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Construction symmetric ciphers using the cast design procedure5825886
Abstract
A new design procedure for constructing a family of DES-like Substitution-Permutation Network (SPN) cryptosystems with desirable cryptographic properties including provable resistance to differential cryptanalysis, linear cryptanalysis, and related-key cryptanalysis is described. New cryptosystems called CAST ciphers, constructed according to the procedure, are also described. Details of the design choices in the procedure are given, including those regarding the component substitution boxes (s-boxes), the overall framework, the key schedule, and the round function. A fully specified example CAST cipher, an output of this design procedure, is presented as an aid to understanding the concepts and to encourage detailed analysis by the cryptologic community.
Claims
What is claimed is:
1. In a data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of a predetermined bitlength comprising a plurality of consecutive transformation rounds of half of each data block, each consecutive transformation round comprising steps of:
combining the half data block with a first masking key of predetermined length using a first binary operation to generate a first modified half data block;
combining the first modified half data block with a second masking key of predetermined length using a second and different binary operation to generate a second modified half data block;
processing the second modified half data block by a plurality of (m.times.n) mutually different substitution boxes to generate a third modified half data block, m and n being positive integers; and
XORing the third modified half data block with the remaining half of the data block to generate a transformed half data block of a transformation round.
2. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 1, wherein the first binary operation is addition modulo 2.sup.n, or subtraction modulo 2.sup.n, or bitwise XOR, and the second binary operation is multiplication modulo (2.sup.n -1), or multiplication modulo (2.sup.n +1).
3. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 1, wherein the first binary operation is addition modulo 2.sup.n, or subtraction modulo 2.sup.n, or bitwise XOR, and the second binary operation is a circular shift by a number of bits specified by the second masking key.
4. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 1, wherein all first masking keys and all second masking keys for all the transformation rounds are generated before the first transformation round is performed.
5. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 4, wherein all first masking keys and all second masking keys for all the transformation rounds are generated by a plurality of partially bent-function-based (m.times.n) substitution boxes from the key bits, where the key bits comprise a key pattern of z bytes in the following order: k1, k2, k3, . . . , k(z-1), kz, z being a positive integer.
6. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 5, wherein each data block contains 64 bits, the substitution boxes are eight partially bent-function-based 8.times.32 s-boxes, S1, S2, S3, . . . , S8, and the key bits comprise a key pattern of 10 bytes in the following order: k1, k2, k3, . . . , k9, k0.
7. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 6, wherein the transformation round function means has a first plurality of partially bent-function-based (m.times.n) s-boxes for processing key bits to generate a first masking key and a second masking key, and a second plurality of partially bent-function-based (m.times.n) s-boxes for processing the second modified data half.
8. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 7, wherein the first plurality of s-boxes comprises four partially bent-function-based 8.times.32 s-boxes and the second plurality of s-boxes comprises four partially bent-function-based 8.times.32 s-boxes.
9. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 5, wherein the transformation round function means has a first plurality of partially bent-function-based (m.times.n) s-boxes for processing key bits to generate a first masking key and a second masking key, and a second plurality of partially bent-function-based (m.times.n) s-boxes for processing the second modified data half.
10. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 1, wherein one or more consecutive transformation rounds include mutually different sets of first and second binary operations.
11. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 10, wherein particular binary operations for use in any particular round are chosen in dependence upon the value of certain predetermined bits of the first masking key or the second masking key, or upon the value of certain predetermined bits of the half data block being operated upon.
12. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 10, wherein particular binary operations for use in each transformation round are fully specified for all implementations of the method and is independent of any key bits or data bits.
13. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 12, wherein the binary operations addition modulo 2.sup.n, subtraction modulo 2.sup.n, and bitwise XOR can be used to combine the half data block with the first masking key and to combine the s-box outputs which result from the processing of the second modified half data block.
14. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 13, wherein three different transformation rounds are used:
Type 1: I=((Kmi+D)<<<Kri) O=((S1›Ia! S2›Ib!)-S3›Ic!)+S4›Id!
Type 2: I=((Kmi D)<<<Kri) O=((S1›Ia!-S2›Ib!)+S3›Ic!) S4›Id!
Type 3: I=((Kmi-D)<<<Kri) O=((S1›Ia!+S2›Ib!) S3›Ic!)-S4›Id!
where "D" is the original input to the transformation round, "Ia",-"Id", are the most significant byte through least significant byte of I, respectively, and "O", is the output of the transformation round and "+", and "-", are addition and subtraction modulo 2.sup.32, " ", is bitwise XOR, and "<<<", is the circular left-shift operation.
15. The data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of predetermined bitlength according to claim 14, wherein twelve transformation rounds are used in total and
rounds 1, 4, 7, and 10 use transformation round Type 1,
rounds 2, 5, 8, and 11 use transformation round Type 2, and
rounds 3, 6, 9, and 12 use transformation round Type 3.
Description
FIELD OF THE INVENTION
The invention resides generally in symmetric cryptosystems and their construction procedures. In particular, it is directed to new ciphers which belong in a family of DES-like substitution-permutation network cryptosystems and to methods of cryptographically transforming plaintext into ciphertext using such novel ciphers. The invention relates also to procedures for constructing such new ciphers.
BACKGROUND OF THE INVENTION
This invention relates to a design procedure for a family of symmetric encryption algorithms. The ciphers produced, known as CAST ciphers, are provably resistant to differential cryptanalysis, linear cryptanalysis, and related-key cryptanalysis. Furthermore, they can be shown to posses a number of desirable cryptographic properties such as avalanche, Strict Avalanche Criterion (SAC), Bit Independence Criterion (BIC), and an absence of weak and semi-weak keys. CAST ciphers are based on the well-understood and extensively-analyzed framework of the Feistel cipher--the framework used in DES--but with a number of improvements (compared to DES) in both the round function and the key schedule which guarantee good cryptographic properties in fewer rounds than DES. These ciphers therefore have very good encryption/decryption performance (comparing very favourably with many alternatives of similar cryptographic strength) and can be designed with parameters which make them particularly suitable for software implementations on 32-bit machines.
Some aspects of the CAST design procedure were discussed in "Designing S-Boxes for Ciphers Resistant to Differential Cryptanalysis", C. M. Adams and S. E. Tavares, Proceedings of the 3rd Symposium on the State and Progress of Research in Cryptography, Rome, Italy, Feb. 1993, pp. 181-190; "Simple and Effective Key Scheduling for Symmetric Ciphers", C. M. Adams, the Workshop Record of the Workshop on Selected Areas in Cryptography (SAC 94), May 5-6 1994, pp.129-133; and "Designing DES-Like Ciphers with Guaranteed Resistance to Differential and Linear Attacks", C. M. Adams, the Workshop Record of the Workshop on Selected Areas in Cryptography (SAC 95), May 18-19 1995, pp.133-144. U.S. Pat. No. 5,511,123 (Adams), issued Apr. 23, 1996 also describes CAST cipher in more detail.
The search for a general-purpose design procedure for symmetric encryption algorithms is motivated by a number of factors, including the following:
(1) Despite years of speculation and warning regarding the inevitable limit to the useful lifetime of the Data Encryption Standard (DES), this algorithm remains firmly entrenched in a number of environments, partly because there is no obvious candidate for a DES replacement with acceptable speed and security.
(2) New and powerful cryptanalytic attacks have forced re-designs of suggested candidates such as FEAL in "Differential Cryptanalysis of FEAL and N-Hash", by E. Biham and A. Shamir, in Advances in Cryptology: Proc. of Eurocrypt '91, Springer-Verlag, 1992, pp.1-16; LOKI in "Differential Cryptanalysis of Snefru, Khafre, REDOC-II, LOKI, and Lucifer", by E. Biham and A. Shamir, Advances in Cryptology: Proc. of CRYPTO '91, Springer-Verlag, 1992, pp.156-171; and IDEA in "A Proposal for a New Block Encryption Standard", by X. Lai and J. L. Massey, Advances in Cryptology: Proc. of EUROCRYPT 90, Springer-Verlag, 1991, pp.389-404. Thus, such attacks must be accounted for and avoided in the design procedure itself, so that algorithms produced by the procedure are known to be immune to these attacks.
(3) The continued disparity between "domestic-strength" cryptography and "exportable-strength" cryptography, along with the potential for multiple flavours of exportable-strength cryptography (perhaps depending on "commercial escrow" considerations), means that the paradigm of a single DES replacement algorithm almost certainly has to be abandoned in favour of a design procedure describing a family of algorithms where keysize is at least one parameter defining a specific instance of the family. Recent cipher proposals such as RC-2, RC-4, and RC-5 have recognized and addressed this requirement.
The CAST design procedure to which the present invention relates is based upon a framework which has been extensively analysed by the cryptologic community for several decades. The CAST framework is the "Substitution-Permutation Network" (SPN) concept used in Feistel structure.
FIG. 1 illustrates a general Feistel-structured SPN. Referring to the figure, basic operation is as follows. A message block of n bits is input and split into a left half L and a right half R. The right half and a subkey K.sub.i are input to a "round function", f.sub.1, the output of which is used to modify (through XOR addition) the left half. Swapping the left and right halves completes round one. This process continues for as many rounds as are defined for the cipher. After the final round (which does not contain a swap in order to simplify implementation of the decryption process), the left and right halves are concatenated to form the ciphertext.
