# Computer underground Digest Wed Aug 11 1993 Volume 5 : Issue 60 ISSN 1004-042X Editors: Ji

Computer underground Digest Wed Aug 11 1993 Volume 5 : Issue 60 ISSN 1004-042X Editors: Jim Thomas and Gordon Meyer (TK0JUT2@NIU.BITNET) Archivist: Brendan Kehoe Shadow-Archivists: Dan Carosone / Paul Southworth Ralph Sims / Jyrki Kuoppala Ian Dickinson Copie Editor: Etaoin Shrdlu, Senior CONTENTS, #5.60 (Aug 11 1993) File 1--CuD #5.59 Glitch & Some Belated Thanks from CuD to "helpers" File 2--Computers, Freedom & Privacy, '94 -- Conference INFO File 3--Congressional Fellowships for PhD/s-telecommunications File 4--$50,000 Fine for "Software Theft" (Canadian News) File 5--SKIPJACK Review (Encryption Background and Assessment) Cu-Digest is a weekly electronic journal/newsletter. Subscriptions are available at no cost electronically from tk0jut2@mvs.cso.niu.edu. The editors may be contacted by voice (815-753-0303), fax (815-753-6302) or U.S. mail at: Jim Thomas, Department of Sociology, NIU, DeKalb, IL 60115. Issues of CuD can also be found in the Usenet comp.society.cu-digest news group; on CompuServe in DL0 and DL4 of the IBMBBS SIG, DL1 of LAWSIG, and DL1 of TELECOM; on GEnie in the PF*NPC RT libraries and in the VIRUS/SECURITY library; from America Online in the PC Telecom forum under "computing newsletters;" On Delphi in the General Discussion database of the Internet SIG; on the PC-EXEC BBS at (414) 789-4210; and on: Rune Stone BBS (IIRG WHQ) (203) 832-8441 NUP:Conspiracy; RIPCO BBS (312) 528-5020 CuD is also available via Fidonet File Request from 1:11/70; unlisted nodes and points welcome. EUROPE: from the ComNet in LUXEMBOURG BBS (++352) 466893; In ITALY: Bits against the Empire BBS: +39-461-980493 ANONYMOUS FTP SITES: UNITED STATES: ftp.eff.org (192.88.144.4) in /pub/cud etext.archive.umich.edu (141.211.164.18) in /pub/CuD/cud halcyon.com( 202.135.191.2) in /pub/mirror/cud aql.gatech.edu (128.61.10.53) in /pub/eff/cud AUSTRALIA: ftp.ee.mu.oz.au (128.250.77.2) in /pub/text/CuD. EUROPE: nic.funet.fi in pub/doc/cud. (Finland) ftp.warwick.ac.uk in pub/cud (United Kingdom) COMPUTER UNDERGROUND DIGEST is an open forum dedicated to sharing information among computerists and to the presentation and debate of diverse views. CuD material may be reprinted for non-profit as long as the source is cited. Authors hold a presumptive copyright, and they should be contacted for reprint permission. It is assumed that non-personal mail to the moderators may be reprinted unless otherwise specified. Readers are encouraged to submit reasoned articles relating to computer culture and communication. Articles are preferred to short responses. Please avoid quoting previous posts unless absolutely necessary. DISCLAIMER: The views represented herein do not necessarily represent the views of the moderators. Digest contributors assume all responsibility for ensuring that articles submitted do not violate copyright protections. ---------------------------------------------------------------------- Date: Tue, 3 Aug 1993 18:31:44 CDT From: CuD Moderators Subject: File 1--CuD #5.59 Glitch & Some Belated Thanks from CuD to "helpers" By now, those who receive CuD from the mailing list are aware of a major glitch that occurred in #5.59. The good news is that the glitch was *NOT* our error (or even a human error). It was a software glitch in the mailer, apparently resulting from an overload. It has hopefully been corrected, but we will likely move to another distribution site to accommodate the growing list. We estimate that CuD currently has a readership of about 80,000, only about 1.8 percent of whom are on the mailing list, so the glitch did not affect most readers. Nonetheless, we are embarrassed and regret any inconvenience it caused. We're also pleased with the CuD readers' response when they discovered the glitch. Only one displayed the mildest of pique. The rest ranged from a matter of fact "oops" to floor-rolling funny lines. Proving, of course, what we've suspected all along: CuD readers are a bright, gentle, and forgiving lot. The best line comes from Scott Best: Of course, if "glitch"'s keep happening, they soon become "snafu"'s. And snafus become bugs. And, finally, bugs will ulitimately become performance features. And, while we're at it: Gordon Meyer and I put out CuD, and--if we run a good issue--we generally receive a few accolades. But, CuD is actually a collective enterprise that depends heavily on readers for contributions and other services. Without them, we couldn't continue. Some belated thanks to people who have been helpful over the past few months: 1. Special enthusiastic gratitudinous thanks to the folks at Central Michigan University who provided us with a site for mailing out CuDs. Their patience and assistance have been invaluable in reducing mailing time and the load on NIU's system. There have been fewer bounces, faster delivery, and (we hope) better service. 