
internal state of the prover immediately following this round) is independent of
thm or the associated witness. We rely on this fact in Section 4.1.
Next, we informally describe our modification of the Feige-Shamir ZK argu-
ment of knowledge [19] which will allow the prover to prove where
thm is sent as part of the second round yet is only sent as part of the last
round (indeed, it need not be known until the beginning of that round). We use
the notation used in the description of the Feige-Shamir protocol in [18, Prot.
8.2.62]. Our modified protocol proceeds as follows:
1. The first round is as in the original protocol, and includes values
2. The prover chooses a random and computes
(cf. Section 2). Let ok denote the statement that Equiv was formed correctly.
3. Let denote the statement: (this
The prover sends Equiv and also
statement is reduced to a single graph
the first message of the WI proof system described above.
4. The verifier™s third message is as in the original protocol, except that the
verifier additionally chooses and sends a random
5. The prover decommits (as in Sec. 2) to R. Let prg be the statement that
is pseudorandom (i.e., s.t. for G a PRG). Let
be the statement (reduced to a single graph The prover
completes the WI proof system, as above, for the statement
6. The verifier checks the decommitment of R, and verifies the proof as before.
We claim the following about the above proof system:
It is complete and sound (for a poly-time prover) for thm and (As
argued earlier, rounds 2“4 constitute a proof of knowledge for As in [18]
“ relying on the one-wayness of “ this implies that if a poly-time prover
can cause a verifier to accept with “high” probability, then a witness for
can be extracted with essentially the same probability. If ok is true,
then with all but negligible probability prg will not be true. Soundness of
the proof of knowledge sub-protocol then implies that is true. But this
means that is true.)
It is zero-knowledge. (In addition to simulating for as in [18], the sim-
ulator also uses the equivocal commitment property to decommit to an R
such that prg is true.)
It is an argument of knowledge for thm (we have already argued as much
above).




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Security, Liberty, and Electronic
Communications
Susan Landau
Sun Microsystems
susan.landau@sun.com

Dedicated to the memory of Dorrie Weiss.


1 Introduction

We live in perilous times. We live in times where a dirty bomb going off in lower
Manhattan is not unimaginable. We live in times where the CIA interrogations
of al Qaeda leaders were so harsh that the FBI would not let its agent participate
[36]. We live in times when security and liberty are both endangered.
We also live in times of unimaginable technical creativity. It is faster to use
Instant Messaging to query a colleague halfway across the world than it is to
walk down the hallway and ask the question, when Google can search four billion
web pages faster than the time it takes to pull the right volume of the Oxford
English Dictionary off the library shelf. We live surrounded by a plethora of
communicating and computing devices ” telephones, PDAs, cell phones, lap-
tops, PCs, computers ” and this is only the beginning of the communications
revolution.
September 11th presaged a radical change in terrorist intent, a radical change
that few had anticipated. The U.S. government responded to September 11th
in a number of ways, including the passage of the U.S.A. Patriot Act, which
qualitatively extended the government™s electronic-surveillance capabilities. The
Patriot Act engendered strong debate (though not in Congress, where the law
passed handily). The most controversial issue regarding the changes in electronic-
surveillance law was that the requirement that foreign intelligence be a “primary”
reason for a Foreign Intelligence Surveillance Act (FISA) wiretap was modified
to foreign intelligence need only be a “significant” reason for a FISA tap.
Absent from the debates on the Patriot Act was an acknowledgement of
the radical changes that had occurred in communications technologies since the
passage of the first Federal wiretap statute in 1968. Communications technol-
ogy has changed in numerous ways over the past forty years ” there is now
wide availability of mobile communications, a vast increase in connectivity, and
packet-switched systems are being employed for telephony ” but there has been
no commensurate review of electronic-surveillance laws. We are in a peculiar
state: we communicate using mobiles phones and laptops, but the laws govern-
ing electronic surveillance were developed at a time of fixed-location circuit-based
switching systems. Instead of a full-scale reevaluation of surveillance laws, over
the last two decades we have pursued a path of minor tweaks to the electronic-
surveillance laws. The result is an electronic-surveillance regime that may be well

M. Franklin (Ed.): CRYPTO 2004, LNCS 3152, pp. 355“372, 2004.
© International Association for Cryptologic Research 2004
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out of sync with the times. This has serious implications for security, liberty, tech-
nology, and innovation. In this paper, we examine electronic-surveillance laws in
light of current threats and new technologies. We begin by examining the climate
in which wiretap laws came to be enacted.

2 The Political Climate at the Time of the Wiretap Act
The sixties were a time of turmoil in the United States, a time of political
protest, and civil unrest. In 1963, President John Kennedy was assassinated in
a motorcade in Dallas, Texas. In 1965 Malcolm X was killed as he delivered
a speech in an auditorium in Harlem. In April 1968, Martin Luther King was
killed, and two months later, Robert Kennedy, who was running for President,
was shot moments after he learned he had won the California primary. There had
been civil rights marches in Washington in the early 1960s, and anti-Vietnam
protests in the latter half of the decade. In the summer of 1964, downtown
Newark burned; in 1965, the Watts section of Los Angeles; in 1967, downtown
Detroit.
It was against this backdrop that the President™s Commission on Law En-
forcement and Administration of Justice presented its report. Organized crime
had been a problem in the United States since Prohibition, but, because FBI Di-
rector J. Edgar Hoover ignored it, so did the Federal government. Several events
in the late 1950s and early 1960s changed that.
The first was the discovery, on November 15, 1957, by a New York state
trooper, of a meeting of organized crime bosses. The trooper was doing routine
morning rounds when he discovered far too many black limousines for the tiny
upstate town of Apalachin. The trooper set up a roadblock; the crime bosses
fled, and “the next day, the nation awoke to headlines like ˜Royal Clambake for
Underworld Cooled by Police,™ and ˜Police Ponder NY Mob Meeting; All Claim
They Were Visiting Sick Friend™ [13, pp. 168-9]. Meanwhile, while counsel to the
Senate Select Committee on Improper Activities in the Labor or Management
Field, Robert Kennedy had uncovered ties between the unions and organized
crime. When he became attorney general, Kennedy made organized crime a
priority [29]. And finally, an organized crime turncoat, Joseph Valachi, broke
the code of silence by testifying to a Senate investigating committee in 1963.
This confluence of events made pursuing organized crime a law-enforcement
priority in the late 1960s. The complications of investigating organized crime
” the reluctance of victims to testify, so-called victimless crimes (e.g., prostitu-
tion), and the corruption of local law enforcement made electronic surveillance
a particularly valuable tool. The Commission concluded, “A majority of the
members of the Commission believe that legislation should be enacted granting
carefully circumscribed authority for electronic surveillance to law enforcement
officers. . .” [33, p. 203].
But, as noted in [13, p. 170],:
Not all experts agreed with the commission™s conclusions. Attorney Gen-
eral Clark prohibited all use of wiretaps by federal law-enforcement of-