The parameters which can be selected for the framework are the blocksizes (the number of bits in both the plaintext and ciphertext data blocks) and the number of rounds. For all cases "higher" typically means greater security but (particularly for the number of rounds) reduced encryption/decryption speed. In practice, it is common to choose the plaintext and ciphertext blocksizes to be equal so that the encryption process results in no data expansion (an important consideration in many applications).
The round function contains substitution boxes (s-boxes). An m.times.n s-box is an (m.times.n) lookup table which substitutes, or replaces, the input of m bits with the output of n bits in a nonlinear way so that any change to the input vector results in a random-looking change to the output vector which is returned. The substitution layer in an SPN cipher is of critical importance to security since it is the primary source of nonlinearity in the algorithm. The dimensions m and n of an m.times.n s-box can be of any size; however, the larger the dimension m, the (exponentially) larger the lookup table. For this reason m is typically chosen to be less than 10. The CAST design procedure makes use of substitution boxes which have fewer input bits than output bits (e.g., 8.times.32); this is the opposite of DES and many other ciphers which use s-boxes with more input bits than output bits (e.g., 6.times.4).
The design of a good key schedule is a crucial aspect of cipher design. Keying in the CAST design procedure is done in the manner typical for Feistel networks. That is, an input key (a "primary key") is used to create a number of subkeys according to a specified key scheduling algorithm; the subkey for a given round is input to the round function for use in modifying the input data for that round.
The critical difference between the key schedule proposed in the CAST design procedure and other schedules described in the open literature is the dependence upon substitution boxes for the creation of the subkeys. Other key schedules (the one in DES, for example) typically use a complex bit-selection algorithm to select bits of the primary key for the subkey for round I. Any weaknesses in this bit selection algorithm can lead to simple cryptanalysis of the cipher, regardless of the number of rounds. The schedule proposed in CAST uses a very simple bit-selection algorithm and a set of "key schedule s-boxes" to create the subkey for each round. These s-boxes must possess specific properties to ensure cryptographically good key schedules. This aspect is described in detail in the above-mentioned U.S. Patent.
The round function in CAST, as stated above, makes use of s-boxes which have fewer input bits than output bits. This is accomplished as follows. Within the round function the input data half is modified by the subkey for that round and is split into several pieces. Each piece is input to a separate substitution box, the s-box outputs are combined, and the result is the output of the round function. Although each m.times.n s-box on its own necessarily causes data expansion (since m<n), using the set of s-boxes in this way results in no expansion of the message half, allowing the SPN to have input and output blocksizes which are equal.
The round function design must involve a specific measure to guard against differential and linear attacks. Differential and linear cryptanalysis appear to be fairly general-purpose attacks which may be applied to a variety of substitution-permutation network (DES-like) ciphers. Both methods work on the principle of finding high-probability attacks on a single round and then building up "characteristics" (sets of consecutive rounds which interact in useful ways). Characteristics which include a sufficient number of rounds can lead to cryptanalysis of the cipher. The probability of a characteristic is equal to the product of the probabilities of the included rounds. This "characteristic probability" determines the work factor of the attack. If the work factor of the attack is less than the work factor for exhaustive search of the key space, the cipher is theoretically broken.
From the above description it can be seen that adding rounds to a DES-like cipher can always be done to increase the work factor of a differential or linear attack, until the work factor surpasses that of exhaustive key search. This makes the cipher computationally resistant to these attacks. The disadvantage of this approach is that the encryption/decryption speed of the cipher is reduced, perhaps drastically, since each added round slows the cipher down by a factor of 1/N, where N is the number of rounds in the original cipher.
An alternate approach which has been pursued by a number of researchers is to decrease the attack probability of an individual round by improving the properties of the round s-boxes. This results in a lower characteristic probability for the same number of rounds and therefore has the potential to make the cipher resistant to these attacks without degrading throughput. However, there is always the possibility that for a given cipher the round probability cannot be made low enough to avoid the need to add rounds. Furthermore, there is always the possibility that for a given cipher the best characteristic has not yet been found (and when it is found, it will render the cipher breakable).
The design procedure of the invention uses neither of the above approaches. Instead, the invention applies a slight alteration to the typical DES-like round function which renders it "intrinsically immune" (as opposed to computationally immune) to differential and linear cryptanalysis. Such an alteration is generally applicable to all DES-like ciphers and may, in some ciphers, be added with little degradation in encryption/decryption speed.
OBJECTS OF THE INVENTION
It is therefore an object of the invention to provide a novel construction procedure for symmetric ciphers.
It is another object of the invention to provide novel symmetric ciphers which have one or more desirable properties such as resistance to differential cryptanalysis, linear cryptanalysis, and related-key cryptanalysis.
It is a further object of the invention to provide a method of cryptographically transforming plaintext into ciphertext using novel round functions.
SUMMARY OF THE INVENTION
Briefly stated, according to one aspect, the invention relates to a data encryption method of cryptographically transforming plaintext into ciphertext in data blocks of a predetermined bitlength comprising a plurality of consecutive transformation rounds of half of each data block. Each consecutive transformation round comprises steps of combining the half data block with a first masking key of predetermined length using a first binary operation to generate a first modified half data block and combining the first modified half data block with a second masking key of predetermined length using a second (different) binary operation to generate a second modified half data block. The method further includes steps of processing the second modified half data block by a plurality of (m.times.n) mutually different substitution boxes to generate a third modified half data block and XORing the third modified half data block with the remaining half of the data block to generate a transformed half data block of a transformation round.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a known SPN (Substitution-Permutation Network) cipher; and
FIG. 2 shows a round function according to one embodiment of the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION
As was stated previously, the primary parameter options in framework design are blocksize(s) and number of rounds. It is preferable in many applications if the plaintext and ciphertext blocksizes are equal (therefore hereafter referred to the blocksize of a cipher), but aside from the constraint that the blocksize be large enough to prevent an exhaustive compilation of plaintext/ciphertext pairs for a single key, the only real blocksize consideration is ease of implementation. On current machines, 64 bits (the blocksize of DES) is an attractive choice because left and right data halves and other variables fit nicely into 32-bit registers. However, in the future another choice may be attractive for other reasons.
The number of rounds in the framework appears to be a much more important and delicate decision. There need to be enough rounds to provide the desired level of security, but not so many that the cipher is unacceptably slow for its intended applications. In an SPN of the Feistel type it is clear that the left half of the input data is modified by the output of the round function in rounds 1, 3, 5, 7, and so on, and the right half is modified in rounds 2, 4, 6, 8, and so on. Thus, it is clear that for equal treatment of both halves the number of rounds must be even. However, it is less obvious how many rounds is "enough".
Differential and linear cryptanalysis, the two most powerful attacks currently known for DES-like ciphers, have helped to quantify this design parameter. It has long been known, for example, that DES with 5 or 6 rounds can be broken, but not until 1990, with the introduction of differential cryptanalysis, was it clear why 16 rounds were actually used in its design--fewer rounds could not withstand a differential attack. With subsequent improvements to the differential attack and with the introduction of linear cryptanalysis, it now appears that 18-20 rounds would be necessary for DES to be theoretically as strong as its keysize.
A prudent design guideline, therefore, is to select a number of rounds which has an acceptably high work factor for both differential and linear cryptanalysis and then either add a few more rounds or modify the round function to make these attacks even more difficult (in order to add a "safety margin"). The design procedure according to one embodiment chooses the second approach for both security and performance reasons.
FIG. 2 illustrates the round function according to one embodiment of the invention. This embodiment uses a 64-bit blocksize and 8.times.32 s-boxes. Referring to the figure, a 32-bit data half is input to the function along with a subkey K.sub.i. These two quantities are combined using operation "a" and the 32-bit result is split into four 8-bit pieces. Each piece is input to a different 8.times.32 s-box (S.sub.1, . . . , S.sub.4). S-boxes S.sub.1 and S.sub.2 are combined using operation "b"; the result is combined with S.sub.3 using operation "c"; this second result is combined with S.sub.4 using operation "d". The final 32-bit result is the output of the round function.
The round function according to one embodiment is to use XOR additions of 32-bit quantities for all operations (a, b, c, and d). Other, more complex, operations may be used for other embodiments as will be discussed later with respect to operation a.
S-boxes used in this embodiment are described in detail in the above-referenced U.S. Patent but a similar description will be given below for completeness. For the design of m.times.n (m<n) s-boxes, let n be an integer multiple of m; in particular, let n=rm where r>1 and r is chosen such that m<log.sub.2 C(n,n/2)=log.sub.2 ("n choose n/2"). Such s-boxes can be constructed as follows. Choose n distinct binary bent vectors .phi..sub.i of length 2.sup.m such that linear combinations of these vectors sum (modulo 2) to highly nonlinear vectors. Furthermore, choose half the .phi..sub.i to be of weight (2.sup.m-1 +2.sup.(m/2)-1) and the other half to be of weight (2.sup.m-1 -2.sup.(m/2)-1); these are the two weights possible for binary bent vectors of length 2.sup.m. Set the n vectors .phi..sub.i to be the columns of the matrix M representing the s-box. Check that M has 2.sup.m distinct rows and that the Hamming weight of each row and the Hamming distance between pairs of rows is close to n/2 (i.e., that the set of weights and the set of distances each have a mean of n/2 and some suitably small, but nonzero, variance). As well, if the i.sup.th row of M is denoted by r.sub.i, it should be verified that (r.sub.i .sym.r.sub.j).noteq.(i.sym.j) for any i,j.epsilon.{1, . . . , 2.sup.m }, i.noteq.j so that a non-zero input XOR is never equal to its resulting output XOR in the s-box (which may greatly facilitate finding a differential characteristic for the cipher). This latter condition will, in general, hold if the Hamming distance condition is met. If these conditions are not all satisfied, continue choosing suitable bent vectors (i.e., candidate .phi..sub.i) and checking the resulting matrix until the conditions are satisfied. Note that it is not difficult to construct 8.times.32 s-boxes which meet these conditions. The Appendix found at the end of the disclosure gives a few sets of example s-boxes.
