W. Diffie and M. Hellman, \Exhaustive cryptanalysis of the NBS Data Encryption Standard. " Computer, vol. 10, no. 6, 74-84 (June 1977).  Home/Search   Document Not in Database   Summary   Related Articles   Check

..... 22 B.2 Driver chip: driver.vhdl . 24 B.3 Cryptographic Engine: crypt.vhdl . 26 1 INTRODUCTION 2 Implementation Year Cost per Blocks s Chips Time, Ref chip per 1M given 1M Diffie Hellman 77 20 1M 50k 17 days [DH77] Hoornaert, et al. 84 40 1.1M 25k 30 days [HGD85] AMD 84 19 218k 53k 72 days [AMD84] Wayner 92 30 448k 31k 30 days [Way93] VLSI Technology 92 170 3M 6k 47 days [VLS91] DEC 92 300 16M 3k 16 days [Ebe93] Wiener 93 11 50M 58k 4 hours [Wie94] Paper study. These tend to be rather ....

....a European team led by the Swiss Federal Institute of Technology in Zurich exhausted the key space of 48 bit RC5 in 13 days. The 56 bit key length of the Data Encryption Standard, DES, has likewise been claimed too small; Diffie and Hellman objected at the time of the standard s adoption, in 1977 [DH77] A number of papers have provided estimates of the cost and time of breaking DES using brute force search. Custom hardware invariably performs much better than software for this task; DES is not particularly suited to software implementation due to its employment of bit permutations and ....

[Article contains additional citation context not shown here]

W. Diffie and M. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, 10(6):74--84, June 1977.

....computational power of the Internet. Special purpose hardware data points. At the cost of a one time investment a hardware attack is substantially faster than a software attack. In 1977 a 20 million parallel DES key searching machine was proposed with an expected search time of 12 hours (cf. [10]) in 1980 corrected to 50 million and 2 days (cf. 9] In a 1993 design by M. Wiener (cf. 31] the cost and expected time were down to one million dollar and 3.5 hours, respectively. In 1998 a 130,000 machine was built with an expected search time of 112 hours (cf. 16] see also [12] ....

....1999 (cf. 6] This factoring effort was estimated to cost at most 20 years on a PC with at least 64Mbytes of memory (or a single day on 7500 PCs) This time was spent almost entirely on the sieving step. It is less than 10 Mips Years and corresponds to fewer than 3 10 operations, whereas L[10 ] = 2 10 (omitting the o(1) This shows that L[n] overestimates the number of operations to be carried out for the factorization of n. The run time given here is the actual run time of the RSA155 factoring effort and should not be confused with the estimates given in [29] which appeared around ....

W. Diffie, E. Hellman, Exhaustive cryptanalysis of the NBS Data Encryption Standard, Computer, v. 10 (1977), 74-84.

....so that a software search using a generalpurpose computer is about twice as fast as a hardware implementation. The possibility of breaking DES encryption should also be considered. Although the issue of DES key recovery hardware has been debated for almost as long as the standard has been around [Diffie 1977] [Hellman 1979] it wasn t until 1993 that complete constructional details for a DES breaking machine were published [Wiener 1993] this type of device has since become known as a Wiener machine after the author of the paper) This would recover a DES key in 3.5 hours for a US 1M investment in ....

Whitfield Diffie and Martin Hellman, "Exhaustive Cryptanalysis of the NBS Data Encryption Standard", IEEE Computer, Vol.10, No.6 (June 1977), p.74.

....power of the Internet. 2.2.5 Special purpose hardware data points. At the cost of a one time investment a hardware attack is substantially faster than a software attack. In 1977 a 20 million dollar parallel DES key searching machine was proposed with an expected search time of 12 hours [11]. We write [ 20 million, 12 hours, 1977] hardware for this design. In [10] it was corrected to [ 50 million, 2 days, 1980] hardware. Mike Wiener published a detailed [ 1 million, 3.5 hours, 1993] hardware design [43] and special purpose [ 130,000, 112 hours, 1998] hardware was actually built ....