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Security, Liberty, and Electronic Communications 357

ficers. He told Congress: ˜I know of no Federal conviction based upon
any wiretapping or electronic surveillance, and there have been a lot of
big ones.¦ I also think that we make cases effectively without wire-
tapping or electronic surveillance. I think it may well be that with the
commitment of the same manpower to other techniques, even more con-
victions could be secured, because in terms of manpower, wiretapping,
and electronic surveillance is very expensive.” [8, p. 320] Clark pointed
out that in 1967, without using wiretaps, federal strike forces had ob-
tained indictments against organized-crime figures in nine states, and
that “each strike force has obtained more indictments in its target city
than all federal indictments in the nation against organized crime in as
recent a year as 1960” [8, pp. 79-80]

President Johnson publicly supported Clark™s opposition to wiretapping, and
the President proposed limiting wiretapping to national-security cases [9, p. 222].
But political turmoil and the Crime Commission™s report led Congress in a differ-
ent direction, and in 1968 it passed the Omnibus Crime Control and Safe Streets
Act of 1968 (18 USC §2510“2521), Title III of which legalized law-enforcement
wiretaps in criminal investigations. Because of the very invasive nature of the
search, wiretaps were limited to a list of twenty-six crimes specified in the act,
including murder, kidnapping, extortion, gambling, counterfeiting, and sale of
marijuana. The Judiciary Committee™s report explained that “each offense was
chosen because it was intrinsically serious or because it is characteristic of the
operations of organized crime,” [44, p. 97].
President Johnson was ambivalent about wiretaps. He had used them ” on
Martin Luther King during the Democratic convention in 1964 and on Vice Pres-
ident Humphrey in 1968 ” but the President described the Title III provisions
for wiretapping as undesirable [9, p. 1842]. Nonetheless Johnson signed the bill.
Because of the invasive nature of electronic surveillance, Congress decided that
there should be stringent oversight, and that review of a federal wiretap warrant
application must be done by a federal district court judge.
The judge must determine that (i) there is probable cause to believe that an
individual is committing, has committed, or is about to commit an indictable
offense; (ii) there is probable cause to believe that communications about the
offense will be obtained through the interception; (iii) normal investigative pro-
cedures have been tried and either have failed, appear unlikely to succeed, or
are too dangerous; and (iv) there is probable cause to believe that the facilities
subject to surveillance are being used or will be used in the commission of the
crime (§2518 (3)(a-d)).
Title III covers procedures for obtaining wiretaps for law-enforcement inves-
tigation. In 1972, in a court case involving “domestic national-security issues,”
the Supreme Court ordered an end to warrantless wiretapping, even for national-
security purposes. Because of Watergate, and the discovery of numerous so-called
national-security wiretaps that were actually wiretaps for political purposes [42],
it took until 1978 before Congress was actually able to frame and pass legisla-
tion authorizing procedures for obtaining wiretaps for national-security investi-
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358 Susan Landau

gations: the Foreign Intelligence Surveillance Act. The judge, a member of the
Foreign Intelligence Surveillance Court, a court of eleven judges appointed from
seven of the United States judicial circuits (§1803 (a)), must determine (i) that
there is probable cause that the target is a foreign or target of a foreign power,
(ii) that there is probable cause that the targeted communications device is be-
ing used by the foreign power or its agent, that (iii) that a primary purpose of
the surveillance is to obtain foreign intelligence information, and that (iv) such
information cannot reasonably by obtained by other investigative techniques. 1
Title III and FISA form the basis for U.S. wiretap law. There are also state
statutes (approximately half of all criminal wiretaps in the United States are
done under state wiretap warrants). The rules governing state wiretaps must be
at least as restrictive as those governing Title III.
There have been several updates and modifications to the federal wiretap
statutes, which will be discussed after examining the changes in communications
technology over the last four decades.


3 Current Threats
In the U.S. we are currently seeing a strident debate on surveillance technologies,
most especially datamining. This paper is not the place for a full discussion of the
methods and means used in terrorist investigations. In the context of reexamin-
ing electronic-surveillance laws, however, it is useful to make some observations
about terrorism and terrorist investigations.
By any measure, terrorism is a very difficult offense to investigate or prevent.
In many cases, the first crime committed is the only crime. There is no trail.
The investigative reporter, Seymour Hersh, described CIA efforts in southern
Lebanon during the 1980s,

... when the C.I.A. started to go after the Islamic Jihad, a radical Lebanese
group linked to a series of kidnappings in the Reagan years, ˜its people
systematically went through documents all over Beirut, even destroying
student records.™

One of the hallmarks of modern terrorist groups is the shifting and diffuse
organizational structure [39, p. 271]. On the one hand, this means that elimi-
nating the leadership does not necessarily eliminate the problem. On the other,
diffuse and ever-changing structures create weaknesses within the organization.
One that can be exploited is the terrorists™ need for communication.
In this situation, traffic analysis often proves more useful than wiretapping.
Wiretaps can be confused by encryption, even encryption of a very simple sort.
Seymour Hersh reported that,

1
The law provides that “[N]o United States person may be considered a foreign power
or an agent of a foreign power solely upon the basis of activities protected by the
first amendment to the Constitution of the United States” (§1805(a)(3)(A)).

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Security, Liberty, and Electronic Communications 359

The terrorists coped with the American ability to intercept conversations
worldwide by constantly changing codes ” often doing little more than
changing the meanings of commonly used phrases.

The problem is being unable to decode the language is not new. It can even
occur without deliberate intent by the criminal or terrorist group. The National
Research Council report, Cryptography™s Role in Securing the Information So-
ciety described an FBI wiretap of police officers who were allegedly guarding a
drug shipment. The FBI agents overhead a conversation in which the officers
discussed murdering an individual who had filed a police brutality complaint.
The bureau was unable to decode a participant™s “street slang,” and was thus
unable to prevent the murder [10, p. 88].
The inability to understand surveilled conversations does not mean that the
surveillance is useless. In particular, traffic analysis has become an extremely
valuable aspect of surveillance, and one cannot confuse traffic-analysis efforts in
quite the same way as one confuses content analysis. One example of the value
of traffic analysis is that Osama Bin Laden stopped using a cell phone in late
2001 because of the tracking capabilities of U.S. intelligence.
Even “anonymous” cellphones can be used for tracking. In a case in 2002,
investigators tracked al Qaeda members through terrorists use of prepaid Swiss-
com phonecards. These had been purchased in bulk ” anonymously. But when
investigators discovered through a wiretap on an intercepted call that “lasted
less than a minute and involved not a single word of conversation” that they
were on to an al Qaeda group, the agents tracked the users of the bulk purchase
[45]. The result was the arrest of a number of operatives and the break-up of
al Qaeda cells. You can run, but you can™t hide. Anonymity is not all that it is
cracked up to be.
One important aspect of terrorist investigations is to “follow the money.”
Many terrorist groups hide behind legitimate charitable groups, but these are
groups with money trails [39, p. 274]. (We should note, however, that “following
the money” is not a straightforward issue in terms of civil liberties. The Patriot
Act section dealing with money laundering and terrorist financing is controversial
admidst claims that its provisions have been applied to charitable groups with
no ties to terrorist activities.) Money trails can be complicated to follow, and
the terrorists do a good job of hiding trails by passing money through many
intermediaries, but the fact is that there is a trail. Once there is trail, it can be
investigated.
The current terrorist threat is very different from earlier terrorist movements.
A different from earlier terrorism threats, such as the Russian nihilists of the
nineteenth century or the Palestinian terrorists of the 1970s, is the huge reser-
voir of potential recruits. Globalization complicates the problem. (Indeed, one
legitimately argue that globalization is a large part of the problem ” but that
is a topic for a different paper.) In the late 1990s, Senators Hart and Rudman
chaired a national security commission study to examine emerging threats. In
a prescient observation, the Hart-Rudman report in early 2001 warned of the
likelihood of catastropic domestic attacks caused by international terrorism. The