The key schedule used in the embodiment has three main components: a relatively simple bit-selection algorithm mapping primary key bits to "partial key" bits; one or more "key transformation" steps; and a set of "key schedule s-boxes" which are used to create subkeys from partial keys in each round. An example key schedule for an 8-round algorithm employing a 64-bit key is as follows.
Let KEY=k.sub.1 k.sub.2 k.sub.3 k.sub.4 k.sub.5 k.sub.6 k.sub.7 k.sub.8, where k.sub.i is the i.sup.th byte of the primary key. The partial keys K'.sub.i are selected from the primary key according to the following bit-selection algorithm: K'.sub.1 =k.sub.1 k.sub.2, K'.sub.2 =k.sub.3 k.sub.4, K'.sub.3 =k.sub.5 k.sub.6, K'.sub.4 =k.sub.7 k.sub.8, K'.sub.5 =k.sub.4 'k.sub.3 ', K'.sub.6 =k.sub.2 'k.sub.1 ', K'.sub.7 =k.sub.8 'k.sub.7 ', K'.sub.8 =k.sub.6 'k.sub.5 ', where KEY is transformed to KEY'=k.sub.1 'k.sub.2 'k.sub.3 'k.sub.4 'k.sub.5 'k.sub.6 'k.sub.7 'k.sub.8 ' between round 4 and round 5. The key transformation step is defined by:
k.sub.1 'k.sub.2 'k.sub.3 'k.sub.4 '=k.sub.1 k.sub.2 k.sub.3 k.sub.4 .sym.S.sub.1 ›k.sub.5 !.sym.S.sub.2 ›k.sub.7 !;
k.sub.5 'k.sub.6 'k.sub.7 'k.sub.8 '=k.sub.5 k.sub.6 k.sub.7 k.sub.8 .sym.S.sub.1 ›k.sub.2 '!.sym.S.sub.2 ›k.sub.4 '!.
The bytes of KEY' are used to construct the final four partial keys, as shown above. The set of partial keys is used to construct the subkeys K.sub.i using key schedule s-boxes S.sub.1 and S.sub.2 :
K.sub.i =S.sub.1 (K'.sub.i,1).sym.S.sub.2 (K'.sub.i,2)
where K.sub.i,j denotes the j.sup.th byte of K.sub.i. Although a similar schedule can be constructed for a 12- or 16-round system or for different block or key sizes, for simplicity of notation and concreteness of explanation, the theorems below apply to the specific example given here.
As discussed previously, the number of rounds and the properties of the round function s-boxes can be chosen to guarantee computational immunity to differential and linear cryptanalysis. In a further embodiment, an extra work in the round function--specifically, some care in the choice of operation "a", is provided which can conceivably give intrinsic immunity to these attacks (in that these attacks can no longer be mounted).
The goal behind modifying the round function is to eliminate the possibility of both differential and linear cryptanalytic attacks against the cipher. This is done by inserting a nonlinear, key-dependent operation before the s-box lookup to effectively mask the inputs to the set of s-boxes. If these inputs are well "hidden", then s-box properties (such as the input XOR to output XOR mapping, or linearity) cannot be exploited in a general round function attack because the actual inputs to the s-boxes will not be known.
More specifically, according to one embodiment, the following modification to the round function f is provided:
f(R, K)=f(R, K.sub.1, K.sub.2)=S(a(R.sym.K.sub.1, K.sub.2))
where a(.cndot., .cndot.) is an operation with properties as defined below. For DES, the expansion operation can be placed either around R or (R.sym.K.sub.1)--that is, f(R, K)=S(a(E(R).sym.K.sub.1, K.sub.2)) or f(R, K)=S(a(E(R.sym.K.sub.1), K.sub.2))--depending on whether K.sub.1 is 32 or 48 bits in length. As well, the permutation operation can be placed around S(.cndot.) as is done in the current round definition.
Several properties are required of the function a(.cndot., .cndot.). These will be discussed below, but they are enumerated here for reference.
(1) The subset sum operation must not be distributive over a(.cndot., .cndot.)
(2) a(.cndot., .cndot.) must represent a nonlinear mapping from its input to its output, so that any linear change in either input leads to a nonlinear change in the output vector.
(3) a(.cndot., .cndot.) must be relatively simple to implement in software (in terms of code size and complexity).
(4) a(.cndot., .cndot.) must execute efficiently (no more slowly than the remainder of the round function, for example).
(5) a(.cndot., .cndot.) must effectively "hide" its R (or E(R)) input if K.sub.1 and K.sub.2 are unknown (in the sense that there must be no way to cancel the effect of the keys in the round function using an operation on a single R value or a pair of R values).
A function which appears to encompass all the properties listed above is modular multiplication, for an appropriate choice of modulus. If R, K.sub.1, and K.sub.2 are 32 bits in length, two candidate moduli are (2.sup.32 -1) and (2.sup.32 +1). A simple algorithm to carry out multiplication modulo (2.sup.32 -1) in a high-level language using only 32-bit registers has been reported and multiplication with this modulus is shown to be a "complete" operation (in that every input bit has the potential to modify every output bit), so that this modulus appears to satisfy nonlinearity, simplicity, and data hiding. However, this modulus does not satisfy the fifth property ideally, since zero always maps to zero, and (2.sup.32 -1) always maps to either (2.sup.32 -1) or zero (depending on the implementation), regardless of the key in use. (Note, however, that in a practical implementation it is a simple matter to ensure that the computed subkey K.sub.2 is never equal to 0 or to (2.sup.32 -1), and masking R with K.sub.1 ensures that it is not easy for the cryptanalyst to choose R such that (R.sym.K.sub.1) is equal to 0 or to (2.sup.32 -1).)
The modulus (2.sup.32 +1) may be a better choice with respect to property five than (2.sup.32 -1) if either of two simple manipulations are performed. Firstly, each input can be incremented by one, so that the computation is actually done with (R+1) and (K+1). Thus the arguments belong to the set ›1, 2.sup.32 ! rather than ›0, 2.sup.32 -1!, avoiding both the zero and the (2.sup.32 +1) "fixed point" inputs. Alternatively, the inputs can be left as is (so that the computation is done with R and K), with only the zero input mapped to the value 2.sup.32 (and the 2.sup.32 output mapped back to zero). Implementation of multiplication using this modulus is thus only slightly more difficult using a high-level language with 32-bit registers than for the modulus (2.sup.32 -1), and on platforms where the assembly language instructions give access to the full 64-bit result of a 32-bit multiply operation, the modular reduction can be accomplished quite simply and efficiently. Furthermore, as for (2.sup.32 -1), multiplication with this modulus represents a nonlinear mapping from input to output.
In order to ensure that the modular multiplication does not perform badly with respect to property five, it is necessary that the subkey K.sub.2 be relatively prime to the modulus. Thus, when the subkeys are being generated, the K.sub.2 used in each round must not have 3, 5, 17, 257, or 65537 as factors if the modulus n=(2.sup.32 -1), and must not have 641 or 6700417 as factors if n=(2.sup.32 +1).
Finally, it appears that either modulus can be used to satisfy property one, since the subset sum operation is not distributive over modular multiplication.
A CAST cipher implemented with a blocksize and keysize of 64 bits, four 8.times.32 s-boxes S.sub.1 . . . S.sub.4 in the round function, and 32-bit subkeys in each round, has been shown to have a work factor for differential and linear attacks which is greater than exhaustive search of the key space if 12 or more rounds are used. If operations a, b, c, and d are all XOR addition, the round function f may be computed simply as:
f(R, K)=S.sub.1 (B.sup.(1)).sym. . . . .sym.S.sub.4 (B.sup.(4))
where B=R.sym.K and B.sup.(j) is the j.sup.th byte of B. Application of the technique described in this section yields the modified computation of operation "a", where f remains identical but B is now computed as
B=((R.sym.K.sub.1)*K.sub.2) mod n.
Examination of the assembly language instructions required for the modular multiplication step alone (using either (2.sup.32 -1) or (2.sup.32 +1) as the modulus) shows that multiplication takes approximately the same amount of time as the remainder of the round on a Pentium-class PC, so that there is a performance impact of about a factor of two, compared with a version of CAST where operation "a" is simple XOR addition.
According to further embodiments of the invention, a number of options are available both for the round function operations and for the framework design which do not appear to compromise security and do not degrade encryption/decryption performance of the resulting cipher. In fact, for some choices it appears that security or performance may be enhanced, thus motivating the use of these alternatives in practice.
Thus far throughout the specification, the operations a, b, c, and d in the round function have been given as the eXclusive-OR of two binary quantities (i.e., addition modulo 2). It should be clear, however, that other binary operations may be used instead. Particularly attractive are addition and subtraction modulo 2.sup.32, since these operations take no more time than XOR and so will not degrade encryption/decryption performance in any way. Experimental evidence suggests that using such alternative operations may significantly increase security against linear cryptanalysis, but in any case appears to make both linear and differential characteristics more difficult to find.