2. Thanks to Mike Stack, Mike Preis, and the other computer gurus at NIU who have been helpful in redirecting mail, patient and calm despite the habitually crashed mailer (prior to the mailserv switch) and have remained low-key and supportive despite the strain we've placed on the system. Thanks also to Neil Rickert, just on general principle. Someday, the NIU administrators may find it in their hearts to replace WYLBUR, an archaic operating system, but until then, these guys--along with Phil Rider and others--nurse us along with humor and invariable magic. 3. Thanks to everybody who sends in articles. We often hear that somebody didn't send something--such as a news blurb or other info--because they assumed somebody else would do it. WHEN IT DOUBT, SEND! It's better that we have multiple copies of something than none--so, keep the articles and news blurbs coming. We're especially in need of local or regional "computer crime" cases that we might not see in the Chicago or New York papers. 4. Thanks to all the people who complimented us (as well as to those who offered constructive criticism). And, thanks to those who felt like flaming but hit the delete key instead. 5. Thanks to the BBS readers who lack Net access, but who nonetheless send in their contributions via disk or call with information. Sometimes we can't run it, but the information is crucial to keeping us informed about the BBS world. 6. We're indebted to a number of individuals and groups who've been supportive and helpful over the years. These include the LOD crowd, PHRACK folk, Pat and Bruce at Mindvox (telnet mindvox.phantom.com), John McMullen for allowing reprints of his piece, Joe Abernathy for the same, Netta Gilboa of Gray Areas (one of the most promising new 'Zines to come along), Jack Ricard of Boardwatch (an essential 'Zine for anybody interested in the BBS world), Dark Adept, Kim Clancy, Dr. Ripco, and many, many others. And, of course, Chenko Kaninovich and Maggie T. Katt. These, and others we don't have space to name (short-term memory loss notwithstanding) have been invaluable over the years, and we're grateful. 7. Thanks to Bill Cook and the Secret Service, without whom there would be no Cu-Digest. There are others we've probably forgotten to acknowledge, so thanks to all of them. And, of course, thanks to Pat Townson, CuD's symbolic progenitor. ------------------------------ Date: Tue, 3 Aug 1993 18:31:44 CDT From: CuD Moderators Subject: File 2--Computers, Freedom & Privacy, '94 -- Conference INFO "Computers, Freedom & Privacy '94" George B. Trubow, General Chair Timothy R. Rabel, Conference Coordinator John Marshall Law School 315 South Plymouth Court Chicago, IL 60604 e-mail = cfp94@jmls.edu voice = (312) 987-1419 fax = (312) 427-8307 *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Conference Announcement and Call for Papers Computers, Freedom, and Privacy 1994 23-26 March 1994 Announcement The fourth annual conference, "Computers, Freedom, and Privacy," will be held in Chicago, Il., March 23-26, 1994. This conference will be jointly sponsored by the Association for Computing Machinery (ACM) and The John Marshall Law School. George B. Trubow, professor of law and director of the Center for Informatics Law at The John Marshall Law School, is general chairman of the conference. The advance of computer and communications technologies holds great promise for individuals and society. From conveniences for consumers and efficiencies in commerce to improved public health and safety and increased knowledge of and participation in government and community, these technologies are fundamentally transforming our environment and our lives. At the same time, these technologies present challenges to the idea of a free and open society. Personal privacy is increasingly at risk from invasions by high-tech surveillance and monitoring; a myriad of personal information data bases expose private life to constant scrutiny; new forms of illegal activity may threaten the traditional barriers between citizen and state and present new tests of Constitutional protection; geographic boundaries of state and nation may be recast by information exchange that knows no boundaries as governments and economies are caught up in global data networks. Computers, Freedom, and Privacy '94 will present an assemblage of experts, advocates and interested parties from diverse perspectives and disciplines to consider the effects on freedom and privacy resulting from the rapid technological advances in computer and telecommunication science. Participants come from fields of computer science, communications, law, business and commerce, research, government, education, the media, health, public advocacy and consumer affairs, and a variety of other backgrounds. A series of pre-conference tutorials will be offered on March 23, 1994, with the conference program beginning on Thursday, March 24, and running through Saturday, March 26, 1994. The Palmer House, a Hilton hotel located at the corner of State Street and Washington Ave. in Chicago's "loop," and only about a block from The John Marshall