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:: skipjack.txtSkipjack Review - includes the algorithm |

[ Permission to make this document available was obtained directly from Dorothy Denning. -- MODERATOR ] 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. -------------------------------------------------------------------------- LaTeX Appendix -------------- \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}