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360 Susan Landau

report observed, “All borders will become more porous.” [41, p. 2] This has al-
ready happened in Europe. While the borders have become porous, apparently
cooperation between different nations™ law enforcement has not yet followed suit.
Terrorism is not a passing phenomenon. It will be with us for a long time. It
is important that we respond to the threat in a way that simultaneously protects
our security and our liberty.

4 Changing Communications Technology
The first hundred of years the telephone saw change: from local systems entirely
mediated by operators to global networks entirely run by electronic switching
systems. There was innovation: mobile phone, first deployed n 1946 [6, 215],
faxes, and modems. There was development of infrastructure: optical fibers and
communication satellites, as well the digitization of the backbone network.
Yet slightly more than a generation ago, the telephone remained a fixed
device: a black machine with a rotary dial that transmitted voice (also data;
from the beginning, the telephone was also a data-transmission network data,
e.g., telegraph). In the sixties innovation was the introduction of the “Princess”
phone (in colors!: white, beige, pink, blue, or turquoise) and Touchtone ser-
vice (buttons instead of rotary dials), while industry got Centrex, an automatic
switching exchange for large offices, and “data-phones” (modems) [6, p. 266].
What occurred in the first century was growth: ten million phone users in 1900,
one hundred million in 1960, five hundred million in 19902.
The innovation of the first hundred years of the telephone pales in contrast
to the growth and changes of the last decade and a half. There were 1.4 billion
users in 2000, 400 million of those cell phone users. There probably has been as
much innovation in telephony in the last quarter century as there had been in
the previous one hundred years.
Recent telecommunications growth has been spurred by three technical de-
velopments: mobile technology, greater bandwidth, and the Internet. AT&T has
had car phones since 1946 [6, p. 215], but such service was rare and expensive
until the early 1990s. Mobile technology took off with the 1983 development of
“cell” technology. In under a decade, cell phones have become ubiquitous, as has
the wireless Internet. Once the Web appeared, the race to install broadband was
on. In 1999, less than 10% of U.S. households had broadband; by early 2004,
the percentage was 45% [32]. The shift to Internet communications is the most
fundamental of the changes. The Internet enabled email, (which is the killer app
of the Internet) [34], Instant Messaging, and the nascent technology: VoIP (voice
over IP).
This is only the beginning of the communications revolution. We are moving
from a circuit-based system based on transmitting voice to a high-speed, packet-
switched network transmitting data. The pervasiveness of our communication
systems will shift all that we do. These social and technological changes should
be taken into account the discussion of electronic-surveillance laws.
2
These numbers are international.

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Security, Liberty, and Electronic Communications 361

5 The 2004 Questions
5.1 What Is the Current Legal Framework?
Title III and FISA set the framework for U.S. electronic-surveillance laws. Since
their passage (in 1968 and 1978 respectively), there have been three major Fed-
eral laws that affected wiretapping: the Electronic Communications Privacy Act
(ECPA), the Communications Assistance for Law Enforcement Act (CALEA),
and the U.S.A. Patriot Act.
ECPA updated Title III and FISA to apply to “electronic communications,”
defined as communications carried by wire or radio and not involving the human
voice. ECPA was less strict about the type of crimes for which there could be in-
terception: any federal felony may be investigated using interception of electronic
communications. ECPA also modified the rules for electronic communications.
In contrast to Title III and FISA, which required naming the device and person
to be tapped, ECPA allowed for “roving wiretaps” ” wiretaps with unspecified
locations ” if there was demonstration of probable cause that the subject was
attempting to evade surveillance by switching telephones. In recognition of the
greater ease in obtaining signalling information, ECPA provided for traffic anal-
ysis. Under ECPA, a subpoena is needed for all pen registers, which record all
numbers dialed from a phone, and all trap-and-trace devices, which record all
numbers dialed to a phone. Furthermore, under ECPA, law enforcement only
needs a search warrant, rather than the more stringent wiretap warrant, to ac-
cess stored communications (voice mail or email that has been read and then
stored).
The Communications Assistance for Law Enforcement Act (CALEA) in 1994
was very controversial. In 1992 the FBI pressed for a “Digital Telephony” bill,
which required that all telephone-switching equipment be designed to accom-
modate wiretapping. Civil-liberties groups and the telecommunications industry
opposed the bill, and there were no sponsors of it.
The FBI returned to Congress in 1994 with a modified version, the “Commu-
nications Assistance for Law Enforcement Act,” which included a $500 million
authorization (but not appropriation) to the telecommunications companies for
modifications to old equipment (this caused the telecommunications companies
to drop their opposition). The bill required that any equipment deployed after
January 1, 1995 would have to meet law-enforcement interception standard; the
Department of Justice would determine which would be the standards-setting or-
ganization. This bill passed in the waning days of 1994 after certain civil-liberties
groups dropped their opposition.
From the start, implementation of CALEA went badly. The Department of
Justice put the FBI, an agency not known for expertise in telecommunications,
in charge of setting the implementation standards. In October 1995 the FBI
announced its requirements, which would have entailed capacity to simultane-
ously monitor thirty thousand lines [19] [20] [13, p. 197], a striking number at
a time when the total number of annual Title III and FISA surveillances, in-
cluding pen registers and trap-and-trace devices, was a quarter of that. (In 1995
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362 Susan Landau