As mentioned above, in one embodiment an extra computation (using extra key bits) is added to the operation "a" in the round function. The specific computation mentioned is multiplication with another 32-bit subkey using a modulus of either (2.sup.32 -1) or (2.sup.32 +1). However, it was noted that this addition can degrade performance by as much as a factor of two. An alternative is rotation (i.e., circular shifting) by a given number of bits. This operation is similar to the central operation of the cipher RC-5, except that this is a key-dependent rotate (controlled by a 5-bit subkey) rather than a data-dependent rotate, since data-dependent rotation may be less appropriate for a Feistel-type structure.
This extended "a" operation in a further embodiment with a 64-bit blocksize is then
a(R, K)=a(R, K.sub.1, K.sub.2)=((R.cndot.K.sub.1)<<<K.sub.2),
where ".cndot." is any binary operation (such as XOR or addition modulo 2.sup.32), "<<<" is the circular left shift operator, K.sub.1 is a 32-bit subkey, and K.sub.2 is a 5-bit subkey. The primary advantage of the rotation operation over modular multiplication is speed: on typical computing platforms an n-bit rotation (0.ltoreq.n.ltoreq.31) can be accomplished in a small number of clock cycles, thus causing minor performance degradation in the overall cipher. Rotation satisfies property (1) mentioned above because it prevents a linear attack for all cases except the extreme case where the input subset considered consists of the full set of input bits. It is highly unlikely that this extreme case applied in every round of an N-round cipher will describe a successful linear characteristic for the cipher.
The discussion thus far mentioned that the binary operation in a, b, c, and d must be the same in all four instances (e.g., XOR). However, different binary operations can be employed. For example, it is perfectly acceptable for b and d to use addition modulo 2.sup.32 while c uses XOR (this is precisely the combination used in the Blowfish cipher). Certainly many variations are possible, and while it is not clear that any one variation is significantly better than any other, it does appear to be the case that the use of different operations within a, b, c, and d can add to the security of the overall cipher (note that the IDEA cipher has long advanced the conviction that operations over different groups contribute to cipher security).
Another design option is to vary the definition of the round function itself from round to round. Thus, in an N-round cipher there may be as many as N distinct rounds, or there may be a smaller number of distinct rounds with each type of round being used a certain number of times. The variations in the round definitions may be due to the kinds of options mentioned in the previous subsection or may be more complex in nature.
Whether the idea of a number of distinct rounds in a cipher adds in any significant way to its cryptographic security is an open question. However, it certainly appears to complicate the analysis of the cipher, which is sometimes effective in complicating the cryptanalysis of the cipher.
In order to facilitate detailed analysis of the CAST design procedure, and as an aid to understanding the procedure itself, an example CAST cipher is provided in this section with some examples given in the Appendix. This 12-round cipher has a blocksize of 64 bits and a keysize of 80 bits; it uses the rotation operation to provide intrinsic immunity to linear and differential attacks; it uses a mixture of XOR, addition and subtraction (modulo 2.sup.32 ) for the operations a, b, c, and d in the round function; and it uses three variations of the round function itself throughout the cipher. Finally, the 8.times.32 s-boxes used in the round function each have a minimum nonlinearity of 74 and a maximum entry of 2 in the difference distribution table.
This example cipher appears to have cryptographic strength in accordance with its keysize (80 bits) and has very good encryption/decryption performance: over 1 MByte/sec on a 486-DX2 66 MHz PC, and over 2.5 MBytes/sec on a 90 MHz Pentium.
Pairs of Round Keys
This instance of a CAST cipher uses a pair of subkeys per round; a 32-bit quantity K.sub.m is used as a "masking" key and a 5-bit quantity K.sub.r is used as a "rotation" key.
Non-Identical Rounds
Three different round functions are used in this example CAST cipher. The rounds are as follows (where "D" is the original input to the f function and "I.sub.a "-"I.sub.d " are the most significant byte through least significant byte of I, respectively). Note that "+" and "-" are addition and subtraction modulo 2.sup.32, " " is bitwise XOR, and "<<<" is the circular left-shift operation.
Type 1: I=((K.sub.mi +D)<<<K.sub.ri) f=((S1›I.sub.a ! S2›I.sub.b !)-S3›I.sub.c !)+S4›I.sub.d !
Type 2: I=((K.sub.mi D)<<<K.sub.ri) f=((S1›I.sub.a !-S2›I.sub.b !)+S3›I.sub.c !) S4›I.sub.d !
Type 3: I=((K.sub.mi -D)<<<K.sub.ri) f=((S1›I.sub.a !+S2›I.sub.b !) S3›I.sub.c !)-S4›I.sub.d !
Rounds 1, 4, 7, and 10 use f function Type 1.
Rounds 2, 5, 8, and 11 use f function Type 2.
Rounds 3, 6, 9, and 12 use f function Type 3.
Key Schedule
Let the primary 80-bit key be A=a1a2a3a4a5a6a7a8a9a0, where each a.sub.i is a byte.
Let K.sub.m1, . . . , K.sub.m12 be twelve 32-bit masking subkeys (one per round).
Let K.sub.r1, ,K.sub.r12 be twelve 32-bit rotate subkeys (one per round); only the least significant 5 bits are used in each round. See the Appendix for a detailed description of how to generate K.sub.mi and K.sub.ri from A.
Substitution Boxes
This example CAST cipher uses eight substitution boxes: s-boxes S1, S2, S3, and S4 are round function s-boxes; S5, S6, S7, and S8 are key schedule s-boxes. See Appendix for the s-box contents. The CAST design procedure can be used to produce a family of encryption algorithms which are provably resistant to differential cryptanalysis, linear cryptanalysis, and related-key cryptanalysis. CAST ciphers also possess a number of other desirable cryptographic properties and have good encryption/decryption speed on common computing platforms. Analysis of the procedure described in this paper by members of the cryptologic community is strongly encouraged so as to increase confidence in the various aspects of the design presented.
APPENDIX
__________________________________________________________________________
This appendix provides full details of the example CAST cipher given
above.
Key Schedule
Let the primary 80-bit key be A = a1a2a3a4a5a6a7a8a9a0, where each
a.sub.i is a byte.
Let K.sub.m1, . . . , K.sub.m12 be twelve 32-bit masking subkeys (one per
round).
Let K.sub.r1, , K.sub.r12 be twelve 32-bit rotate subkeys (one per
round); only the least
significant 5 bits are used in each round.
Let b1 . . . b8, through g1 . . . g8 and bw, bx, by, bz through gw, gx,
gy, gz be intermediate (temporary) bytes.
Let Si›! represent s-box i and let " " represent XOR addition.
The subkeys are formed from the primary key as follows.
Masking Subkeys
b1b2b3b4 = a1a2a3a4 S5›a6! S6›a8! S7›a5! S8›a7! S7›a9!
b5b6b7h8 = a5a6a7a8 S5›b1! S6›b3! S7›b2! S8›b4! S8›a0!
bwbxbybz = b5b6b7b8 S5›a9! S6›a0! S7›a9! S8›a0!
Km1 = S5›b1! S6›b2! S7›b8! S8›b7! S5›bw!
Km2 = S5›b3! S6›b4! S7›b6! S8›b5! S6›bx!
Km3 = S5›b5! S6›b6! S7›b4! S8›b3! S7›by!
Km4 = S5›b7! S6›b8! S7›b2! S8›b1! S8›bz!
c1c2c3c4 = b1b2b3b4 S5›b5! S6›b7! S7›b6! S8›b8! S7›bw!
c5c6c7c8 = b5b6b7b8 S5›c2! S6›c4! S7›c1! S8›c3! S8›bx!
cwcxcycz = c5c6c7c8 S5›bw! S6›bx! S7›by! S8›bz!
Km5 = S5›c4! S6›c3! S7›c5! S8›c6! S5›cw!
Km6 = S5›c2! S6›c1! S7›c7! S8›c8! S6›cx!
Km7 = S5›c8! S6›c7! S7›c1! S8›c2! S7›cy!
Km8 = S5›c6! S6›c5! S7›c3! S8›c4! S8›cz!
d1d2d3d4 = c1c2c3c4 S5›c5! S6›c7! S7›c6! S8›c8! S7›cw!
d5d6d7d8 = c5c6c7c8 S5›d2! S6›d4! S7›d1! S8›d3! S8›cx!
dwdxdydz = d5d6d7d8 S5›cw! S6›cx! S7›cy! S8›cz!
Km9 = S5›d4! S6›d3! S7›d5! S8›d6! S5›dw!
Km10 = S5›d2! S6›d1! S7›d7! S8›d8! S6›dx!
Km11 = S5›d8! S6›d7! S7›d1! S8›d2! S7›dy!
Km12 = S5›d6! S6›d5! S7›d3! S8›d4! S8›dz!
Rotate Subkeys
e1e2e3e4 = d1d2d3d4 S5›d6! S6›d8! S7›d5! S8›d7! S7›dw!
e5e6e7e8 = d5d6d7d8 S5›e1! S6›e3! S7›e2! S8›e4! S8›dx!
ewexeyez = e5e6e7e8 S5›dw! S6›dx! S7›dy! S8›dz!
Kr1 = S5›el! S6›e2! S7›e8! S8›e7! S5›ew!
Kr2 = S5›e3! S6›e4! S7›e6! S8›e5! S6›ex!