Law School buildings, will be the conference headquarters. Room reservations should be made directly with the hotel, mentioning The John Marshall Law School or "CFP'94" to get the special conference rate of$99.00, plus tax. The Palmer House Hilton 17 E. Monroe., Chicago, Il., 60603 Tel: 312-726-7500; 1-800-HILTONS; Fax 312-263-2556 Call for Papers and Program Suggestions The emphasis at CFP'94 will be on examining the many potential uses of new technology and considering recommendations for dealing with them. Specific suggestions to harness the new technologies so society can enjoy the benefits while avoiding negative implications are solicited. Proposals are requested from anyone working on a relevant paper, or who has an idea for a program presentation that will demonstrate new computer or communications technology and suggest what can be done with it. Any proposal must: state the title of the paper or program; describe the theme and content in a short paragraph; set out the credentials and experience of the author or suggested speakers; and should not exceed two pages. If an already completed paper is being proposed for presentation, then a copy should be included with the proposal. Student Papers and Scholarships It is anticipated that announcement of a student writing competition for CFP'94 will be made soon, together with information regarding the availability of a limited number of student scholarships for the conference. Timetables Proposals for papers and programs are being accepted at this time. It is intended that program committees will be finalized by August 1, 1993. Proposals must be received by October 1, 1993. Communications Conference communications should be sent to: CFP'94 The John Marshall Law School 315 S. Plymouth Ct. Chicago, IL 60604 (Voice: 312-987-1419; Fax: 312-427-8307; E-mail: CFP94@jmls.edu) ------------------------------ Date: Mon, 2 Aug 1993 18:29:01 CDT From: CuD Moderators Subject: File 3--Congressional Fellowships for PhD/s-telecommunications CONGRESSIONAL FELLOWSHIPS for Ph.D. level scholars of any discipline who have a demonstrated interest in telecommunications and in public policy. Candidates must show promise of making a significant contribution to the public's understanding of the political process. Ten month program of practical experience on Capitol Hill begins November 1994 and concludes August 1995. Application deadline, DECEMBER 1, 1993. Information: Director, Congressional Fellowship Program, American Political Science Association, 1527 New Hampshire Ave., N.W., Washington, DC 20036. ph 202-483-2512. ------------------------------ Date: Tue, 10 Aug 93 16:34:27 CDT From: Mitch Pravatiner Subject: File 4--$50,000 Fine for "Software Theft" (Canadian News) The following story from the July 24 _Vancouver Sun_ business section may be of interest, especially the final paragraph.$50,000 FINE FOR SOFTWARE THEFT TORONTO--The first corporation in Canada to be charged with software theft has pleaded guilty and been fined $50,000. Rexcan Circuits Inc., of Belleville, Ont., has also agreed to submit to a software audit by the Canadian Alliance Against Software Theft, a computer industry association. Related charges against two senior Rexcan executives were dropped. Rexcan, a circuit board manufacturer employing 200, is a subsidiary of Kuriko Electrical Industry Co. Ltd of Japan. Software theft occurs when a single computer disk is used to load software into more than one computer. ------------------------------ Date: Mon, 02 Aug 1993 15:23:28 -0400 (EDT) From: denning@CS.GEORGETOWN.EDU(Dorothy Denning) Subject: File 5--SKIPJACK Review (Encryption Background and Assessment) SKIPJACK Review Interim Report The SKIPJACK Algorithm Ernest F. Brickell, Sandia National Laboratories Dorothy E. Denning, Georgetown University Stephen T. Kent, BBN Communications Corporation David P. Maher, AT&T Walter Tuchman, Amperif Corporation July 28, 1993 (copyright 1993) Executive Summary The objective of the SKIPJACK review was to provide a mechanism whereby persons outside the government could evaluate the strength of the classified encryption algorithm used in the escrowed encryption devices and publicly report their findings. Because SKIPJACK is but one component of a large, complex system, and because the security of communications encrypted with SKIPJACK depends on the security of the system as a whole, the review was extended to encompass other components of the system. The purpose of this Interim Report is to report on our evaluation of the SKIPJACK algorithm. A later Final Report will address the broader system issues. The results of our evaluation of the SKIPJACK algorithm are as follows: 1. Under an assumption that the cost of processing power is halved every eighteen months, it will be 36 years before the cost of breaking SKIPJACK by exhaustive search will be equal to the cost of breaking DES today. Thus, there is no significant risk that SKIPJACK will be broken by exhaustive search in the next 30-40 years. 