the average Title III wiretap ran for 29 days [1, p. 13]. There is no public in-
formation about the length of FISA taps.) There were strong objections to the
methodology the FBI used to arrive at this figure and the bureau decided to
reexamine the capacity issue. Their new methodology required capacity to run
sixty-thousand surveillances simultaneously3 [20][13, p. 198]. Recognizing that
the delay in developing compliance standards made it impossible for the telecom-
munication companies to meet the law™s deadline (October 1, 1998, four years
after the passage of CALEA), the FCC granted an extension til June 2000 [22].
There was also a fight about location information for cellular calls. During
hearings on CALEA, FBI Director Freeh had promised that the bill would not
expand wiretapping powers[24, p. 29], and the legislative report stated that
“call-identifying information shall not include any information that may disclose
the physical location of the subscriber” (CALEA §103 a2B). Nonetheless the
FBI proposed that the cellular telecommunications group adopt a standard that
would enable law enforcement to quickly establish the location of a wireless
user [30]. In a 2000 decision, the U.S. Court of Appeals upheld the location
standard implementedas a result of CALEA (United States Telecommunications
Association et al. v. FCC and U.S., 99-1442, U.S. Court of Appeals).
In CALEA, Congress defined “information services,” distinguishing it from
“telecommunications services.” Information services were defined as “(A) mean[ing]
the offering of a capability generating, acquiring, storing, transforming, process-
ing, retrieving, utilizing, or making available information via telecommunica-
tions; and (B) includes“ (i) a service that permits a customer to retrieve stored
information from, or file information for storage in, information storage facilities;
(ii) electronic publishing; and (iii) electronic messaging services; but (C) does
not include any capability for a telecommunications carrier™s internal manage-
ment, control, or operation of its telecommunications network” (CALEA §102
(6)). The bill explicitly states that the interception requirements do not apply
to information services (CALEA §103 (b)(2)(A)).
Over time, the list of crimes for which Title III is applicable grew substan-
tially. It now lists 98 offenses, including computer fraud and abuse (18 U.S.C.
§2516). Even though the vast majority of wiretapping investigations concentrate
on drug trafficking and organized crime[2, Table 3], the law is not so tightly
focused as had been at its inception.

5.2 How Exposed Is Personal Information?

Changes in technology as well as social norms means that individuals leave tracks
wherever they go in modern society. A generation ago, individuals scrawled their
names on a card inside the book they borrowed from a library; now book bor-
rowing records library are entered into a central database. A generation ago,
individuals received a hotel key; now the “key” is a plastic card that includes a
3
In both cases, the proposed monitoring capacity appears as a percentage of phone
lines. Thus, if number of phone lines increases, required monitoring capacity would
do so proportionally.

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strip that may or may not have the lodger™s name and credit-card information
on it. A generation ago, an individual gave a name for a plane ticket, and then
may have sold the ticket to a friend; now the name on government-issued IDs
must match name on the the ticket. As Jeffrey Rosen has observed, we are the
“naked crowd” [37].
One significant change over the last several decades is the major loss of
anonymity that has resulted from credit cards becoming the payment method
of choice. The financial dossiers created enable tracking and identification of
individuals in a way that plunking three hundred dollars down for a used car
does not. Because credit cards have essentially become required for travel (at
least for car rental and hotel reservations), credit-card records provide excellent
after-the-fact records of where individuals have been, when (and, in some cases,
with whom). Evidence of this is in the tracking of the September 11th hijackers.
By September 14, 2001, law enforcement had put together a impressive dossier
on the hijackers: where and how they had purchased their tickets, where they
were living before the attacks, and where they had gone to and flight school (not
all of them had) [23]. It was in the ubiquitous trail that individuals leave as part
of modern life.
We leave video tracks not just at the airport and the ATM, but at totally
unexpected stops. Timothy McVeigh had no intention of leaving a trail when he
rented a truck in Junction City Kansas but, as noted in [13, p. 267], he had.
Investigators ¦ used photos from several days before the explosion to
prove that Timothy McVeigh was the “Robert D. Kling” who, on the
afternoon of April 17, 1995, in Junction City, Kansas, rented the Ryder
truck used in the bombing. Days and weeks after the bombing inves-
tigators meticulously reconstructed McVeigh™s movements on April 17.
Surveillance photos taken at a McDonalds about a mile from the Ry-
der agency showed McVeigh at the restaurant at 3:49 and 3:57 PM on
that day. Shortly afterward, “Kling” rented the truck. When prosecutors
claimed that the McDonalds™s photo was of McVeigh, his lawyer did not
dispute the point. The photo was taken several days before there was
any hint it would be useful in a criminal case ”and then the evidence
was available when needed[5].
Imminent changes in technology will create even more detailed trails. Sensors,
low-cost wireless devices, will monitor the environment and report back: “The
elderly patient has a blood pressure of 110/70,” “The room is at 75 degrees.”
RFID (Radio Frequency ID) devices will report about items an individual carries
on his person: clothes, currency, a book. The sensor and RFID communications
will often occur without the individual™s knowledge4.
It is not clear how an expiring milk carton informing the supermarket that
it is time for a new dairy order will benefit tracking of terrorists and criminals.
But one wouldn™t necessarily have anticipated that an intercepted phone call in
which no words were spoken and that was paid for via an anonymously-purchased
4
The Internet will be the communications medium.

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prepaid card would have led to a major breakthrough in a terrorist investigation
either. The fact that data storage is dropping in price encourages the storage of
transactional information, information that will be accessible to investigators.
It is not currently the case that an individual™s data is arbitrarily subject to
law enforcement perusal. The question of under what circumstances government
can do data mining is currently a subject of much debate and some studies (e.g.,
[40]). In thinking about federal wiretap statutes, it is important to put the issue
in context, and in particular to be cognizant that there is much more data easily
accessible on individuals than there was at the time of the passage of the Wiretap
Act. Under appropriate circumstances, that data is available to law-enforcement
and national-security officials.

5.3 What Is the Effect of Communications Surveillance on Liberty?
We have briefly examined the changes in communications technology and in the
accessibility of individual™s private data at the dawn of the twenty-first century.
We need to begin at the beginning, the time of the founding of the United States.
As Whitfield Diffie has remarked,
[P]rior to the electronic era conversing in complete privacy required nei-
ther special equipment nor advanced planning. Walking a short distance
away from other people and looking around to be sure that no one
was hiding nearby was sufficient. Before tape recorders, parabolic mi-
crophones, and laser interferometers, it was not possible to intercept a
conversation held out of sight and earshot of other people. No matter
how much George III might have wanted to learn the contents of Han-
cock™s private conversations with Adams, he had no hope of doing so
unless he could induce one or the other to defect to the Crown[13, p. 2].
In the United States, the founders reacted to the broad searches by British
solders under general writs of assistance by restricting government power through
the Fourth Amendment of the U.S. Constitution,
The right of the people to be secure in their persons, houses, papers and
effects against unreasonable searches and seizures shall not be violated,
and no Warrants shall issue but upon probable cause, supported by Oath
or affirmation, and particularly describing the place to be searched, and
the persons or things to be seized.
“No warrants shall issue but upon probable cause ¦ and particularly de-
scribing the place to be searched, and the persons or things to be seized.” This
would be significant when it came time to apply the Fourth Amendment to com-
munications surveillance. Justice Louis Brandeis wrote in his famous dissent in
the Olmstead case,
The evil incident to invasion of the privacy of the telephone is far greater
than that involved in tampering with the mails. Whenever a telephone
line is tapped, the privacy of the persons at both ends of the line is

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invaded, and all conversations between them upon any subject, and al-
though proper, confidential, and privileged, may be overheard. Moreover,
the tapping of one man™s telephone line involves the tapping of the tele-
phone of every other person whom he may call, or who may call him. As
a means of espionage, writs of assistance and general warrants are but
puny instruments of tyranny and oppression when compared with wire
tapping [4, pp. 475-6].