W. Die, E. Hellman, Exhaustive cryptanalysis of the NBS Data Encryption Standard, Computer, v. 10 (1977), 74-84.

....as DES to differential and linear cryptanalysis. The (apparent) strength of Double and two key triple DES against cryptanalysis coupled with the proven strength against generic attacks seem to make a strong combination that is absent for DESX. The basic meet in the middle attacks are due to [5, 12]. Even and Goldreich provide some time space tradeoffs for meet in the middle attacks [6] and Van Oorschot and Wiener [14] reduce the space requirements. Even and Goldreich [6] had shown that the cascade of m ciphers is at least as strong as its strongest component. Maurer and Massey [10] argued ....

W. Diffie and M. Hellman, "Exhaustive cryptanalysis of the NBS data encryption standard," Computer, Vol. 10, No. 6, pp. 74--84, June 1977.

....chaining; it prevents repeated text in the message from yielding correspondingly repeated sections of ciphertext. Other such modes of operation for the use of DES, as well as proposed techniques for key management, have been published by the National Bureau of Standards. Die and Hellman [50] argue that the choice of a 56 bit key makes DES vulnerable to a brute force attack. For 20 million one might be able to build a machine consisting of 2 20 chips, each of which can test 2 20 keys second, so that in 2 16 seconds (18:2 hours) the entire key space can be searched for the key ....

W. Die and M. E. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, 10:74-84, June 1977.

....part [4] They extrapolated their results for the algorithm to project a cost of 45,000 for a full cryptanalytic machine that would search through the entire key space in one year. There is much published research on custom hardware cryptanalytic machines for DES, dating as far back as 1977 [6]. Wiener is currently considered the best estimate of custom hardware performance [7] Gray and Kean implemented DES on the fine grained Configurable Array Logic device. This design faithfully implemented the standard DES architecture, thus exploiting the bit level parallelism but not partial ....

W. Diffie and M. E. Hellman, "Exhaustive Cryptanalysis of the NBS Data Encryption Standard," in IEEE Computer, vol. 10, 1977, pp. 74-84.

....was demonstrated that even in software a 56 bit key does not provide sufficient protection, when a DES key was found by exhaustive search using implementations distributed on the Internet. However, the problem of the small key size was pointed out already shortly after the publication of the DES [6]. Therefore, often the DES is used in a triple encryption scheme, where a plaintext is encrypted thrice with 3 independent keys, called triple DES. In another variant, called two key triple DES, the plaintext is first encrypted with a key K1, then decrypted with a key K2, and finally encrypted ....

....subkeys would need to be generated and thus the key schedule of DEAL would become more complex. 2. 1 Security of DEAL What can we say about the security of DEAL in general First note that for DEAL with 6 respectively 8 rounds a simple meet in the middle attack (similar to the one on doubleDES [6, 17]) will find the keys in the time of about 2 168 respectively 2 224 encryptions, 5 independent of the key schedule. For DEAL 192 this attack is faster than an exhaustive search for the key, but also requires a very large memory. Nevertheless, we suggest to do at least 8 rounds of encryption ....

W. Diffie and M. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, pages 74--84, 1977.

....encryption algorithm in the world. Despite its popularity, DES has been plagued with controversy. Some cryptographers objected to the closed door design process of the algorithm. The debate about whether DES key is too short for acceptable commercial security has raged for many years [DH79], but recent advances in distributed key search techniques have left no doubt in anyone s mind that its key is simply too short for today s security applications [Wie94, BDR 96] TripleDES has emerged as an interim solution in many high security applications, such as banking, but it is too slow ....

W. Die and M. Hellman, \Exhaustive Cryptanalysis of the NBS Data Encryption Standard," Computer, v. 10, n. 3, Mar 1979, pp. 74-84.

....encryption algorithm in the world. Despite its popularity, DES has been plagued with controversy. Some cryptographers objected to the closed door design process of the algorithm. The debate about whether DES key is too short for acceptable commercial security has raged for many years [DH79], but recent advances in distributed key search techniques have left no doubt in anyone s mind that its key is simply too short for today s security applications [Wie94, BDR 96] TripleDES has emerged as an interim solution in many high security applications, such as banking, but it is too slow ....