2. There is no significant risk that SKIPJACK can be broken through a shortcut method of attack. 3. While the internal structure of SKIPJACK must be classified in order to protect law enforcement and national security objectives, the strength of SKIPJACK against a cryptanalytic attack does not depend on the secrecy of the algorithm. 1. Background On April 16, the President announced a new technology initiative aimed at providing a high level of security for sensitive, unclassified communications, while enabling lawfully authorized intercepts of telecommunications by law enforcement officials for criminal investigations. The initiative includes several components: A classified encryption/decryption algorithm called "SKIPJACK." Tamper-resistant cryptographic devices (e.g., electronic chips), each of which contains SKIPJACK, classified control software, a device identification number, a family key used by law enforcement, and a device unique key that unlocks the session key used to encrypt a particular communication. A secure facility for generating device unique keys and programming the devices with the classified algorithms, identifiers, and keys. Two escrow agents that each hold a component of every device unique key. When combined, those two components form the device unique key. A law enforcement access field (LEAF), which enables an authorized law enforcement official to recover the session key. The LEAF is created by a device at the start of an encrypted communication and contains the session key encrypted under the device unique key together with the device identifier, all encrypted under the family key. LEAF decoders that allow an authorized law enforcement official to extract the device identifier and encrypted session key from an intercepted LEAF. The identifier is then sent to the escrow agents, who return the components of the corresponding device unique key. Once obtained, the components are used to reconstruct the device unique key, which is then used to decrypt the session key. This report reviews the security provided by the first component, namely the SKIPJACK algorithm. The review was performed pursuant to the President's direction that "respected experts from outside the government will be offered access to the confidential details of the algorithm to assess its capabilities and publicly report their finding." The Acting Director of the National Institute of Standards and Technology (NIST) sent letters of invitation to potential reviewers. The authors of this report accepted that invitation. We attended an initial meeting at the Institute for Defense Analyses Supercomputing Research Center (SRC) from June 21-23. At that meeting, the designer of SKIPJACK provided a complete, detailed description of the algorithm, the rationale for each feature, and the history of the design. The head of the NSA evaluation team described the evaluation process and its results. Other NSA staff briefed us on the LEAF structure and protocols for use, generation of device keys, protection of the devices against reverse engineering, and NSA's history in the design and evaluation of encryption methods contained in SKIPJACK. Additional NSA and NIST staff were present at the meeting to answer our questions and provide assistance. All staff members were forthcoming in providing us with requested information. At the June meeting, we agreed to integrate our individual evaluations into this joint report. We also agreed to reconvene at SRC from July 19-21 for further discussions and to complete a draft of the report. In the interim, we undertook independent tasks according to our individual interests and availability. Ernest Brickell specified a suite of tests for evaluating SKIPJACK. Dorothy Denning worked at NSA on the refinement and execution of these and other tests that took into account suggestions solicited from Professor Martin Hellman at Stanford University. NSA staff assisted with the programming and execution of these tests. Denning also analyzed the structure of SKIPJACK and its susceptibility to differential cryptanalysis. Stephen Kent visited NSA to explore in more detail how SKIPJACK compared with NSA encryption algorithms that he already knew and that were used to protect classified data. David Maher developed a risk assessment approach while continuing his ongoing work on the use of the encryption chip in the AT&T Telephone Security Device. Walter Tuchman investigated the anti-reverse engineering properties of the chips. We investigated more than just SKIPJACK because the security of communications encrypted with the escrowed encryption technology depends on the security provided by all the components of the initiative, including protection of the keys stored on the devices, protection of the key components stored with the escrow agents, the security provided by the LEAF and LEAF decoder, protection of keys after they have been transmitted to law enforcement under court order, and the resistance of the devices to reverse engineering. In addition, the success of the technology initiative depends on factors besides security, for example, performance of the chips. Because some components of the escrowed encryption system, particularly the key escrow system, are still under design, we decided to issue this Interim Report on the security of the SKIPJACK algorithm and to defer our Final Report until we could complete our evaluation of the system as a whole. 