Experiences with government surveillance, extensively described elsewhere
(see e.g., [13, pp. 137-150, 172-179, 271-2], [42], demonstrated serious dangers to
political discourse and public expression. During the period from the 1940s to the
1970s, for example, Supreme Court justices, White House staffers, members of
the National Security Council, Congressional staffers, civil-rights leaders, includ-
ing Martin Luther King and Ralph Abernathy Jr, anti-Vietnam War protesters,
and journalists were wiretapped. These breaches made Congress wary of provid-
ing law-enforcement and national-security investigators with such a potentially
invasive tool. This is why the requirements for a wiretap warrant are significantly
more stringent than those for a “normal” search warrant 5.
Wiretaps intrude on a conversation between two people and thus require the
high level of wiretap search warrant before tapping can commence. But there
is no similar level of protection for transactional information on what number
is being called and what number is calling. The legal rationale is that such
transactional information is already being shared with a third party (in this
case, the telephone switch) and the communicating parties do not have any
expectation of privacy on the data. Thus a subpoena, which can be obtained
from a magistrate, suffices for pen registers and trap-and-trace devices6.
5
It is also why public reporting of Title III wiretaps is required; each year, the Admin-
istrative Office of the U.S. Courts produces a report listing each Title III wiretap of
the previous year (ongoing taps are not reported until they have ceased to be used),
including the D.A., the judge issuing the wiretap search warrant, the length of or-
der, the “most” serious crime for which the wiretap was ordered (there may be more
than one for a single wiretap), the number of incriminating and non-incriminating
calls picked up on the wiretap, the cost of the surveillance, etc. (Except for annually
reporting to Congress the number of surveillances, there are no public disclosure
requirements for FISA wiretaps.)
6
This paper concentrates on the technology side of the electronic-surveillance issues,
not the policy. Nonetheless, we would be remiss if we did not point out that traffic
analysis, though usually less intrusive than content surveillance, may nonetheless
cause severe privacy breaches. One such example occurred in the 1980s FBI investi-
gation of CISPES, the Committee in Solidarity with the People of El Salvador, an
American group which supported the opposition to the El Salvadorian government.
On the basis of an informer™s information, the FBI started an investigation of CIS-
PES, eventually culminating in files on more than twenty-three hundred individuals.
Much of the information was obtained through phone records. The investigation was
not justified; the group was not a terrorist organization, and in 1988, FBI Direc-
tor William Sessions told Congress that, “[T]here was no reason ¦ to expand the
investigation so widely” [38, p. 122].

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366 Susan Landau

In this paper we are focusing our discussion on technology implications of
wiretapping rather than policy issues. Nonetheless, as we consider the role of
surveillance in current communications technology, we must never lose sight of
Brandeis™s words, “As a means of espionage, writs of assistance and general
warrants are but puny instruments of tyranny and oppression when compared
with wire tapping [4, pp. 476].”


6 Telephony and the Internet:
Two Different Architectures

The Public Switched Telephone Network (PSTN) was built to maximize the
quality of voice transmissions and everything in the network was designed to
that end. The Internet was designed for reliability, a very different quality. The
PSTN uses circuit switching to transmit information from sender to receiver,
the Internet, packet switching. The PSTN and the Internet have fundamentally
different architectures. This simple fact means that many of the surveillance
tasks do not directly translate from one domain to the other.


6.1 Electronic Surveillance on the Internet

Consider, for example, the effect of packet-based technology on the transmittal
of transactional information. In telephony, signaling information appears at the
beginning of the call and is separated from call contents. In packet-switched
systems such as the Internet, because data is broken into “packets,” each one of
which has the addressing information, contents do not have the same physical
separation from the “signalling” information (probably more properly called
transactional information in this case).
Furthermore, electronic communications typically present more personally-
identifiable information present in the so-called transactional information. At a
minimum, this may simply include place of business, e.g., susan.landau@sun.com.
But it may include much more, e.g., if the transactional information is the result
of a google search, the URL will reveal the search terms 7.
7
That “pen registers” and “trap-and-trace devices” garner additional information
when used in packet-switching network systems than they do in traditional circuit-
switched telephony systems did not escape the notice of technologists and civil-
liberties groups. When the news of Carnivore, the FBI™s Internet monitoring system
became public in the summer of 2000, one of the criticisms of the system was that
the transactional information that Carnivore was sweeping up was more than the
government was entitled to under the limited subpoena power used for pen regis-
ters and trap-and-trace devices. Carnivore was quite controversial. In the summer
of 2001, it looked as if there might Congressional action limiting Carnivore™s use.
Instead September 11th happened. The Patriot Act gave law enforcement explicit
power to use subpoenas for pen registers and trap-and-trace devices on electronic
communications (§216).

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An even more crucial different between the PSTN and the Internet is that in
the Internet, the intelligence is at the endpoints. The underlying network system
is simple, while the endpoints can deploy complex systems. This fundamental
architectural idea is what makes the Internet so versatile. Applications can be
designed far beyond what the original designers of the Internet had in mind. And
indeed, innovation has flourished because the endpoints competed and created
new services. No one needs to depend on the infrastructure company to do the
innovation for them.
The design flexibility comes at a price that we do not often think of as a price:
the Internet is hard to control. This does not mean political or border controls
(though those are also often difficult to implement on the Internet) but design
control. This is not a bug; it is an extremely attractive feature. In a sharp, and
deliberate, distinction from the telephony network, the Internet was designed
to be loosely controlled. The layered approach to network design provides that
effect and is what has enabled much of Internet innovation.
For those that choose to invest the effort, Internet communications can be
fully protected. The Internet design of intelligence at the endpoints complicates
wiretapping, which is useless if end systems adequately protect their commu-
nications (although a wiretapped encrypted conversation will still provide traf-
fic information). In recent years, protecting the privacy of communications has
become an important security goal. Indeed, the U.S. government has moved
in the direction of simplifying the deployment of communications security in
commercial equipment, partially as a result of the government™s move to pur-
chasing COTS (commercial off the shelf) equipment rather than the purchase of
custom-designed systems. Instead of restricting the use of cryptography, the U.S.
government has recently encouraged a number of security efforts, including the
development of the 128-bit Advanced Encryption Standard and the deployment
of Elliptic Curve Cryptosystems. Attempts to build wiretapping capabilities into
Internet protocols would seem to go against these efforts.
At the same time, as an IETF Network Working Group studying the issue of
architecting wiretap requirements into Internet protocols observed, “the use of
existing network features, if deployed intelligently, provide extensive opportuni-
ties for wireteapping” [35].