Kr3 = S5›e5! S6›e6! S7›e4! S8›e3! S7›ey!
Kr4 = S5›e7! S6›e8! S7›e2! S8›e1! S8›ez!
f1f2f3f4 = e1e2e3e4 S5›e5! S6›e7! S7›e6! S8›e8! S7›ew!
f5f6f7f8 = e5e6e7e8 S5›f2! S6›f4! S7›f1! S8›f3! S8›ex!
fwfxfyfz = f5f6f7f8 S5›ew! S6›ex! S7›ey! S8›ez!
Kr5 = S5›f4! S6›f3! S7›f5! S8›f6! S5›fw!
Kr6 = S5›f2! S6›f1! S7›f7! S8›f8! S6›fx!
Kr7 = S5›f8! S6›f7! S7›f1! S8›f2! S7›fy!
Kr8 = S5›f6! S6›f5! S7›f3! S8›f4! S8›fz!
g1g2g3g4 = f1f2f3f4 S5›f5! S6›f7! S7›f6! S8›f8! S7›fw!
g5g6g7g8 = f5f6f7f8 S5›g2! S6›g4! S7›g1! S8›g3! S8›fx!
gwgxgygz = g5g6g7g8 S5›fw! S6›fx! S7›fy! S8›fz!
Kr9 = S5›g4! S6›g3! S7›g5! S8›g6! S5›gw!
Kr10 = S5›g2! S6›g1! S7›g7! S8›g8! S6›gx!
Kr11 = S5›g8! S6›g7! S7›g1! S8›g2! S7›gy!
Kr12 = S5›g6! S6›g5! S7›g3! S8›g4! S8›gz!
Substitution Boxes
This example CAST cipher uses eight substitution boxes: s-boxes S1, S2,
S3, and S4 are round function s-boxes; S5, S6, S7, and S8 are key
schedule s-boxes. The s-box contents are written in hexadecimal and
are to be read left to right, top to bottom. Two example sets of s-boxes
are given on the following pages.
S-Box S1 (Examp1e 1)
c6b00b1e
d08d094d
959cb449
8d531db4
4be173c6
5768439b
128a2452
0f3ff37a
d13e2600
cd088c51
8e296754
9f7f55ff
5faef124
4ed3e8bd
08a43a43
1b77f7fb
c0a9ed79
7281c4b7
4b776caa
ff75ab5d
f91a4cf9
4a7a7a4d
71514583
cbd5d1d5
caa98800
7576516c
4150fdfb
fb37f9fa
f657b43f
4f3ff3ef
7c612b9d
cf7ffdfb
80ea38a2
68922405
da4fa8f7
3c8a46c1
d21cdbce
3194b822
8498a509
666378af
b05d8ac2
5264708c
e8dff3ba
07c9c831
e359af3f
0d6fabfc
b5a05a25
5977d3f8
890c5e39
84a28601
8b67ff16
80ac9028
88e79bf2
854511f5
8f7fb425
8b76c5ff
6bca5bc1
6bd93db0
679a19e8
627efbcb
6d5f6ad8
6abfdf50
66a6c4f9
6b7fb9f8
851ac1cd
539ee5ca
3fa7791e
ee4adaa3
b0da1081
64722b5c
0180ed45
dd7d3aa9
03286987
d66be246
bdc2aa87
6cc198bc
3c263a67
ec8925ba
83bed710
586d1abc
8ab38c7e
71898970
e87ca369
1d254b1e
0b7d85ba
f92f979a
6b618a40
986c1e92
c99ac587
3e1e14ab
a2aa30b8
586432ad
44497b78
bd6536bc
273fc5ca
dc6530bc
c3ee7b71
8b904102
005567f4
4f918356
f8abbe8d
b2ded2e5
36926a4e
7461b37c
c2f5ce45
8946951b
0b15be3d
443505f2
f14de078
bf3566fb
3fba3326
7a6d3ebf
c3b8b63e
e7bb4246
384d3281
12fe72eb
8b0c54b5
a640fe22
744f7db6
588f08b8
28471d46
00f0f3f7
d44154ff
f16f301c
6edd219b
48e51a03
9cf8aefe
b86574bf
8d06d47d
491bf432
a62a7926
64c7daf8
5a574491
9cfe7ee5
7b1cf91c
b6a92e10
78ac797c
bebeb314
559ffa1e
96cd88a4
a63a2e77
654535e1
8932c728
42e10a85
813f9826
8b1599e9
72e1a3d3
76e14e07
40a8918b
43eac70a
b2e5daf9
b2610e8a
131fd57e
16c20411
eae620a3
e2a12694
ddc56b61
d6a92685
2df394d0
26e96085
c97a6fc3
a104515b
ebd9278e
851c83ad
a3aeae9c
ca028754
8d0e7a7f
eff5a7e5
fbe9df9c
91d2c5e8
d149aec6
be79154a
9ac9b069
f6f97688
b4362776
d0e12e86
cabca364
1d36537e
20d17279
f93a7752
21510485
fcd5aeba
cccb2967
12c21880
305a0c9d
e86de2ec
de0c0486
0bea2485
d6c97583
03290a12
3734fb8c
e2e92486
c153e151
75f7e74a
f3ee4b8e
4821e210
ae93d829
101be9dd
97e9cff4
2b14183c
0545c904
ba2222fc
398bc832
8a8cba18
6a4d1acb
d8e00719
5dd7d584
ee04183d
c4da06de
d7e22bd1
0e1593ef
1b4e51bb
7d30a737
6f40d522
b72aeac5
ae273e32
bfd36706
a255be29
76e3121f
6e0d123c
00245bd9
1b0c1c29
c9528578
da0c523d
8581d3ef
2df9cba3
1e3c1772
b9f8b9c5
56e63420
f6b7126c
c0fb4ac7
620893c9
86be64e4
250fdf80
1d7c1cbe
b27a2776
572200d1
fb5c4470
c1d3b18a
6c043c3e
8ff7b49c
f1d068c6
9c044011
e4976a6e
3d45343d
402fbe92
28041f0b
5ec42a38
7c28b5e5
0cbbd354
6228b66e
170410ad
cab4c13f
be8c30be
d2956e74
ae0c163e
S-Box S2 (Example 1)
c2ad2c5e
194d87b3
82c127ce
56bb0629
688a0d7a
b726d1c2
21f3de43
f4cd6b22
88c5295c
5eba71a7
cb14e9b7
16b6d157
24dc2fa1
fa5958f5
6b72774c
bb2283d0
069d6a56
83fbdc6d
11c78559
9d32faea
16239af7
9f7254a5
0618cfa8
83d22ba1
508f6b36
de7acca9
447b55a7
c75ad1a1
41475489
cf33d385
57b890e7
d110d7a1
61152b5e
38882409
d9ac7bdd
88258fbd
2659d784
75568779
9616f2b3
c805baaa
01c014da
55670ac4
bfc6df20
e732d018
4ff1eb6d
1d72f223
fc6b158c
a7b3fe37
a4aaa246
549d7b56
6d3a1124
93107081
597c701a
aba2f99c
966ed435
6fa506d5
c805995f
3304b3b4
0739aba1
f662d3ee
3be6a0a9
ceb8822e
f732c5b5
0d3e5645
cb70db1c
40d450f7
b358b096
3ea2f1f9
a1479a2c
2fbb2e31
d8ee0991
55d05cf0
29d8fe9e
a777e6e6
53591efc
df2b260a
4d05f86b
c3c407a3
326fc08c
bbef3432
0e505514
12262b00
b99a5217
a4af05ab
c7faa510
d73f23c7
7e513060
6a4bb4e7
d1123474
cfe33bff
65e6eae9
7ed726c0
115a0beb
062e24e5
afa567b7
b88da0e3
684cdc1c
5911bb51
0035c48d
303c784f
4fd460d6
7dcb70aa
2f8b2d63
195ccd68
9059cb18
a4aad589
ff8b0863
ceaf2777
b66814a3
84efa545
d5f6a24e
e73a09d5
ace39d04
fd40c427
3d67ee62
6a8d8fe2
78e56ff9
23ef86de
eea723ff
b678d983
891cce1d
da9d0cee
1ea434e7
4fef24bd
5bbbd7cf
07a57d7e
cfaf32e7
94e76107
69f7a056
427b29bd
69fd88cc
4f858823
37e3a276
181c52ca
38e1754b
19d5e52a
63fe8254
45d8ddad
645e65b7
4d8c5f11
3da381a1
1541fcf9
3248f846
16610998
affeed5e
4c89506b
5a9d2a5d
b6027ee0
695f19fb
8430dead
9d564aaa
7cee8dad
1bb5cf3e
f54445a5
ef49d2a3
0c505deb
de54f681
340a5d8f
2c811eed
c80859e9
ca43a756
c3b6870b
a292fcd7
a11b01b5
6f505c8c
6e4c0c71
0f2450b9
077b34a2
caf7b6d2
ce2eabc2
a0ad7228
ac085e5c
60ee6869
66695e2f
05529a84
0896747f
0dc5254e
fbe7fa5c
96629628
6820f489
1060d712
e4c07b94
8d005835
72ffa0d9
33333457
c81137b4
ac2aodad
5d685fa6
22952fa5
d1820424
bc084bbd
4640d80d
6fd5a8eb
241d0106
a79be06b
e863800c
51d1cadf
1f7e52c6
9e035d66
d7372d07
dd1caa69
93eab513
13ec6d03
5bee57b3
eb85a994
a3235c50
24aab079
69534185
a8cc2de3