2. Overview of the SKIPJACK Algorithm SKIPJACK is a 64-bit "electronic codebook" algorithm that transforms a 64-bit input block into a 64-bit output block. The transformation is parameterized by an 80-bit key, and involves performing 32 steps or iterations of a complex, nonlinear function. The algorithm can be used in any one of the four operating modes defined in FIPS 81 for use with the Data Encryption Standard (DES). The SKIPJACK algorithm was developed by NSA and is classified SECRET. It is representative of a family of encryption algorithms developed in 1980 as part of the NSA suite of "Type I" algorithms, suitable for protecting all levels of classified data. The specific algorithm, SKIPJACK, is intended to be used with sensitive but unclassified information. The strength of any encryption algorithm depends on its ability to withstand an attack aimed at determining either the key or the unencrypted ("plaintext") communications. There are basically two types of attack, brute-force and shortcut. 3. Susceptibility to Brute Force Attack by Exhaustive Search In a brute-force attack (also called "exhaustive search"), the adversary essentially tries all possible keys until one is found that decrypts the intercepted communications into a known or meaningful plaintext message. The resources required to perform an exhaustive search depend on the length of the keys, since the number of possible keys is directly related to key length. In particular, a key of length N bits has 2^N possibilities. SKIPJACK uses 80-bit keys, which means there are 2^80 (approximately 10^24) or more than 1 trillion trillion possible keys. An implementation of SKIPJACK optimized for a single processor on the 8-processor Cray YMP performs about 89,000 encryptions per second. At that rate, it would take more than 400 billion years to try all keys. Assuming the use of all 8 processors and aggressive vectorization, the time would be reduced to about a billion years. A more speculative attack using a future, hypothetical, massively parallel machine with 100,000 RISC processors, each of which was capable of 100,000 encryptions per second, would still take about 4 million years. The cost of such a machine might be on the order of$50 million. In an even more speculative attack, a special purpose machine might be built using 1.2 billion $1 chips with a 1 GHz clock. If the algorithm could be pipelined so that one encryption step were performed per clock cycle, then the$1.2 billion machine could exhaust the key space in 1 year. Another way of looking at the problem is by comparing a brute force attack on SKIPJACK with one on DES, which uses 56-bit keys. Given that no one has demonstrated a capability for breaking DES, DES offers a reasonable benchmark. Since SKIPJACK keys are 24 bits longer than DES keys, there are 2^24 times more possibilities. Assuming that the cost of processing power is halved every eighteen months, then it will not be for another 24 * 1.5 = 36 years before the cost of breaking SKIPJACK is equal to the cost of breaking DES today. Given the lack of demonstrated capability for breaking DES, and the expectation that the situation will continue for at least several more years, one can reasonably expect that SKIPJACK will not be broken within the next 30-40 years. Conclusion 1: Under an assumption that the cost of processing power is halved every eighteen months, it will be 36 years before the cost of breaking SKIPJACK by exhaustive search will be equal to the cost of breaking DES today. Thus, there is no significant risk that SKIPJACK will be broken by exhaustive search in the next 30-40 years. 4. Susceptibility to Shortcut Attacks In a shortcut attack, the adversary exploits some property of the encryption algorithm that enables the key or plaintext to be determined in much less time than by exhaustive search. For example, the RSA public-key encryption method is attacked by factoring a public value that is the product of two secret primes into its primes. Most shortcut attacks use probabilistic or statistical methods that exploit a structural weakness, unintentional or intentional (i.e., a "trapdoor"), in the encryption algorithm. In order to determine whether such attacks are possible, it is necessary to thoroughly examine the structure of the algorithm and its statistical properties. In the time available for this review, it was not feasible to conduct an evaluation on the scale that NSA has conducted or that has been conducted on the DES. Such review would require many man-years of effort over a considerable time interval. Instead, we concentrated on reviewing NSA's design and evaluation process. In addition, we conducted several of our own tests. 