6.2 The Risks Wiretapping Poses to Internet Security

Under CALEA, telecommunications systems deployed after January 1, 1995
must be built wiretap accessible. Suppose one were to call for that same require-
ment on the Internet. Does such an obligation make sense? Can it be architected
in? What does it do to security requirements?
Wiretapping is an architected security breach. Saying that Internet commu-
nication protocols necessarily must have wiretapping requirements built in is to
say that security loopholes must be built into communication protocols. It means
that privacy of the communication must be deliberately violated and in a way
that does not alert the sender or recipient.
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368 Susan Landau

Of course, U.S. law-enforcement and national-security agents are not the only
ones interested in wiretapping the Internet; foreign governments are as well. Any
technology that is designed to simplify Internet wiretapping by U.S. intelligence
may well be exploited by foreign-intelligence services. During the discussions on
CALEA, there were concerns about the security problems created by “building
in” wiretapping capablities for digital telephony [15]. Such fears pale when mea-
sured against designing such capabilities for the Internet. Internet wiretapping
technology, found and reverse engineered by foreign-intelligence services, could
enable massive surveillance of U.S. “persons” (citizens and corporations). Used
in combination with inexpensive automated search technology, this could lead
to serious security breaches.
There is risk to the U.S. economy (the potential loss of corporate informa-
tion). There is risk to U.S. national security (through the provision of cost-
effective massive intelligence gathering). There is risk to the freedom of U.S.
citizens. These are the risks [7] that the European governments responded to
when, in 1999, they decided to liberalize their cryptographic export-control pol-
icy. As did the United States when it liberalized its cryptographic export-control
policies shortly afterwards [14].
If we were to build access for U.S. law enforcement or national security into
Internet communications, such protocol design would have be done very carefully.
Can it be? It is highly doubtful. As the IETF Network Working Group observed,
any protocol designed with wiretapping capabilities built in is inherently less
secure than it would be without the wiretapping capability. Building wiretapping
requirements into network protocols makes the protocols more complex. As is
well known, complex protocols are prone to security flaws. The secure Internet is
a challenge. Despite best efforts, security breaches slip into many protocols. No
one wants to see deliberately-architected security breaches. In 2000 the IETF
Network Working Group decided not to consider requirements for wiretapping
as part of the IETF standards process [35].


7 What Is the Right Tradeoff
for Communications Surveillance?
What are the costs to communications technology of continuing to enable wire-
taps? A recent FBI petition to the FCC gives an illustration. The bureau argued
that “CALEA™s purpose is to help lawful electronic surveillance keep pace with
changes in telecommunications technology as telecommunications services mi-
grate to new technologies” [21, pp. 3-4] and stated that thus “CALEA is appli-
cable not only to entities and services that employ circuit-mode technology, but
also to entities and services that employ packet-mode technology” [21, p. 6]. The
Bureau urged the FCC to declare that any service providing voice communica-
tions, including Voice over IP (VoIP), should be viewed as a “telecommunications
carrier.”
The breadth of this claim is startling. Were the FCC to grant the peti-
tion (unknown at the time of this writing), this would put the FBI squarely in

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the middle of designing IETF protocols. What would the technological cost of
granting this petition be? One can scarcely imagine. At a minimum, granting the
petition would “drive up costs, impair and delay innovation, threaten privacy,
and force development of the latest Internet innovations offshore” according to
a response filed by a coalition of industry and civil-liberties groups [26]. As we
have observed earlier, it would also threaten security.
Does the value of wiretapping justify trying to preserve the tool? This, of
course, depends on whom you ask. As the FBI was pressing the Digital Telephony
bill in the early 1990s, the bureau argued that wiretapping was a critical tool in
the fight against organized crime. The FBI presented claims that court-ordered
wiretaps resulted in over seven thousand convictions, three hundred million dol-
lars in fines levied, and over three-quarters of a billion dollars in recoveries,
restitutions, and court-ordered forfeitures over a six-year period [18]. But White
House staffers [3], the Treasury Department [28], and the Vice-President™s office
[31] all disputed the FBI numbers.
There is no question that wiretapping can be effective in some cases. Its most
important value may be as a deterrent: knowing that law enforcement is listen-
ing in, criminals and terrorists stay off the line. Or they speak in code: “The
big guy is coming. He will be here soon.” [45] Making the use of electronic com-
munications difficult for criminals and terrorists denies them one of the greatest
technological advances of the last century.
As we have seen, greater surveillance value may come from traffic analy-
sis, which has already shown remarkable benefits in the fight against terrorism.
Given the U.S. government™s shift on cryptographic export controls, one might
reasonably argue that intelligence agencies have come to the same conclusion.
The debate about electronic surveillance must not occur in isolation. U.S.
wiretapping laws were passed when the opportunity to easily obtain massive,
automatically-created, data trails did not exist. Video cameras in McDonalds,
at ATM machines, E-Z pass automatically recording the trip through the toll
booths, sensors and RFID tags are all aspects of this changing technology. One
has just to look at disappearance of pay phones8 to realize how much the way we
communicate, both in frequency and in mode, has substantially changed from
only a generation ago.
If Congress were not to preserve law-enforcement™s capability to wiretap,
what investigative tools might be offered in trade? A clear one is easy access to
communications transactional information. One of the non-controversial aspects
of the Patriot Act is that it simplified the procedure for obtaining pen register
and trap-and-trace orders, no longer requiring an application in each jurisdiction,
but letting a single application suffice. Traffic analysis has become significantly
easier to obtain and it may be appropriate to trade further capabilities in this
direction. For example, the decreasing costs of storage have made record saving
much less onerous. Might it be appropriate to require service providers to keep
records of communications (which numbers, when, for how long) for a specified
8
The new wing at Bradley Airport in Hartford, Connecticut, which has twelve gates,
has exactly two pay phones.

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370 Susan Landau

period in exchange for deciding that communications systems will not be required
to be built wiretap accessible?
The threat of terrorism will confront our society for a long time. But we
should not necessarily be extending a 1960s wiretap law into the twenty-first
century. Instead we should be examining first principles to determine what
surveillance laws are appropriate for current challenges. Wiretapping became
a law-enforcement tool in the late 1920s; its use was codified in the 1960s and
1970s. If attempting to preserve the tool in order to enable investigators to hold
onto this capability would freeze communications in an antiquated technology,
that may be the wrong route for our society to take. It may be that few security
benefits accrue from the requirement that electronic communications be designed
“wiretap accessible” while efforts to do so significantly impede innovation. It is
time to fully examine electronic surveillance: it value, needs, and costs. Such a
discussion is a necessity in our complicated times. It is crucial as we attempt to
solve the current threats to security and liberty.


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March 15, 16, 22, 23, April 5, 7, 10, 12, 19, 20, 26 and 27, 1967, Ninetieth Congress,
First Session, 1967.
45. Van Natta Jr., Don and Desmond Butler, “How Tiny Swiss Cellphone Chips Helped
Track Global Terror Web,” New York Times, 4 March 2004, p. A1.




TEAM LinG
An Improved Correlation Attack
Against Irregular Clocked
and Filtered Keystream Generators

Håvard Molland and Tor Helleseth
The Selmer Center*
Institute for Informatics,
University of Bergen,
Norway



Abstract. In this paper we propose a new key recovery attack on ir-
regular clocked keystream generators where the stream is filtered by a
nonlinear Boolean function. We show that the attack is much more ef-
ficient than expected from previous analytic methods, and we believe it
improves all previous attacks on the cipher model.
Keywords: Correlation attack, Stream cipher, Boolean functions, Irreg-
ular clocked shift registers.