W. Di#e and M. Hellman, "Exhaustive Cryptanalysis of the NBS Data Encryption Standard," Computer, v. 10, n. 3, Mar 1979, pp. 74--84.

....computational power of the Internet. Special purpose hardware data points. At the cost of a one time investment a hardware attack is substantially faster than a software attack. In 1977 a 20 million parallel DES key searching machine was proposed with an expected search time of 12 hours (cf. [10]) in 1980 corrected to 50 million and 2 days (cf. 9] In a 1993 design by M. Wiener (cf. 29] the cost and expected time were down to one million dollar and 3.5 hours, respectively. In 1998 a 130,000 machine was built with an expected search time of 112 hours (cf. 14] see also [12] ....

....(cf. 6] This factoring effort was estimated to cost at most 20 years on a PC with at least 64Mbytes of memory (or a single day on 7500 PCs) This time was spent almost entirely on the sieving step. It is less than 10 4 Mips Years and corresponds to fewer than 3 10 17 operations, whereas L[10 155 ] = 2 10 19 (omitting the o(1) This shows that L[n] overestimates the number of operations to be carried out for the factorization of n. The run time given here is the actual run time of the RSA155 factoring effort and should not be confused with the estimates given in [27] which appeared ....

W. Diffie, E. Hellman, Exhaustive cryptanalysis of the NBS Data Encryption Standard, Computer, v. 10 (1977), 74-84.

....1. DES Attack Complexity 2. 1 Analysis Following are the major cryptanalytic attacks against DES: 1976: For a very small class of weak keys, DES can be broken with complexity 1 [HMS 76] 1977: Exhaustive search will become possible within 20 years, breaking DES with complexity 2 56 [DH77]. 1980: A time memory tradeo# can break DES faster at the expense of more memory. DES can be broken with time complexity 1 and 2 56 memory. 1982: For a very small class of semi weak keys, DES can be broken with complexity 1 [Dav82] 1985: A meet in the middle attack can break 6 round ....

W. Di#e and M.E. Hellman, "Exhaustive Cryptanalysis of the NBS Data Encryption Standard," Computer, v. 10, n. 6, Jun. 1977, pp. 74--84.

....encryption algorithm in the world. Despite its popularity, DES has been plagued with controversy. Some cryptographers objected to the closed door design process of the algorithm. The debate about whether DES key is too short for acceptable commercial security has raged for many years [DH79], but recent advances in distributed key search techniques have left no doubt in anyone s mind that its key is simply too short for today s security applications [Wie94, BDR 96] TripleDES has emerged as an interim solution in many high security applications, such as banking, but it is too slow ....

W. Diffie and M. Hellman, "Exhaustive Cryptanalysis of the NBS Data Encryption Standard," Computer, v. 10, n. 3, Mar 1979, pp. 74--84.

....could lower the operation count by a factor of 10 or 100, this means that even n = 1279 should not be considered safe, since it could then be broken using a less ambitious machine. Note that a machine using 10 6 chips running at around 10 nanoseconds per cycle was proposed by Diffie and Hellman [24] for finding a DES key in about a day through exhaustive search. Such a machine was generally thought to be too ambitious for the then current technology, but it seems to be generally accepted that it could be built for some tens of millions of dollars by 1990. On the other hand, n 2200 is ....

W. Diffie and M. E. Hellman, Exhaustive cryptanalysis of the NBS Data Encryption Standard, Computer 10 (1977), 74-84.

....that it may not recertify DES again. 5.2 Has DES been broken DES has never been broken , despite the efforts of many researchers over many years. The obvious method of attack is brute force exhaustive search of the key space; this takes 2 55 steps on average. Early on it was suggested [28] that a rich and powerful enemy could build a special purpose computer capable of breaking DES by exhaustive search in a reasonable amount of time. Later, Hellman [36] showed a time memory trade off that allows improvement over exhaustive search if memory space is plentiful, after an exhaustive ....