4.1 NSA's Design and Evaluation Process SKIPJACK was designed using building blocks and techniques that date back more than forty years. Many of the techniques are related to work that was evaluated by some of the world's most accomplished and famous experts in combinatorics and abstract algebra. SKIPJACK's more immediate heritage dates to around 1980, and its initial design to 1987. SKIPJACK was designed to be evaluatable, and the design and evaluation approach was the same used with algorithms that protect the country's most sensitive classified information. The specific structures included in SKIPJACK have a long evaluation history, and the cryptographic properties of those structures had many prior years of intense study before the formal process began in 1987. Thus, an arsenal of tools and data was available. This arsenal was used by dozens of adversarial evaluators whose job was to break SKIPJACK. Many spent at least a full year working on the algorithm. Besides highly experienced evaluators, SKIPJACK was subjected to cryptanalysis by less experienced evaluators who were untainted by past approaches. All known methods of attacks were explored, including differential cryptanalysis. The goal was a design that did not allow a shortcut attack. The design underwent a sequence of iterations based on feedback from the evaluation process. These iterations eliminated properties which, even though they might not allow successful attack, were related to properties that could be indicative of vulnerabilities. The head of the NSA evaluation team confidently concluded "I believe that SKIPJACK can only be broken by brute force there is no better way." In summary, SKIPJACK is based on some of NSA's best technology. Considerable care went into its design and evaluation in accordance with the care given to algorithms that protect classified data. 4.2 Independent Analysis and Testing Our own analysis and testing increased our confidence in the strength of SKIPJACK and its resistance to attack. 4.2.1 Randomness and Correlation Tests A strong encryption algorithm will behave like a random function of the key and plaintext so that it is impossible to determine any of the key bits or plaintext bits from the ciphertext bits (except by exhaustive search). We ran two sets of tests aimed at determining whether SKIPJACK is a good pseudo random number generator. These tests were run on a Cray YMP at NSA. The results showed that SKIPJACK behaves like a random function and that ciphertext bits are not correlated with either key bits or plaintext bits. Appendix A gives more details. 4.2.2 Differential Cryptanalysis Differential cryptanalysis is a powerful method of attack that exploits structural properties in an encryption algorithm. The method involves analyzing the structure of the algorithm in order to determine the effect of particular differences in plaintext pairs on the differences of their corresponding ciphertext pairs, where the differences are represented by the exclusive-or of the pair. If it is possible to exploit these differential effects in order to determine a key in less time than with exhaustive search, an encryption algorithm is said to be susceptible to differential cryptanalysis. However, an actual attack using differential cryptanalysis may require substantially more chosen plaintext than can be practically acquired. We examined the internal structure of SKIPJACK to determine its susceptibility to differential cryptanalysis. We concluded it was not possible to perform an attack based on differential cryptanalysis in less time than with exhaustive search. 4.2.3 Weak Key Test Some algorithms have "weak keys" that might permit a shortcut solution. DES has a few weak keys, which follow from a pattern of symmetry in the algorithm. We saw no pattern of symmetry in the SKIPJACK algorithm which could lead to weak keys. We also experimentally tested the all "0" key (all 80 bits are "0") and the all "1" key to see if they were weak and found they were not. 4.2.4 Symmetry Under Complementation Test The DES satisfies the property that for a given plaintext-ciphertext pair and associated key, encryption of the one's complement of the plaintext with the one's complement of the key yields the one's complement of the ciphertext. This "complementation property" shortens an attack by exhaustive search by a factor of two since half the keys can be tested by computing complements in lieu of performing a more costly encryption. We tested SKIPJACK for this property and found that it did not hold. 4.2.5 Comparison with Classified Algorithms We compared the structure of SKIPJACK to that of NSA Type I algorithms used in current and near-future devices designed to protect classified data. This analysis was conducted with the close assistance of the cryptographer who developed SKIPJACK and included an in-depth discussion of design rationale for all of the algorithms involved. Based on this comparative, structural analysis of SKIPJACK against these other algorithms, and a detailed discussion of the similarities and differences between these algorithms, our confidence in the basic soundness of SKIPJACK was further increased. Conclusion 2: There is no significant risk that SKIPJACK can be broken through a shortcut method of attack. 