The Data by D. Coppersmith Encryption Standard (DES) and its strength against attacks The Data Encryption Standard (DES) was During the early 1970s, it became apparent that the developed by an IBM team around 1974 and commercial sector also has a legitimate need for adopted as a national standard In 1977. Since cryptography. Corporate secrets must be transmitted that time, many cryptanalysts have attempted between distant sites, without the possibility of to find shortcuts for breaking the system. In eavesdropping by industrial spies. Personal data on this paper, we examine one such attempt, the databases need to be protected against espionage and method of differential cryptanalysis, published alteration. by Biham and Shamir. We show some of the A familiar example is the communication between an safeguards against differential cryptanaiysis automatic teller machine (ATM) and a central computer. that were built into the system from the The user inserts a magnetic card and types a few numbers. beginning, with the result that more than 1015 The ATM sends messages to the computer. The computer bytes of chosen plalntext are required for this checks the account balance and returns a message attack to succeed. authorizing the ATM to dispense funds. Obviously, if these messages are unprotected, a thief can tap the wires, find the message authorizing the dispensing of funds, and send Introduction multiple copies of that message to the ATM, thereby Cryptography has long been in use by governments, “cleaning out” the supply of cash from the ATM. diplomatic particularly in the realms of military and In the early 1970s, a banking customer asked IBM to military communication. It is hard to imagine develop a system for encrypting ATM data. With this or communication without cryptography; ciyptanalysis, problem as a starting point, a team was formed from secretly deciphering the opponent’s messages, is perhaps Disclaimer of even greater value. Much has been written about The present author participated in the design and test of DES, particularly in th.e and strengthening them against differential c,yptanalynis. [1] for design of the S-boxes in cryptography in the military; see reference Naturally, this author has nrrong opinions about DES and Its history. Any opinions example. in this pnper are those of the author and are not necessarily shared by IBM. use is permitted withoat payment of royalty provided that (I) cacti eCopy,4bt 1994 by International Business Machines Corporation. Copying in printed form for private inctuded on the first page. The title and abstract, but no other portions, of reproduction is done without alteration and (2) the Journal referertcc and IBM copyright notice are and other information-scrvice systems. Permission to republish any other this paper may be copied or distributed royalty free withoat further permission by computer-based portion of this paper must be obtaincd from the Editor. 243 0. cOPPERSMITH IBM 3. RES, l)EVELOP, VOL. 38 NO. 3 MAY 1994 people at two IBM Sites (Kingston and Yorktown Heights, m17 are then created in sixteen rounds, according New York). Developers included Roy Adler, Don to the procedure described below. Finally, the 64-bit Coppersmith, Horst Feistel, Edna Grossman, Alan ciphertext c is generated by applying the inverse Konheim, Carl Meyer, Bill Notz, Lynn Smith, Walt permutation 1P1 to the two message halves , m17 fl16 Tuchman, and Bryant Tuckerman. This team, along with (Notice the inversion: , m17 m16 rather than the natural several consultants, developed cryptographic a algorithm. order. This is to allow decryption and encryption to use This algorithm was then submitted to the National Bureau the same hardware.) of Standards (NBS, which later became the National The plaintext message halves and intermediate message Institute of Standards and Technology, or NIST) and halves , , m6 m, , m2 n7 are related as follows: was adopted in 1977 as a national standard: the Data m11 = m,1 1, = , Encryption Standard, or DES. The National Security flk, m) i 1, 2, 16. Agency (NSA) also provided technical advice to IBM. Here k is the secret 56-bit key, and i is the number of the The entire algorithm was published in the Federal round (from 1 through 16). Also, k(s) is a selection of 48 Register [2], but the design considerations, which we bits from the 56 bits of k; this selection, or key schedule present here, were not published at that time. The design (described in [2]), depends on the round number, i. The took advantage of knowledge of certain cryptanalytic symbol