W. Diffie and M.E. Hellman. Exhaustive cryptanalysis of the NBS Data Encryption Standard. Computer, 10:74--84, 1977.

....NEC 78K0S SuperMAP 2048 bit 1 KB 24 KB 8 KB 1.8V to 5.5V 5 Mhz 40 Mhz 0. 35 m expected in forthcoming months modular exponentiation based schemes [34] There exist many different ways of performing a modular multiplication, among which Montgomery [7] De Waleffe Quisquater [13] or Sedlak [12] provide methods that are still the most commonly used in hardware implementations. Naturally, the best internal architecture of a coprocessor relies strongly on the choice of modular multiplication algorithm (see [6, 9] for details) Size doubling techniques : algorithmic tools for emulating a ....

....co processors for public key cryptography: The State of the Art, IEEE Micro, pp. 14 24, June 1996. 10] NIST. FIPS PUB 186, February 1, 1993, Digital Signature Standard. 11] J. Omura, A Public Key Cell Design for Smart Card Chips, IT Workshop, Hawaii, USA, November 27 30, 1990, pp. 983 985. [12] R. Rivest, A. Shamir and L. Adleman, A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of the ACM, vol. 21, no. 2, p.120 126, February 1978. 13] C. Schnorr, Efficient identification and signatures for smartcards, Advances in Cryptology: EUROCRYPT 89 (G. ....

[Article contains additional citation context not shown here]

W. Diffie, M. E. Hellman, Exhaustive Cryptanalysis of the NBS Data Encryption Standard, Computer, Vol. 10, No. 6, pp. 74-84, June 1977.

....82.2 days 365 days 6 78.8 hours 23.1 days 603 days 21.4 years 128 years 7 85.3 days 832 days 102 years 2.03 kyears 16.4 kyears 8 6.07 years 82.1 years 6.35 kyears 193 kyears 2. 03 myears Table 1: Brute Force Cracking Times of Speed Crypt on the DEC 3100 Exhaustive search in hardware is possible[5]. One of the aims of including the salt in the crypt algorithm was to remove the threat of using DES hardware to find passwords. However, it would not be too expensive to build VLSI chips that compute the crypt function and run 1000 times faster than these software implementations, not to mention ....

W. Diffie and M. E. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, 10(6):74--84, June 1977.

....being the Data Encryption Standard [FI46] Although DES has been a worldwide de facto standard since 1977, everybody agrees that it is reaching the end of its life time. The main reason is the size of the key, which is only 56 bits. The key size was already a topic of discussion in the seventies [DH77], and it was shown recently by M. Wiener that at present an exhaustive key search in 3.5 hours requires only 1 million US of equipment [W93] Of more theoretical interest are recent cryptanalytic techniques such as differential [BS93] and linear [Ma93a, Ma94] cryptanalysis which provide ....

W. Diffie and M. Hellman, "Exhaustive cryptanalysis of the NBS data encryption standard," Computer, pp. 74--78, 1977.

....lg m bits, where is the key length of F , n is the block length, and m bounds the number of hx; FXK (x)i pairs the adversary can obtain. 1 Introduction The susceptibility of DES to exhaustive key search has been a concern and a complaint since the cipher was first made public; see, for example, [6]. Careful analysis by Wiener [15] indicates that the problem has now escalated to the point that for 1 million one could build a DES key search engine which, given a hplaintext, ciphertexti pair, would recover the key in about 3.5 expected hours. Many people have suggested overcoming the threat ....

W. Diffie and M. Hellman, "Exhaustive cryptanalysis of the NBS Data Encryption Standard." Computer, vol. 10, no. 6, 74--84 (June 1977).

....of the next iteration simultaneous with the remaining operations in the current iteration. An additional key latch is introduced to buffer the key value for the current iteration on the input to the key mixing XOR stage as shown in Fig. 3. This key parallelism was suggested by Diffie and Hellman [Diffie77] in their timing approach for the proposed DES key search device. They did not include the additional key latch but instead relied on strict control of key shift timing with respect to the overall R L clock timing to prevent a race condition. Our introduction of the key latch allows greater ....