1 Introduction
In this paper we present a new key recovery correlation attack on ciphers based
on an irregular clocked linear feedback shift register (LFSR) filtered by a Boolean
function. The cipher model we attack is composed of two components, the clock
control generator and the data generator and is shown in Fig. 1.

The data generator sub system consists of of length and the non-
linear multivariate function The internal state of is filtered by a
Boolean function The output from is the high linear complexity bit
stream v.
The clock control sub system consists of of length where the output
from is sent through the clock function D(). The output from D() is
the clock control sequence of integers, c, which is used to clock

The effect of the irregular clocking is that v is irregularly decimated and the
positions of the bits in the stream are altered. The result from this decimation
is the keystream z. The secret key in this cipher is the initialization bits
for and
To attack this encryption scheme we need to know the positions the keystream
bits z had in the stream v before v was irregularly decimated. The previous
effective algorithms are not specially designed to attack irregular clocked and
*
This work was supported by the Norwegian Research Council.

M. Franklin (Ed.): CRYPTO 2004, LNCS 3152, pp. 373“389, 2004.
(c) International Association for Cryptologic Research 2004
TEAM LinG
374 Håvard Molland and Tor Helleseth




Fig. 1. The general cipher model we attack in this article


filtered generators. But there exist effective attacks on the data generator sub
system[6,1,10,3,4]. To deal with the irregular clocking, one of two techniques
are often used:
1. Do the attack on the data generator times [7]. The attack is done
one time for each guess for the possible initialization states for If
the attack on the sub system has complexity O(K) the full attack will have
complexity
2. Ignore the clock control generator [3,14,4]. If the attack on the data
generator subsystem needs M keystream bits, we can use the fact[14] that
we know the original v position of every bit in the keystream z. Thus
we can only use every keystream bit in the attack, which means that
we need keystream bits to succeed.
None of these techniques are optimal. The first one leads to large runtime com-
plexity, the second leads to the need for a large number of keystream bits.
Our attack is not designed to attack the data generator subsystem only, but
is especially aimed at irregular clocked and filtered keystream generators as one
system. First we guess the initialization state for From this we can
reconstruct the positions the bits in z had in v. Using the iteration algorithm
from[11] this reconstruction is done using just a couple of operations per guess,
exploiting the cyclic redundancies in This method is fully explained in
Section 4.3. This method gives the guess
where are some keystream bits and the stars are the deleted bits. Then
we test to see if it is likely that the stream is generated by the data generator
subsystem and Hence, we only use a distinguisher test on the the
stream to decide if the guess for is correct. This is easier than to actually
decode the stream to find and then decide if we have found the correct
When is determined, we can use one of the previous attacks on the data
generator sub system to determine
The distinguisher test is to evaluate a large number of low weight parity
check equations on the bit stream All equations are derived from one mul-
tiple of weight 4 of the generator polynomial Surprisingly this test
works much better than expected from previous evaluation methods. In previ-
ous correlation attacks, the Piling up lemma[9] is often used to calculate the
correlation[1,7,6] which the algorithm must decode. Since our algorithm only
uses a distinguisher on we can use a correlation property of the function
TEAM LinG
An Improved Correlation Attack 375

which gives much higher correlation between and the keystream z. Thus we
need fewer parity check equations. This correlation property exists even if the
function is correlation immune in the normal sense.
Our attack has complexity independently of the length of
A cipher based on the model we attack in this paper is LILI-128. To attack the
LILI-128 cipher our algorithm needs about parity check equations. In LILI-
128, thus the runtime for our attack is parity checks, with
virtually no precomputation. We have implemented and tested the attack, and
it works on computers having under 300 MB of RAM, and needs only around
68 Mbyte of keystream data. The precomputation has low runtime complexity
and is negligible. When is found, we can use one of the previous algorithms
to attack the data generator sub system.
A comparable previous correlation attack by Johansson and Jönsson is pre-
sented in [7]. The runtime for the attack is parity checks and the precom-
putations is table lookups. The keystream length is approximately This
attack uses the first technique to handle the irregular clocking.
Recently new algebraic attacks have been proposed by Courtois and Meier[3,
4]. This attack uses the second technique to handle the irregular clocking in
LILI-128. Although the attack has an impressive runtime complexity (an
optimistic estimation for some unknown constant C), the attack needs about
keystream bits to succeed, which is unpractical.
There is also a time-memory trade-off attack against LILI-128 by Markku-
Juhani Olavi Saarinen[14]. This attack needs approximately bits of com-
puter memory and keystream bits. The runtime complexity is claimed to be
DES operations, which is not easy to compare with our runtime complexity.
But the high use of computer memory and keystream bits also makes this attack
unpractical.

2 A Correlation Property of Nonlinear Functions
Let and let be a balanced Boolean function from V to We start
by analyzing the boolean function for a correlation property that we will
use in the attack. A similar property is analyzed in [18] where they look at the
nonhomomorphicity of functions. In this paper we identify the probability


which is crucial for our attacks success rate.

2.1 The Correlation Property
Let and let denote the inner product of
and Define the Walsh coefficients of by




TEAM LinG
376 Håvard Molland and Tor Helleseth

Lemma 1. Let be a function from to and let for
Let and let N denote the number of solutions of




Then



Proof. Each term in the sum below gives a contribution for each solution of
the system of equations, and zero otherwise. Therefore, we have




where the first term comes from the case and a = 0, and the last term
from the case

Corollary 1. If is a balanced function then the number of solutions N of
the system of equations above is,




Proof. Since is balanced we obtain It follows
from Parseval™s identity that the average value of is Hence, it follows
from the Cauchy-Schwartz inequality that which
substituted in the lemma above gives the result.
Corollary 2. The expected number of solutions N of the system of equations
above is,


Proof. An average estimate of N can be found as follows. When there exist two
equal vectors in Equation (2), the two other vectors will also
be equal. When this occurs it follows that the Equation (3) will sum to zero.
TEAM LinG
An Improved Correlation Attack 377

This gives the unbalance that causes the high correlation. Equation (2) implies
Then there are triples in where all
the are distinct and there are therefore triples with one or two pairs
Using this fact and substituting Equation (2) into Equation (3), we
can write




Since for an arbitrary function we can expect that and
take on all binary quadruples approximately equally often when
we expect in the average the last term to be 0. This implies
the result.
Corollary 3. Let be an arbitrary balanced function, and let denote the prob-
ability


then is expected to be and its minimum is

Proof. Since Equation (2) has solutions, it follows from Corollary 1 that the
expected probability is equal to Further from Corollary
2 we obtain that the minimum is
Corollary 4. Given a specific balanced function the probability



is

Proof. Using the N from Lemma 1 we get
It is straightforward to extend Lemma 1 to compute the number of common
solutions of the two equations




and show that the corresponding probability


TEAM LinG
378 Håvard Molland and Tor Helleseth


equals which reduces to the result of Corollary 4 when

we can calculate the expected value of a balanced Boolean
In the case
This implies that
to be
function, with a given
Similar arguments for
as for
the bias is the same for the case
equations with show that these equations give too low correlation, which
would lead to a high runtime complexity for our attack. It turns out that for
the attack needs much more keystream bits to succeed, see the Sections
4.1 and 5.2. Since the correlation bias is exactly the same for and
it is optimal to use