denotes bit-by-bit “exclusive OR” (addition techniques, most prominently the technique of “differential modulo 2), which we call “XOR” in the text. cryptanalysis,” which were not known in the published Now we describe the function There are eight literature. After discussions with NSA, it was decided that f. S-boxes, S1, ... , , S8 described in the standard. Each disclosure of the design considerations would reveal the S-box is a table lookup, using six bits as input and technique of differential cryptanalysis, a powerful providing four bits as output. For each S-box, say S, technique that can be used against many ciphers. This in six consecutive bits are selected from the 48 bits of k(1) turn would weaken the competitive advantage the United namely bits 6j — 5, 6j — 4, , 6j. Also, six States enjoyed over other countries in the field of cryptography. consecutive bits are selected from m, namely bits 4j — 4, 4j — 3, •. , 4j + 1 (mod 32). The “mod 32” Many people speculated, however, that the lack of is shorthand for the convention that = disclosure was due to some “trap door” or hidden for j 1 the bits are 32, 1, 3, = weakness in the DES. One of the purposes of the present 2, 4, 5, and forj 8 the bits are 28, 29, 30, 31, 32, 1. Two adjacent S-boxes paper is to dispel this notion and to indicate that, in fact, share two message bits; for instance, S1 uses the reason for not publishing the criteria lay in the hidden message bits 32, 1, 2, 3, 4, 5, while S. strengths of the algorithm, not hidden weaknesses. uses message bits 4, 5, 6, 7, 8, 9, and they share bits 4 and 5. (Key bits are not shared among S-boxes on one round.) Contents of this paper and are considered to be “adjacent” because they We begin by describing DES, giving enough detail to share message bits 32 and 1. understand what follows. We then describe the attack The six key bits and the six message bits are XORed based on differential cryptanalysis. We continue with a together bitwise, and the resulting six bits are used as disclosure of the design criteria of the S-boxes and input for a table lookup. That is, the six inputs to S-box permutation, and a discussion of the role of these criteria at round i are in defeating differential cryptanalysis. m[4j — 4] k(,)[6j — 5], Description m[4j — 3] k111[6j — of DES 4], We give here a brief description of DES, primarily to establish terminology. We do not provide the various tables that are necessary for a full description of the m[4j + 1] k()[6jj, standard; for those, see [2] or [3]. or, written another way, We wish to encipher a 64-bit plaintext message block m under the 56-bit key k, to produce a 64-bit ciphertext m[4j—4,4j—3,4j—2,4j— I,4j,4j+ 1] message block c E6(m). = (The sizes of message blocks k(1)[6j—5,6j—4,6j--3,6j—2,6j—I,6j]. and keys, 64 bits and 56 bits respectively, are specified in the standard.) Decipherment, or recovering plaintext from Each of the eight S-boxes implements a different table, ciphertext, is denoted D6(c). 26 m = each with entries of four bits each. These tables are The plaintext message block m is subjected to an initial described in the standard. permutation IP, and the result is broken into two 32-bit The eight S-boxes together put out 8 x 4 = 32 bits. 244 message halves, m0 and 1. Intermediate m message halves These bits are permuted according to a permutation P that D. COPPERSMITH IEM I. RES. DEVELOP. VOL. 38 NO. 3 MAY 1994 is fixed for all rounds i. The resulting 32-bit quantity is the That is, value of f(k(), rn). trn = m t rn’. In suminafy, the 64-bit message undergoes a permutation IP to produce two 32-bit message halves rn0 He considers the difference between the intermediate and . Then we compute rn1 32-bit 1, the quantityf(k( m1), message halves: and XOR that quantity with rn0 to produce m,. We use this rn=rn. rn’. new quantity to 2), rn, compute f(k( m,), and XOR that quantity with rn1 to produce . We continue m3 in a like The input to S-box , for S1 example, at round i of the fashion until m16 and m7 have been computed. These two encipherment of message rn is message halves are interchanged and then subjected to the ‘, 1[32, rn 1,2,3,4,5] k(1)[1,2,3,4,5,6j, permutation IP to produce the ciphertext c. f Decryption is easily accomplished by a user in and the input to S1 at round i of the encipherment of possession of the same key k. First, one applies the message rn is permutation I? to c to produce the message halves rn[32,1,2,3,4,5j k1>[1,2,3,4,5,61. Next, , rn16 one computes rn17 f(k(16), rn16) and XORs that quantity with m17 to recover rn1,.