Whitfield Diffie and Martin E. Hellman, Exhaustive Cryptanalysis of the NBS Data Encryption Standard , IEEE Computer Vol. 10 No. 6, June 1977 pp. 74-84

....powerful aid to the cryptanalyst. We conclude by outlining some likely changes to the underlying protocols that may strengthen them against these attacks. 1 Introduction DES, the Data Encryption Standard [NBS77] is a strong cipher that is hobbled by an overly short key. This criticism is not new [DH77]; more recently, designs have been published for machines that can exhaustively search the key space in a short time for a comparatively modest investment [Wie94] Most such designs assume blocks of known plaintext, though at least one [WB94] relies on statistical properties of the underlying ....

Whitfield Diffie and Martin E. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, 10(6):74--84, June 1977.

....chosen when very little change needs to be made to the algorithm to accommodate a 64 bit key. While arguments will continue over various explanations which have been offered, most agree that the key seems to be somewhat shorter than it needs to be. In 1977 Diffie and Hellman published an article [48] claiming that a machine could be built for about 20 million which would find a DES key by exhaustive search in around 12 hours of computation time. 4. DES 17 Since then others have repeated the analysis and the most recent in depth analysis conducted by Wiener [148, 149] has concluded that a ....

W. Diffie and M.E. Hellman. Exhaustive cryptanalysis of the NBS Data Encryption Standard. Computer, 10:74--84, 1977.

.... a PK cryptosystem must satisfy several design and functional criteria with perhaps none more critical than resistance to semi exhaustive n gram attack an attack whose feasibility for increasingly larger block sizes is each day made easier by an ever growing parallelism in computer architectures [5] coupled with seemingly limitless increases in storage density and declining cost per bit of mass storage. While any key is presumed possible for a private key system subjected to exhaustive key enumeration, only a fraction of all possible input values need be considered in an n gram attack ....

Diffie, W. and M. Hellman. 1977. Exhaustive Cryptanalysis of the NBS Data Encryption Standard. Computer 10, 6, 74--84.

....block cipher involving 64 bit data encryption with a 56 bit key, which was adopted by the U.S. National Institute of Standards and Technology in 1976. DES has been widely used in bank activities and Internet communications. The security of DES has been extensively investigated by many researchers [2, 15, 3, 4, 26, 6, 23, 9, 5, 20]. DES can be implemented in hardware as well as software. In this paper, we will consider DES as a nonlinear feedback shift register (NLFSR) with input. From this point of view, we will apply the tools for pseudo random sequence analysis to the S boxes in DES, i.e. the feedback function when DES ....

W. Diffie and M.E. Hellman, Exhaustive cryptanalysis of the NBS data encryption standard, Computer, Vol. 10, No. 6, pp. 74-84, June 1977.

....via software, as general purpose computers are orders of magnitude slower at this task than specialized hardware. The earliest estimate came not long after DES was ratified as a national standard. Whit Diffie and Martin Hellman designed a system containing a large number of custom designed chips [11]. They estimated that their 20 million architecture could recover a DES key each day. After their paper appeared, great controversy ensued. Some argued that the mean time between failures would be inherently so small that the machine could never work; Diffie and Hellman refuted these objections, ....

Whitfield Diffie and Martin E. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, 10(6):74--84, June 1977.

....security. 1 The results of this paper were presented in part at the 1990 IEEE Symposium on Information Theory, Jan. 14 19, 1990, San Diego, CA. 1. Introduction An important general question in cryptography, which has, for instance, been addressed (but not answered) by Diffie and Hellman ([2], p. 83) and Merkle and Hellman [5] is whether multiple encryption with a certain cipher increases its cryptographic security. In this paper, we consider the more general question of the security of cascade ciphers where the component ciphers can be distinct. Can, for example, DES be weakened by ....

W. Diffie and M.E. Hellman, Exhaustive Cryptanalysis of the NBS Data Encryption Standard, IEEE Computer Magazine, Vol. 10, No. 6, June 1977, pp. 74-84.