2.2 Analysis of Some Functions

In Table 1 we have analyzed some functions using Corollary 4. This correlation
is surprisingly high. Let be the best linear approximation to
the LILI-128 function. Due to the design of the previous attacks[6,7,10] the
channel noise has been independent of the stream u generated by Thus
the Piling up lemma [9], is used to evaluate the
crossover correlation which the algorithms must be able to decode. Using
the Piling up lemma for weight equations, the correlation for LILI-128
will be From Table 1 we have the correlation
The reason for the higher correlation, is that our attack only uses a distinguisher
on the data generator sub system, and not a complete decoder. Hence, in our
key recovery attack on the clock control system, we can use Corollary 4 from
Section 2.1 to calculate the correlation. To test the corollary we generated 2000
random and balanced Boolean tables for and calculated the average
correlation. The result was that the average was 0.501466 which is close to the
theoretical expected




3 A General Model

Here we define a general model for irregular clocked and filtered stream ciphers,
and some well known properties for the model.
TEAM LinG
An Improved Correlation Attack 379

3.1 General Model
Let and be the feedback polynomials for the shift registers
of length and of length We let and
be the initialization states for and The initial-
ization states define the secret key for the given cipher system.
From we can calculate a clock control sequence c in the following way.
Let be a function where the input
is the inner state of after feedback shifts and A is the number of
values that can take. Let be the probability
produces the stream which is filtered by The output
from is or the equivalent The
clock decides how many times is clocked before the output bit is
taken as keystream bit Thus the keystream is produced by
where is the total sum of the clock at time that is
This gives the following definition for the clocking of
Definition 1. Given bit stream v and clock control sequence c, let z = Q(c, v)
be the function that generates z of length M by



where

If the function Q(c, v) can be considered as a deletion
channel with input v and output z. The deletion rate is




The D() function described above can in this model be among others the shrink-
ing generator, the step-1/step-2 generator and the stop and go generator. Next
we define the (not complete) reverse of Definition 1.
Definition 2. Given the clock control sequence c and keystream z, let the func-
tion be the (not complete) reverse of Q, defined as



where and for the entries in where is deleted.
When this occurs we say that is not defined.

The length of will be Given a stream z of length M, the
expected length N of the stream v is




TEAM LinG
380 Håvard Molland and Tor Helleseth

Note that the only difference between this definition and Definition 1, is that v
and z have switched sides. Thus is a reverse of Q(c, v). But since some
bits are deleted, the reverse is not complete and we get the stream
The probability for a bit being defined is This happens
when holds for some It follows that the sum
will be defined if and only if all of the bits in the sum are defined.
Thus the sum will be defined for given in with probability



4 The Attack
4.1 Equations of Weight 4
To succeed with our attack we need to find exactly one weight 4 equation


that holds over all u generated by for This corresponds to finding a
multiple of weight 4. There exist several algorithms for finding
such a multiple, see among others [13,2,5,17,12].
In this paper we use the fast search algorithm in [12,11], which is a modified
version of the David Wagner™s Generalized Birthday Algorithm[17]. If the stream
u has length N, this algorithm has runtime complexity O(N logN) and memory
complexity O(N), where N is of order The algorithm is effective in practice,
and we have succeeded in finding multiples of the generator polynomial of high
degree, see Section 6.3 for an example. We refer to Appendix C in [11] for the
details for this search algorithm.
Next, we let the input vector to the Boolean function be


where defines the tapping positions from the internal state
of after feedback shifts. Substituting the vector (9) into the Equation
(8) we have that always holds for Since
we have from Corollary 4 that the equation



will hold for with probability
Remark 1. In [8] the multiple of of weight is exploited to define
an iterative decoding attack on regularly clocked LFSRs filtered by Boolean
functions. The constrained system




TEAM LinG
An Improved Correlation Attack 381

is analyzed. This system is similar to the one we use in this paper, but it is used
differently. Since there are limited solutions to this system, the a posteriori prob-
abilities for each of the input bits in
can be calculated. Then these probabilities are put into a Gallager like prob-
abilistic decoding algorithm(SOJA) which outputs However the correlation
property in Corollary 4 is neither identified or exploited in [8].

4.2 Naive Algorithm
Let be a guess for the initialization state Given the keystream z of length
M, we generate and of length
Then we test if is likely to have been generated by
using the following method.
Find entries in where the equation is defined. From this we get a set of
equations. We test the equations, and let the metric for the guess be the
number of equations that hold. When we have the correct guess for we expect
pm of the equations to hold, where is calculated using Corollary 4. Thus, this
is a maximum likelihood decoding algorithm.
The runtime complexity for the attack will be of order since
we have to generate the bit stream of length N for each of the guesses. In
a real attack, N will be a large number and the naive algorithm will have very
high runtime complexity.

4.3 Some Observations
If we use the technique in the previous section the attack has the runtime
In [11, Sec. 3.3] two important observations were made that re-
duce the complexity down to Since these observations will speed
up the attack considerably. We start with an initial guess and
let the guess be the internal state of after feedback shifts, that is

Let be the guess for the clock control sequence
defined by Let be the
corresponding guess for of length We can now give a iterative
method for generating from

Lemma 2. We can transform into using the following
method: Delete the first entries in append the
entries at the end, and replace with for

Proof. See Appendix B.1 in [11].
Lemma 2 shows that we can generate each using just a few operations instead
of N operations, when implemented properly (See Appendix A.1 for the imple-
mentation details). This gives a fast method for generating all possible guesses
for given a keystream z. But using this lemma we still have to search for
TEAM LinG
382 Håvard Molland and Tor Helleseth

entries in where the equations are defined. Since on average we must search
through entries in per equation, we want to avoid this search. In the
next theorem we show how this can be done. The theorem proves that we can
reuse the equation set for in

Theorem 1. If the sum



is defined over then the sum



is defined over

Proof. See Appendix B.2 in [11].

The main result from this theorem is that the equation set defined over will
be defined over when we shift the equations entries to the left over
This means that we can just shift the equations one entry to the left over z, and
we will have a sum that is defined for the guess Thus,
the theorem shows that we can avoid a lot of computations if we let the
guess for the inner state of be

Remark 2. To use the lemma and theorem above we do not put the actual bit
values and restore them to the position in given by Instead
we store the index (the pointer to the position in z) in This means
that holds the position which the keystream bit have in z. But when
we evaluate an equation we use the indices to put in the actual bit values.


4.4 An Efficient Algorithm

Assume we have found an equation The
equation holds over v with probability calculated using Corollary 4. Let the
first guess for the initialization state for s be generate
by and Next we try to find

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