42ab58f9
3d3f02ec
d0607e5e
9779d9e3
73825630
0ae04a9d
ea88ed14
65d76f83
8b224d0c
f12b9212
1a225575
51b6561c
b2e85510
cb631642
2e6ad154
cce5afeb
7dd0e7ac
a4f4bc78
16fd09b8
39221421
892e045d
59467096
e9ddbc9f
549196ef
e01c8b70
3f1f5a94
8a6a56cc
a6886858
100bf6b6
c330d2b9
77e07c62
0a73e5f3
2dc5bad2
29c09691
0e42f415
8e06370e
a372fb29
aa365000
84dd8070
9dd59cea
be777711
ba486d14
9b1a570a
1d37a73c
3760048b
3b6a4310
106610b0
S-Box S3 (Example 1)
86f5c342
c231da03
64140aed
129ec99e
3ef407ec
6fcb995f
e0382359
b9ba0244
72524815
3a759e48
b3491e6d
cb8e4b5e
e61bfda2
91ec2964
27dee3ca
5a3ad1fe
22bdbeco
2dc09f7a
0cdf5081
12ea514f
99f9ae94
980a4411
8fc26e5a
a58ac137
47aa9b46
6b132788
60e5aa94
5fba6f72
d95ebb20
d14249b8
fabb0177
dbb2ef5b
07e182db
73c6cdd8
6777b8e8
0b91adb8
f457a25b
842d2285
8998d5b3
dbd06aa2
bd2bd4d0
e438849d
de35b50b
9d49e649
59a24077
2ec75a8e
1b16c97d
4cefb517
a8560728
94c66e8e
7c4d1ac9
7b1ad37a
dea5f3ad
fd1d191b
13936002
311f4f3d
232cfff2
1dafdb72
de68f9bf
d9822476
4b18fe7b
4098dc82
9382d372
9b986d5e
02bc173a
56211e7b
208c9e97
465edfe6
7a2c93d6
2b8a9d67
44b125e3
3d7ad47c
7352cced
3ac4caa2
52908857
0b475f24
32837b58
553cafdc
33dff722
5e034584
a72d38b8
d9a959d0
680684bb
37738535
d9286aae
b8d21069
2f5af870
7573554f
e6e30fbe
8a4331f2
30343cae
5f6bfb08
8dd72f98
d51bdf40
5e6ac50d
1f7b7b21
a23856a3
265f49a0
b3ffbcd2
1f517bc0
704f34a1
c064a63d
4d514109
cf91bc9a
5dbb5028
e5801277
6ffc3171
dd003233
8dfac44d
2a9fdeb6
af57cd95
18d7216d
0c568150
a126e824
48845eb3
de83c700
1eb43557
9dcdcde3
534b6428
f167db45
63f56b0a
fdf60f08
1ea97dc5
99d3700c
5f516803
c44948fa
17130708
8f50f924
3e6c3e77
b2fc2237
9c5fdeda
2283b18f
84fffbfa
1f54c56f
10617eea
89a3d770
8b8bb8a0
021ae3ca
0a40eb7b
b9931a68
1c520414
a9e5d4d1
9f07974e
20d709e8
9bf44ad1
dd7b42dc
bcd4acb6
e3a3ad7d
e3f452a6
a0011424
ff8b9678
95a33d06
363747d2
589a529b
1ae856a6
65b39345
61014390
21cbb10c
42b2d541
23ab136d
b6ea7bef
828935cc
572cc4da
7b8c55ad
06985ecd
3cb6de11
f9810104
eb49ba96
8d602160
9d55583b
672c491c
67d4367f
232fb845
164aa69b
e38f95f9
f6026905
188df738
adffb308
c4564efb
4253af4c
646c0f3f
cd12e98a
ab9a1124
01b6b60c
db232663
67240f45
24750c8c
a30b5941
bb83p74f
30952596
63cb2f44
e381956c
85da15f0
591319b0
e738b55f
09bc5808
bfd8903f
64ea3ea8
cb1787af
329cfeb7
3574c3a7
fd5448df
546682be
86a5f1ed
37357d11
d2caad96
74f97c59
9b11626d
219b3356
96ed7b89
a7f28773
39c586f8
dcda6943
7f26bfa3
60ecffad
faa55681
28812cd5
8635bb1e
b5c63f63
1a9df8c0
ca7728d7
5a6dd80b
599ceec4
d89d78e8
2ccc5068
e8ef4e4b
3c5b3f1f
d0b37c2a
bd7f37c8
4700a556
82b76a41
40f79351
120f5a67
e312312e
291a3299
d8621dfa
8888c380
6deddd5c
a8316eee
5dc50280
83728ebf
67e0ca5d
0f60f57e
d83544c9
9b82363a
523dc28d
14bdeaf1
fe31dd8b
e4054d64
388224c0
5b4b7709
9ca5f2c4
d0356ec8
0bbb4e11
58a504c1
88b6fee9
S-Box S4 (Example 1)
154b0bc2
9e92acd6
e8d3562e
607b3270
e148e878
7f97f0d6
18af89ad
8cb5df89
4a28e9c0
cf75d66f
aab7d57a
3cb2462b
b5503fbb
3db35e39
558ba589
c784e535
f190ac77
278b7320
ae647e1f
7f8f5d12
6814f368
bfea6e26
264d12e3
fff7fe37
204229c2
f8175a3f
7eb95eff
b135beec
afbd2e64
6eb5fe17
e4d0f00b
3bb53e56
804a28e9
e74801c9
d535853d
a34026c6
d16d31a0
b20c9b68
9bd07dfc
e072d02f
68cc31a2
016ccf1d
3e970216
566919c6
2f8c62ff
5af7fe3f
622e2a72
1fbfde1d
636e0fa0
49aa21c0
d7bed210
e88c49bb
e7f155bc
ddb50597
5931665e
7f370e7e
7559715c
51f5bcb2
dea5f68f
ffd6e11e
faa10c2c
d6355e1e
5f76ff1c
7f89fa91
9a14227a
90de812a
d70faf92
d7a79f88
1e94d1c1
0150192e
4ef2a450
53eaf634
3df59079
20b8ff96
6563fcc6
6b7d7fd7
a39e8607
a36f7785
f357c830
e84bdc8d
7fd485cf
78579ad9
c0b2d7a7
c15b64ea
fe4b8a91
e02f47de
509bfb5e
402b938b
a714903a
bf437783
016d7343
06614715
386b179d
3169d7af
9a860db2
846117ae
0e960151
f9042c75
8aebfca5
7c948b3a
b7b25818
44c3f6d0
250f0044
df2dfdd6
be90485b
5ea962a4
314b2fae
c9ae207e
00438b42
ec2bd783
8c7a93ce
7070e3e1
eca92618
8676c879
996afbac
fe507047
a8ad7c44
ca78a82f
c765dfa6
a0eb6786
d38ed8e4
a6a9154e
a179df37
c08a18a3
947665d4
e1e977a6
e9a8d6a0
805dd72d
67170782
29cc85b6
fa09f946
b685b898
17b2eeb9
4c437d1e
8fd5a2ce
dae9d860
1ed6e781
59abd226
9841d998
c86e604b
648cb1d9
28695051
e655a748
b178e057
86e6a39f
b775dfe3
19b0f07f
2c595352
ff48fd0b
c9386946
77b99522
4929f4dd
5416afa2
6e41505f
c86b543f
e3433b0d
396d2205
1a6bf075
b380786a
8d631036
f5942429
10160b29
87edaa55
75b6ae0e
42953fc0
a3d0b2a8
2c287f9e
d62ef34e
fbb23fe3
17ba4cd4
8c690a74
62bd1d86
5b50e4bc
ad2df05f
31788532
c943dff7
139a00c8
1954ae83
6068dc70
7b5245db
d5af537e
c96fa6ff
a847c89e
a9e9201c
268df73c
27ab3152
487ff8cf
4da846df
e971086c
e0eb5074
88aedafc
895fd079
f7b7d1c5
587f57b5
ba2aff05
1ea6ea9f
f79128ff
4d7b6b19
a67770cc
1a490e22
36f461c7
89990420
686a0fdb
c05ea648
2dbdf79a
894a8612
7f76350e
c1482610
175d75d8
d756c9e5
8899a638
4d729555
76e87b0d
a902bf41
fe908360
290a669e
0cbfe9a5
d6ea821c
8840867c
4be83d0b
7144e403
ba482632
f2297a2c
2d48c631
64b7f26e
b1a5d96a
c7cc2c12
159dfc0d
5bb5a987
8ae020ef
ed08fdd9
368e2148
9211b9e5
57801e92
3c4ad833
e285dbc1
ab60f2fe
640e261c
00d3c371
d9731df4
83a2d68f
2977b8c5
b1430a33
127183d8
e50c8579
415df4b8
c9ec8e99
69cab61b
bfa5b17b
0f086751
885c2e88
2d0b409d
d8599e6b
68c88633
e18f0cbf
4974023a
S-Box S5 (Example 1)
2bb1ce76
a24f25c4
831431d4
0303db1a
08db19f4
8f32c2d9
a9f21d00
35f432ef
2cb25fbf
a02e5aad
8d95f281
1aed8191
17176c34
915730db
b2ea75b1
3d48aae2
0f031db4
d4ecade3
cb717039
196a7209
91aa7df8