....cost and speed of the proposed universal key search machine running a DES Cracker chip. 2 Previous Work Already one year after the Data Encryption Standard was released in 1976, Whitfield Diffie and Martin Hellman published a paper which describes in detail a key search machine for DES [2]. They estimated that for 20 million a keysearch machine could be built which recoveres a DES key within 12 hours. Two papers with quite different results appeared in 1993 [6] and [13] Both papers describe a custom chip design and develop from there a key search machine. Reference [13] ....

W. Diffie and M.E. Hellman. Exhaustive cryptanalysis of the NBS Data Encryption Standard. Computer, 10:74--84, June 1977.

....chaining; it prevents repeated text in the message from yielding correspondingly repeated sections of ciphertext. Other such modes of operation for the use of DES, as well as proposed techniques for key management, have been published by the National Bureau of Standards. Diffie and Hellman [50] argue that the choice of a 56 bit key makes DES vulnerable to a brute force attack. For 20 million one might be able to build a machine consisting of 2 20 chips, each of which can test 2 20 keys second, so that in 2 16 seconds (18:2 hours) the entire key space can be searched for the key ....

W. Diffie and M. E. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, 10:74--84, June 1977.

....relatively short key size. Its cryptographic strength notwithstanding, 56 bits seemed vulnerable to exhaustive search. Diffie and Hellman quickly concluded that a highly parallel custom designed machine could indeed mount a successful brute force attack on DES with a price tag of about 20 million [2], though that estimate was disputed by some. Others have since refined the details of the design and found a more accurate cost estimate [3, 4, 5] in one of the most recent papers, Wiener describes how to build a 1 million machine that can break DES in 3.5 hours with one or two known plaintexts ....

....plaintext or lengthy calculations. This leaves single character, digraph, and trigraph frequency statistics as a natural starting point. Diffie and Hellman proposed a very simple decision strategy: if the high bit of all 8 bytes in the plaintext block is zero, save the key; otherwise, discard it [2]. This strategy has the advantage of being simple and quick. Unfortunately, this test only works for 7 bit text; we would like to handle other types of data, if possible. Furthermore, frequency statistics are a generalization of this strategy, and it seems reasonable to hope they will achieve more ....

Whitfield Diffie and Martin E. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, 10(6):74--84, June 1977.

....surrounding its short 56 bit keys. One of the first criticisms came from Diffie and Hellman who argued that it was feasible to build a machine that could attack DES by exhaustively searching through all 2 56 DES keys, and that the cost of building this machine would decrease rapidly with time [6]. Since then, several attempts have been made to assess the cost and time required for exhaustive key search [7, 8, 10, 15] In recent years, analytic techniques have been found to attack DES. Biham and Shamir s differential cryptanalysis can be used to find a DES key given 2 47 chosen ....

W. Diffie and M. Hellman, "Exhaustive Cryptanalysis of the NBS Data Encryption Standard", Computer, vol. 10, no. 6, June 1977, pp. 74-84.

....We conclude by outlining some likely changes to the underlying protocols that may strengthen them against these attacks. 1. Introduction DES, the Data Encryption Standard [25] is a strong cipher; however, its key length is too short to provide much security against a well financed attacker [14]. More recently, designs have been published for machines that can exhaustively search the key space in a short time for a comparatively modest investment [34] Most such designs assume blocks of known plaintext, though at least one [33] relies on statistical properties of the underlying text. ....

W. Diffie and M. E. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, 10(6):74--84, June 1977.

....strengthen DES which uses the methods described above. This modified DES can be used with existing DES hardware and is much stronger than the standard DES. 1 Introduction Since the Data Encryption Standard was introduced [17] its 56 bit key size was subject to criticism of the research community [10, 9]. It was considered to be too short to withstand exhaustive search attack on a special purpose computer. Recent results [20] show that with todays technology such computer will cost about a million US and will be able to find a key in 3.5 hours in average. In parallel, many researches invested a ....

.... Applied Mathematics Department, Technion Israel Institute of Technology, Haifa 32000, Israel. Several suggestions were made in the last two decades in order to strengthen DES: increase of the number of rounds from 16 to 32, 64 or even more [10] multiple encryption or larger key size[9], independent subkeys (768 bits) 1] dramatic increase of the key scheduling complexity [13, 19] and others. Not considering security features of these solutions we note that most of them either require the design of new hardware or decrease encryption speed considerably. The standard of DES[17] ....