5. Secrecy of the Algorithm The SKIPJACK algorithm is sensitive for several reasons. Disclosure of the algorithm would permit the construction of devices that fail to properly implement the LEAF, while still interoperating with legitimate SKIPJACK devices. Such devices would provide high quality cryptographic security without preserving the law enforcement access capability that distinguishes this cryptographic initiative. Additionally, the SKIPJACK algorithm is classified SECRET NOT RELEASABLE TO FOREIGN NATIONALS. This classification reflects the high quality of the algorithm, i.e., it incorporates design techniques that are representative of algorithms used to protect classified information. Disclosure of the algorithm would permit analysis that could result in discovery of these classified design techniques, and this would be detrimental to national security. However, while full exposure of the internal details of SKIPJACK would jeopardize law enforcement and national security objectives, it would not jeopardize the security of encrypted communications. This is because a shortcut attack is not feasible even with full knowledge of the algorithm. Indeed, our analysis of the susceptibility of SKIPJACK to a brute force or shortcut attack was based on the assumption that the algorithm was known. Conclusion 3: While the internal structure of SKIPJACK must be classified in order to protect law enforcement and national security objectives, the strength of SKIPJACK against a cryptanalytic attack does not depend on the secrecy of the algorithm. -------------------------------------------------- Appendix in LaTeX -------------------------------------------------- \documentstyle{article} \textheight 8.25in \topmargin -.25in \textwidth 6.5in \oddsidemargin 0in \begin{document} \parskip .25in \large \raggedright \setcounter{page}{8} \centerline{\bf Appendix A} {\bf A.1 Cycle Structure Tests} The first set of tests examined the cycle structure of SKIPJACK. Fix a set of keys, $\cal K$, a plaintext, $m$, and a function $h\; : \; {\cal M} \longrightarrow {\cal K}$, where ${\cal M}$ is the set of all 64 bit messages. Let $f \; : \; {\cal K} \longrightarrow {\cal K}$ be defined as $f(k) = h ( SJ(k,m))$ (where $SJ(k,m)$ denotes the SKIPJACK encryption of plaintext $m$ with key $k$). Let $N = |\cal K|$. The expected cycle length of $f$ is $\sqrt{\pi N /8}$. We chose sets of $\cal K$ with $N \; = \; 2^{10}, 2^{16}, 2^{24}, 2^{32}, 2^{40}, 2^{48}, 2^{56}$. For all of these $N$, the mean of the cycle lengths computed across all experiments was close to an expected relative error of $(1/\sqrt{j}$ for $j$ experiments) of the expected cycle length. We did not do this test with larger sets of keys because of the time constraints. \begin{center} \begin{tabular}{lrrrrr} $N$ & \# of exps & Mean cycle len & Expec cycle len & Rel Err & Expec rel err \\ \hline $2^{10}$ & 5000 & 20.4 & 20.1 & .019 & .014 \\ $2^{16}$ & 3000 & 164.7 & 160.4 & .027 & .018 \\ $2^{24}$ & 2000 & 2576.6 & 2566.8 & .004 & .022 \\ $2^{32}$ & 2000 & 40343.2 & 41068.6 & .018 & .022 \\ $2^{40}$ & 1000 & 646604.9 & 657097.6 & .016 & .032 \\ $2^{48}$ & 10 & 8,980,043 & 10,513,561 & .145 & .316 \\ $2^{56}$ & 1 & 28,767,197 & 168,216,976 & .829 & 1 \\ \end{tabular} \end{center} {\bf A.2 Statistical Randomness and Correlation Tests} The second set of tests examined whether there were any correlations between the input and output of SKIPJACK, or between a key and the output. We also looked for nonrandomness in functions of the form $SJ(k,m) \oplus SJ(k,m \oplus h)$ and functions of the form $SJ(k,m) \oplus SJ(k \oplus h , m)$ for all $h$ of Hamming weight 1 and 2 and for some randomly chosen $h$. All results were consistent with these functions behaving like random functions. Given a set of $N$ numbers of $k$-bits each, a chi-square test will test the hypothesis that this set of numbers was drawn (with replacement) from a uniform distribution on all of the $2^k$, $k$-bit numbers. We ran the tests using a 99\% confidence level. A truly random function would pass the test approximately 99\% of the time. The test is not appropriate when $N/2^k$ is too small, say $\leq 5$. Since it was infeasible to run the test for $k = 64$, we would pick 8 bit positions, and generate a set of $N= 10,000$ numbers, and run the test on the $N$ numbers restricted to those 8 bit positions (thus $k=8$). In some of the tests, we selected the 8 bits from the output of the function we were testing, and in others, we selected 4 bits from the input and 4 from the output. Some of the tests were run on both the encryption and decryption functions of SKIPJACK. The notation $SJ^{-1}(k,m)$ will be used to denote the decryption function of SKIPJACK with key $k$ on message $m$. {\bf Test 1: Randomness test on output. } In a single test: Fix $k$, fix mask of 8 output bits, select 10,000 random messages, run chi-square on the 10,000 outputs restricted to the mask of 8 output bits. Repeat this single test for 200 different values of $k$ and 50 different masks, for a total of 10,000 chi-square tests. We found that .87\% of the tests failed the 99\% confidence level chi-square test. This is within a reasonable experimental error of the expected value of 1\%. On the decryption function, there were only .64\% of the tests that failed. This was on a much smaller test set. \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline \# $k$ & \# masks & function, $f(m)$ & mask & \% failed \\ \hline 200 & 50 & $SJ(k,m)$ & 8 of $f(m)$ & .87 \\ \hline 25 & 50 & $SJ^{-1}(k,m)$ & 8 of $f(m)$ & .64 \\ \hline \end{tabular} \end{center} {\bf Test 2: Correlation test between messages and output.} Single test: Fix $k$, fix mask of 4 message bits and 4 output bits, select 10,000 random messages, run chi-square. \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline \# $k$ & \# masks & function, $f(m)$ & mask & \% failed \\ \hline 200 & 1000 & $SJ(k,m)$ & 4 of $m$, 4 of $f(m)$ & 1.06 \\ \hline 25 & 1000 & $SJ^{-1}(k,m)$ & 4 of $m$, 4 of $f(m)$ & 1.01 \\ \hline \end{tabular} \end{center} {\bf Test 3: Randomness test on the xor of outputs, given a fixed xor of inputs. } Single test: Fix $k$, fix mask of 8 output bits, select 10,000 random messages. Let $\cal H$ be the union of all 64 bit words of Hamming weight 1 (64 of these), all 64 bit words of Hamming weight 2 (2016 of these), and some randomly chosen 64 bit words (920 of these). Repeat this single test for all $h \in \cal H$, 50 different masks, and 4 different values of $k$. \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \# $k$ & \# masks & \# $h$ & function, $f(m)$ & mask & \% failed \\ \hline 4 & 50 & 3000 & $SJ(k,m) \oplus SJ(k,m \oplus h)$ & 8 of $f(m)$ & .99 \\ \hline \end{tabular} \end{center} {\bf Test 4: Correlation test between message xors and output xors. } Single test: Fix $k$, fix mask of 4 bits of $h$ and 4 bits of output, select 10,000 random $(m,h)$ pairs. \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline \# $k$ & \# masks & function, $f(m,h)$ & mask & \% failed \\ \hline 200 & 1000 & $SJ(k,m) \oplus SJ(k,m \oplus h)$ & 4 of $h$, 4 of $f(m,h)$ & .99 \\ \hline 25 & 1000 & $SJ^{-1}(k,m) \oplus SJ^{-1}(k,m \oplus h)$ & 4 of $h$, 4 of $f(m,h)$ & 1.02 \\ \hline \end{tabular} \end{center} {\bf Test 5: Correlation test between messages and output xors.} Single test: Fix $k$, fix mask of 4 bits of $m$ and 4 bits of output xor, select 10,000 random messages. Let $\cal H$ be the union of all 64 bit words of Hamming weight 1 (64 of these), some of the 64 bit words of Hamming weight 2 (100 of these), and some randomly chosen 64 bit words (100 of these). \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \# $k$ & \# masks & \# $h$& function, $f(m)$ & mask & \% failed \\ \hline 2 & 1000 & 264 & $SJ(k,m) \oplus SJ(k,m \oplus h)$ & 4 of $m$, 4 of $f(m)$ & .99 \\ \hline \end{tabular} \end{center} {\bf Test 6: Correlation test between keys and output.} Single test: Fix $m$, fix mask of 4 key bits and 4 output bits, select 10,000 random keys. \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline \# $m$ & \# masks & function, $f(k)$ & mask & \% failed \\ \hline 200 & 1000 & $SJ(k,m)$ & 4 of $k$, 4 of $f(k)$ & 1.00 \\ \hline 25 & 1000 & $SJ^{-1}(k,m)$ & 4 of $k$, 4 of $f(k)$ & 1.02 \\ \hline \end{tabular} \end{center} {\bf Test 7: Randomness test on the xor of outputs, given a fixed xor of keys. } Single test: Fix $m$, fix mask of 8 output bits, select 10,000 random keys. Let $\cal H$ be the union of all 80 bit words of Hamming weight 1 (80 of these), all 80 bit words of Hamming weight 2 (3160 of these), and some randomly chosen 80 bit words (760 of these). Repeat this single test for all $h \in \cal H$, 50 different masks, and 2 different values of $m$. \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline \# $m$ & \# masks & \# $h$ & function, $f(k)$ & mask & \% failed \\ \hline 2 & 50 & 4000 & $SJ(k,m) \oplus SJ(k\oplus h,m )$ & 8 of $f(k)$ & .99 \\ \hline \end{tabular} \end{center} {\bf Test 8: Correlation test between key xors and output xors. } Single test: Fix $m$, fix mask of 4 bits of $h$ and 4 bits of output, select 10,000 random $(k,h)$ pairs. \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline \# $m$ & \# masks & function, $f(k,h)$ & mask & \% failed \\ \hline 200 & 1000 & $SJ(k,m) \oplus SJ(k\oplus h,m )$ & 4 of $h$, 4 of $f(k,h)$ & 1.02 \\ \hline 25 & 1000 & $SJ^{-1}(k,m) \oplus SJ^{-1}(k\oplus h,m )$ & 4 of $h$, 4 of $f(k,h)$ & 1.1 \\ \hline \end{tabular} \end{center} \end{document} ------------------------------ End of Computer Underground Digest #5.60 ************************************

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