48d732bb
52c7ea11
9048e28b
ef394063
347ee412
38cac74d
f874a625
69d5909e
b4cba299
b46fa239
608ea099
3d73d51a
98daade4
e6088fb9
4e93582a
c82ceda5
7f8b52cf
108ca1ee
b81f4457
1f973404
b7cb9a2a
d20508da
65667ee7
f6d1e7c3
4848e71b
35ce8218
866eaf6d
06dd7926
3d86adbc
f14dce25
c73906c9
12460656
3796dad3
e89ea68f
d26793c2
23005bd9
1064a315
d87a3298
f43ca15c
2b089b69
022c02d8
d06caa1f
f46cad18
070810b0
18f2d342
3fa9ef55
3ebea5dc
84626376
958f1c4d
b54fcb80
b84dc829
470fa1fe
5d9324a8
702cac04
64505b17
deae3ae2
c6eeeedd
fc530776
e8f154e5
33bee3b2
59515b74
c8cca6f9
add78c8f
0d178bd8
766aec3d
e87a1c51
9ef11c0d
9e84b6f5
f8c31e95
65779d4c
1cc95ca2
a36cc61d
d8725c1e
5ad258fb
3c375e9f
04cea398
86675360
efb1513a
632ea6ec
14959373
8732ac5b
ee31736e
71a2be81
e12eca01
7a766c2d
1ab87e5d
9fdb2461
ef681d41
69f5991d
1977dcdf
83d3517a
2f642f64
943b5329
07f418e7
a384784f
fefbf4c2
4b2f2455
d02354cf
78da6d54
27b9ad0b
8cd9d190
10c3409b
b481dbdb
f1b161be
58915c5f
dcd17cdd
78d1530e
18e9ba0a
579621f8
b08d05ec
f0b35e46
bb4bc9ec
fa6bf6d5
1a6a2918
46a56293
796a5b67
33b79e31
dee4579d
8bdcb08d
c08f9958
80860547
6332a4cd
2e90ae7e
3c735928
c73ca9ef
3ea05561
cad32615
62323980
99460687
673faec9
81d9a697
38e9456f
c7aee50e
2b9b66d5
cba4a719
7c6d34a6
879aa685
65b7e261
9396a505
0a2b4122
4943a9d8
11d9fa81
5d6b5d76
3bb468e9
689a56c3
215491f6
6f0e543b
ae4f7098
e452deb6
a57c8cc6
f0ff8ffb
8141e7fb
df916287
86163764
d5f6abe1
31adddfe
2a16a9b0
20d4aa7d
34c8d2d5
e1d6177a
e44fdeef
ff26e657
e7b697ce
f0d01e91
e3b42209
ef23b200
e3a46060
3eb8ca05
3775b6c4
23b48e47
2734a894
2baf9b33
d2d42881
73cf2492
92f1df7f
c80d4c91
3f29d7be
99280067
74e367aa
ed285ad9
11f51fcb
bca2f6e7
4a7e95f4
16c93071
e8c024be
527429f5
a4d6af86
1f3158d1
157ea087
c2e27c5e
c191276c
e17030bf
f80427fe
227da776
309fa7ee
d6ab4c06
d4ece076
09d9c32b
10e6a261
292b9dda
34dca7fd
f4f5e75c
f0d0a4fc
2c69c85f
4801a8a3
279fdbfd
4f295c4f
78f2e9c0
0fdc57a8
6016bc89
194c5112
4f097162
3610d74e
523e05be
35bd2a82
0707e286
61d3e37e
1550965c
6fb4aa09
07eb7443
fc54a8da
69928340
8f8a53ac
72941a11
8709df96
1864ebe8
f2f496a7
8b9617bc
60f6af73
f8653ffc
1ce6e518
fbfecf2d
123717bc
90f6a77a
7476a97d
S-Box S6 (Example 1)
4301e0aa
934959bd
08a01c00
55804207
8d3d33d7
dd6e22b0
c1361255
156ebfea
07add6f6
d0ceabd1
4a49a184
93ca9f6b
4598280b
9f02c8c4
02c707a1
dfdeff6e
c8c70ddf
993a8ed4
58f14a38
87757d83
48e24911
13cdc99a
d75bd08e
0b6ebf7d
f5421b0d
ac26f7fe
6a7ac372
beef3fe9
71beed43
afea37a8
ec186eb4
b6deffff
47822eaa
31310013
21976592
df3bc04b
e3d39772
1811450b
8440fd32
fefeffe3
7bcd8915
8c05aa0c
142e1875
e87114d4
509514bd
a7cefefc
33e12155
c64ebf64
4e7cb3ef
2b4934fa
ee0dbfea
0036e03f
be0c8274
dc815251
17deac59
f73eff74
d4da34de
3f2615a3
7416f6c3
176caba6
2373be35
42d5fde0
870ddbf0
674ebff5
d09f1a57
d0d1f563
eb3170f8
6318aefc
4babcf28
ce7e1c5c
722afc8f
76f68313
60397e0e
635fd70a
5cd4dd79
545233a5
7201c8d9
7d96b60d
415f6746
4c46c392
5b58e52a
caa2600a
fa6cfef8
e4e4d148
ae797fce
30d12f76
04c2e474
1c768384
76d667ed
6fb6cb05
dce2b387
4977c317
83a211a1
1cfa8341
2f851043
3546c303
d4101457
42a13cfd
a20b414a
bdab3cb0
65c4b98d
7f81fbf7
175c49e8
8d66c31a
5c55e1ed
4f9c46e7
22be2ca8
3be1a81a
678d266f
71da0025
10791bb2
05d68398
ddef9b1a
38d94a14
7c9d430a
17af5cf4
481666ab
ab1d34ad
e447c2a3
8026c38d
3742883e
dcbeb968
9283ce16
f4fc4758
a1ee90d7
c545c919
0490ff07
e4d68309
c588a876
c7d42384
d60de7da
5e2d3958
e6b4788e
e303cbfc
ff7f6a6a
79e354b0
35748d28
be03402a
a9f04a1c
a977e506
170553f0
10cb00ea
843afdec
01531436
465e57c3
3dc7f6ed
8d382192
f9a8072c
f32fa0e8
8fc4b096
3b961b11
41235427
33cbf143
48bb3ca5
739729aa
866254b4
86a78788
71f75da6
c0d1a6a9
b05314a7
491fc7b6
b5aceb5a
772e9e28
0286ab54
18ca6fab
e2ac2d17
2859974d
527314b9
1110720b
62c8d0c7
af93f2cd
54dc7ef9
4288ddc6
bcd7b7c2
f75cc818
88c3543c
c8f14833
6fb4ddf3
13d0d460
b8fb8ad0
0551d80d
a458aa4d
d94375c6
7d73142e
6a577e50
cbbb4f88
35ff1d7b
19f1d0bb
a4ea667e
881816be
f98400ad
51c354ad
d9e9ad73
dbb370a2
8a6374da
074a2a5b
efdd7b89
efec0ae8
b39c7b48
358497b1
9d1fda28
126dc309
4092c919
4110b630
af634cda
ada081db
785d62f3
fd34d732
5a3e40ce
71a0e7cb
d05a6aaa
f5c6541f
ba4b69cf
9327a982
37f0d013
19c49726
0fa0725b
a4d4ffa6
0af0a6a7
2e0557b2
eb448492
cd1816b7
ecb327a6
4c34d7a3
557202b3
c9c3284c
2b4d4508
3fe9a857
1122beac
8ac36c13
64badc6f
7e14d7b8
9977e50b
8eaec3d4
66fc39e8
f8b33dcf
da6f10ec
453cb6e3
2b3b0d07
34a49738
d49d9f3e
33db5ce5
1ebfd778
f09dc9e3
1cb4c32a
fc3b3349
d525e4c4
3594d72f
56303d48
37dc1cbb
1c95da56
f59ec3bd
9988b764
7077ddbf
d5e6dba2
bda497a9
S-Box S7 (Example 1)
813c06d4
67033b80
88a17185
7d7ba354
ace95364
5aa2776a
a4139684
57e084fb
15408c02
fa6ec746
1907265c
ed2fc499
2ca939fb
d53d3805
3b31ffd0
cffe8e5b
3267bfc2
ae1182e9
417891eb
ca159f43
6ae64885
e5bfdd34
1341a399
9d5edc5f
3cbe068c
ba7a97df
5ee36a2a
c7df8efe
7c02fdf2
ef2797db
0e5f8aa5
94df4cff
9f97093b
c080ec10
f05c3a86
b3237184
b8512108
ffd49029
d64f2f23
9bffe9df
dd7e41ad
81a568ba
b3618fff
fb314ec5
e37cee5b
a1fbc0a6
960ec35b
d65fdc7f
3ecb36db
4e29aa7b
ffb9a411
97cd4a9e
e9a64412
828d3d78
22de9cca
473e4e7b
3978b2d5
59f53821
ed464270
9dbefcaf
fbd0aba9
865a9777
3f5ccfda
44fe1edb
17cfb151
77f08429
2ed64a2c
4f585cfd
569aece9
39908cc7
7ef5a109
1587f376
86a3778f
edddb0c7
bf3095dd
d94d331c
db4e4672
a3cf4f88
e946885d
990df1d6
b7d18843
a263b560
910be66e
98e6e0e6
2495f708
34dc2ab1
00b2d438
096d23d2
4b997905
558cac5a
7d145da7
73ecf173