Whitfield Diffie, Martin Hellman, Exhaustive Cryptanalysis of the NBS Data Encryption Standard, IEEE Computer, Vol. 10, No. 6, pp. 74 -- 84, June 1977.

....find k4. The complexity to find k3 is 2 57 . k1 and k2 can then be found with complexity 2 56 each. Thus, the total complexity is about 2 88 . Only 2 35 2 36 chosen plaintexts are required. This complexity is much less than the expected 2 112 complexity of a meet in the middle attack[3], which was claimed for this cryptosystem. 4 A Known Plaintext Attack The complexity and number of required plaintexts of this known plaintext attack are about the same as of the chosen plaintext attack (2 90 complexity, 2 36 known plaintexts) The amount of required memory is however much ....

W. Diffie, M. E. Hellman, Exhaustive Cryptanalysis of the NBS Data Encryption Standard, Computer, Vol. 10, No. 6, pp. 74--84, June 1977.

....then the corresponding key K is likely to be the real key. If T = T 2 then K is likely to be the real key. Otherwise neither K nor K can be the real key. Since testing whether T = T 2 is much faster than an encryption, the computational saving is very close to 50 . Diffie and Hellman[6] suggested exhaustive search of the entire key space on a parallel machine. They estimate that a VLSI chip may be built which can search one key every microsecond. By building a search machine with a million such chips, all searching in parallel, 10 12 keys can be searched per second. The entire ....

....2 57 pairs is more time consuming than exhaustive search for the 2 56 possible keys. 6.4 Summary of the cryptanalysis A summary of the cryptanalytic results appears in table 12. The description # of#pairs#pairs#bitsCharacte S=N Comments rndsneeded used foundristics 4 2 3 2 3 42 1 1 16 [6] 6 2 7 2 7 30 3 1 16 2 16 8 2 15 2 13 30 5 1 10486 15:6[24] 8 2 17 2 13 30 5 1 10486 1:2 [18] 8 2 20 2 19 30 5 1 55000 1:5 [24] The iterative characteristic. 9 2 25 2 24 30 6 1 1000000 1:0 [30] Extension to six rounds. 9 2 26 8 48 7 2 Gamma24 2 29 10 2 ....

W. Diffie, M. E. Hellman, Exhaustive Cryptanalysis of the NBS Data Encryption Standard, Computer, Vol. 10, No. 6, pp. 74--84, June 1977.

....substantially less in large ones. 3 Exhaustive Attack on DES When DES was introduced in 1977, some computer scientists protested that 56 bits were not sufficient because it would be possible to do an exhaustive search of the key space in a short amount of time using a massively parallel computer. [DH77] In their book, Meyer and Matyas [MM82] discount that possiblity and predict that it would just not be physically possible to build the machine until the 1990 s because there were too many physical limitations. Heat and power usage are two major barriers. How easy would it be to build one today ....

Whitfield Diffie and Martin Hellman. Exhaustive cryptanalysis of the nbs data encryption standard. Computer, 10(6):74--84, 1977.

....was certified this way; seventeen man years at IBM were spent fruitlessly trying to break that scheme. Once a method has successfully resisted such a concerted attack it may for practical purposes be considered secure. Actually there is some controversy concerning the security of the NBS method [2]. We show in the next sections that all the obvious approaches for breaking our system are at least as difficult as factoring n. While factoring large numbers is not provably difficult, it is a well known problem that has been worked on for the last three hundred years by many famous ....

Diffie, W., and Hellman, M. Exhaustive cryptanalysis of the NBS data encryption standard. Computer 10 (June 1977), 74-84.

....and m bounds the number of hx; FXK (x)i pairs the adversary can obtain. Keywords: DESX, DES, Key Search, Cryptanalysis, Export Controls 1 Introduction The susceptibility of DES to exhaustive key search has been a concern and a complaint since the cipher was first made public; see, for example, [6]. Careful analysis by Wiener [16] indicates that by 1994 the problem had escalated to the point where for 1 million one could build a DES key search engine that, given a hplaintext, ciphertexti pair, would recover the key in about 3.5 hours on average. There have been many approaches suggested ....

W. Diffie and M. Hellman, "Exhaustive cryptanalysis of the NBS Data Encryption Standard. " Computer, vol. 10, no. 6, 74--84 (June 1977).

....plaintexts. However, the main threat for the security of DES is exhaustive search for the keys on 1 Computer Science Department, Technion Israel Institute of Technology, Haifa 32000, Israel. Email: biham cs.technion.ac.il, WWW: http: www.cs.technion.ac.il biham . special purpose machines[10,27], which can try keys so fast so that all the 2 56 possible keys can be searched within only a few hours. In order to increase the strength of ciphers, multiple encryption was suggested, of which triple encryption became the most popular variant, after double encryption was shown to be ....

.... in all its components (C = EK 3 (EK 2 (EK 1 (P ) A triple encryption variant which uses two keys[26] where K 3 = K 1 ) was believed to be roughly as secure as three key triple encryption, but was shown to be theoretically (but not practically) no more secure than a single encryption[10,23]. Another (seemingly more secure) two key triple DES variant was suggested in [9] Nowadays, triple encryption and its two key variant are candidates for an ANSI standard[1] The most successful attacks on multiple encryption are meet in the middle attacks. Multiple encryption with an even number ....

W. Diffie, M. E. Hellman, Exhaustive Cryptanalysis of the NBS Data Encryption Standard, Computer, Vol. 10, No. 6, pp. 74--84, June 1977.

....been chosen at random, although the permutation structure of the S boxes makes the results somewhat less surprising. 1 Introduction Ever since its introduction [1] the DES has been the subject of debate concerning its security level. The debate can be divided into arguments concerning key size [2, 3] and arguments concerning internal weaknesses in the algorithm itself [4] This paper is concerned with the latter area. While our approaches may open new possibilities for attack on DES, on the positive side, none of our current attacks is applicable to the full DES. Neither do our attacks break ....

W. Diffie and M.E. Hellman. "Exhaustive Cryptanalysis of the NBS Data Encryption Standard". Computer Magazine, 10(6):74--84, June 1977.

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W. Diffie and M. Hellman, \Exhaustive cryptanalysis of the NBS Data Encryption Standard. " Computer, vol. 10, no. 6, 74-84 (June 1977).

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Diffie, W. and M. Hellman, "Exhaustive Cryptanalysis of the NBS Data Encryption Standard", Computer, vol. 10, no. 6, pp. 74-84, June 1977.

No context found.

W. Diffie and M. Hellman, "Exhaustive cryptanalysis of the NBS Data Encryption Standard", Computer vol.10 no.6 (June 1977) pp. 74-84.

No context found.

W. Diffie and M. Hellman, "Exhaustive cryptanalysis of the NBS Data Encryption Standard", Computer vol.10 no.6 (June 1977) pp. 74-84.

No context found.

W. Diffie and M. E. Hellman. Exhaustive Cryptanalysis of the NBS Data Encryption Standard. Computer, 10(6):74--84, June 1977.

No context found.

W. Diffie and M.E. Hellman, Exhaustive cryptanalysis of the NBS Data Encryption Standard, Computer 10 (1977), 74-84.

No context found.

W. Di#e and M. Hellman, "Exhaustive cryptanalysis of the NBS data encryption standard," Computer , vol. 10, no. 6, pp. 74--84, 1997.

No context found.

W. Diffie and M.E. Hellman, Exhaustive cryptanalysis of the NBS Data Encryption Standard, Computer 10 (1977), 74-84.

No context found.

W. Diffie and M.E. Hellman. Exhaustive cryptanalysis of the NBS Data Encryption Standard. Computer, 10:74--84, 1977.

No context found.

W. Diffie and M. E. Hellman. Exhaustive cryptanalysis of the NBS data encryption standard. Computer, 10(6):74-84, June 1977.

No context found.

W. Diffie and M.E. Hellman. Exhaustive cryptanalysis of the NBS Data Encryption Standard. Computer, 10:74--84, 1977.

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