de31067f
d915a85e
f0acf520
e2ac3372
02b47abe
da7213bd
666b4d27
a500ce2d
b2325e85
7ce76380
c92918a6
1998de52
214d3e20
f4171f3f
41163076
8353b940
808b11d2
5f08ff2f
e5f9f4de
28aca3f2
b0adc55a
c85addf6
df8a9f9c
a13e753b
57c53b9f
33efc2f9
34adeb63
530df1f6
c18f495c
b40203a0
baf179f5
c58d8322
2df3d024
5869e0f6
402ff057
3a8d6156
8ac190b3
2ad4aca3
335a6736
92e45475
8316c491
241d83dd
2be081b1
8831d04e
3b9f5bb5
90f1b0f5
82b4b3ff
24d8332c
26526c4a
9eea4d32
94c28ae5
2409d9ee
2af4a963
77c6b548
ac8fe4dc
e5caca77
3111dfb1
69400a03
bdbef538
f4e90bea
760d503d
20a980ea
e0105fcd
ae6ad95a
63972846
2498806c
e588fcc0
bf281b4a
97087e4c
8f771b35
5be76c24
58bee6a5
07ae55fc
016b6618
dcbc3896
c42efd6a
34cb170a
29123f0f
fc923a4d
f6c49970
bd8f38eb
aa24f717
78fdd6ee
7da88bca
253ac16a
15defddc
820e9137
bc107faa
42513027
6e72e8c9
e921caeb
ce89d9ce
b4a16574
810e0f12
07f55786
30098b0b
d04dfd1c
ededc246
758bd93f
4f09496e
03cdd8c9
a5d8ecf5
cad2a360
7f385423
669a84e3
d8d0878f
aef949c3
15a9583c
77835fc7
d8bd388b
bb7cff81
0f453b56
0e4aec3c
b7e7c540
d94a0297
6d05599c
b0bd611d
644b7d3e
a3036ca6
68c64a2d
409d9fc3
87dc0279
51b27d66
9f250b98
7ed5d04b
b0a04490
7c1897bf
a5a65928
9e5b2c34
4d554016
84847cba
56a49b38
15d4f236
aa7a1b67
922fe47a
3162a6f3
d232d58e
7da76a4e
5c25f0ec
f9b63518
77079778
c35fb775
f11a7a3b
5159910a
a187389d
0b283761
34f51e94
9ca40bb8
b4a3cd14
2c5275ae
7dc25545
f51cbff0
03cdb055
80efe8b7
c0ad42bd
454599bc
53a96102
d306cb6c
8fbd93fc
17c50b79
f991796e
6c214a38
3507194d
ae85c91c
S-Box S8 (Example 1)
03755908
8130788b
60b34458
f5a713fb
1b3e6039
84ce8770
62da564e
fad6beb4
10e90337
8e7bb301
687c5e1a
e4c286dd
0470b043
9d7f8fed
672370b0
fcad5e7c
8a7833e0
19203447
1600c2a6
9ffb87ac
adf01f95
3cc7c2ec
2e36e31e
b50f0559
f527ecc1
62dc821e
7ccafc4b
f4efcee8
cbf3b9bf
444f44ec
5c441201
dc8bcabd
0f01e193
0e403103
933c20ef
976db906
5aaf1212
5ad1188c
d9d9f5b3
cc1acfc7
1fe6961f
0b562563
85e12831
913ccce5
5748c7ed
58efe7cd
d3e0e9e7
cc87e7fc
8dbab47f
cbd07112
6a4796f4
24cf2e6d
a427ad45
fca8ae32
590d8ff9
19cd88e9
319e46ed
7a7118a1
de9fba85
98ef87ec
108d0eea
5fafdfee
e4bf444c
b6af8ffe
bb0c22ed
1d4c4774
5ac87aad
efdb2d0c
8f401cc4
24b4b09f
78a42da1
dceac743
6c9138da
d20381f6
940561ff
20babd2a
4a0acbbc
e703b51a
a71c4a55
1cd1258b
34054217
015c03b0
0a7afc51
2583f85b
398b2362
04b9fd09
16489fe9
2d3370ae
215e953c
0aa4b0e9
04b7c0a6
2c93f71f
318dc948
0c337d19
067a2ff6
24f3fd4a
bb7d9a64
fa3c0afc
b9451c02
ed1585f1
22d62be7
60ab6163
23a7c95c
6822fe32
cd9ba7e0
9f2e1b94
cb9a17cc
9540f512
5735f71a
18939f3a
51df9202
0effd009
3fc2c59a
1bac42e5
a63faa1b
9eb3539a
fc5bd4ba
ded6dfd7
6173b40e
43f5b51c
ebe23502
da092656
74e08670
4097bc1b
24f43515
0dd3a41b
bc8138bb
8cd3f40b
9cd38f74
7a168aab
ff37b654
0aa1e1d3
e80a8279
13e26d24
9dfe103e
69b058bc
2be77547
d55d5d4d
53da9c66
b76470b5
5f445603
a2d95981
30e706cc
cb8b3810
117edd8c
a686ce6f
4d2430aa
e0dd7580
fec46dbd
43eb90d0
b1122152
0ac97f71
c6998ae1
7d7a7c56
837c0e7f
2bc93880
34d7e7b3
9be93280
6330d06d
c3ad3091
9c2727fb
7d66c767
4c3af29b
a84b4b2e
05b9f47e
e5fd7edc
c6fd8783
3f7ca18f
6868f83b
9870c76b
bec5ca71
42ba3a89
e05e29c5
0f49b1a1
2424af9b
dba10dd0
1a3c4a03
7c768f7e
31e14484
5bc9dc41
db31db45
ab84700a
e62979f1
860b7a81
aea0389d
cdd7eaad
81ab6889
e7e97180
638b588a
08092982
5bcbb624
2989f992
3b550b6e
f9954aab
3ab3775e
ef2220db
838b017b
4c67a534
987f942e
5073deb4
2860b155
f6da9045
305c5c7c
ece3b4bd
8ec1d203
475a9c89
8f27c3d6
5408bc18
b0fc5384
41050667
2ea1f1a2
c55af588
5540aeb5
a46a50ca
d693a25a
2d0af579
cd1f0ce3
2afdb15e
44fecd6d
ac4afe88
315668bb
cc6af48a
a6f11265
442af899
37a4a3f3
76e50367
59bc3189
0dcc8826
623f3274
2078f8cc
037c4493
44bb6f85
c5ea363b
93f70663
af410a73
f939fc81
9fdce6cd
d0ca36a9
f9e42b81
a626c5da
b7bbc419
b3f54376
42668794
5e4a5e49
5cb25d45
5605fe10
a1a8bdf9
a3ccb88b
ab23b48d
b2502ba5
542bab83
406eb588
480d9c8a
458aad88
bc0a352c
ac0a7d98
S-Box S1 (Example 2)
30fb40d4
9fa0ff0b
6beccd2f
3f258c7a
1e213f2f
9c004dd3
6003e540
cf9fc949
bfd4af27
88bbbdb5
e2034090
98d09675
6e63a0e0
15c361d2
c2e7661d
22d4ff8e
28683b6f
c07fd059
ff2379c8
775f50e2
43c340d3
df2f8656
887ca41a
a2d2bd2d
a1c9e0dE
346c4819
61b76d87
22540f2f
2abe32e1
aa54166b
22568e3a
a2d341d0
66db40c8
a784392f
004dff2f
2db9d2de
97943fac
4a97c1d8
527644b7
b5f437a7
b82cbaef
d751d159
6ff7f0ed
5a097a1f
827b68d0
90ecf52e
22b0c054
bc8e5935
4b6d2f7f
50bb64a2
d2664910
bee5812d
b7332290
e93b159f
b48ee411
4bff345d
fd45c240
ad31973f
c4f6d02e
55fc8165
d5b1caad
a1ac2dae
a2d4b76d
c19b0c50
882240f2
0c6e4f38
a4e4bfd7
4f5ba272
564c1d2f
c59c5319
b949e354
b04669fe
b1b6ab8a
c71358dd
6385c545
110f935d
57538ad5
6a390493
e63d37e0
2a54f6b3
3a787d5f
6276a0b5
19a6fcdf
7a42206a
29f9d4d5
f61b1891
bb72275e
aa508167
38901091
c6b505eb
84c7cb8c
2ad75a0f
874a1427
a2d1936b
2ad286af
aa5Ed291
d7894360
425c750d
93b39e26
187184c9
6c00b32d
73e2bb14
a0bebc3c
54623779
64459eab
3f328b82
7718cf82
59a2cea6
04ee002e
89fe78e6
3fab0950
325ff6c2
81383f05
6963c5c8
76cb5ad6
d49974c9
ca180dcf
380782d5
c7fa5cf6
8ac31511
35e79e13
47da91d0
f40f9086
a7e2419e
31366241
051ef495
aa573b04
4a805d8d
548300d0
00322a3c
bf64cddf
ba57aE8e
75c6372b
50afd341
a7c13275
915a0bf5
6b54bfab
2b0b1426
ab4cc9d7
449ccd82
f7fbf265
ab85c5f3
1b55db94
aad4e324
cfa4bd3f
2deaa3e2
9e204d02
c8bd25ac
eadf55b3
d5bd9e98
e31231b2
2ad5ad6c
954329de
adbe4528
d8710f69
aa51c90f
aa786bf6
22513f1e
aa51a79b
2ad344cc
7b5a41f0
d37cfbad
1b069505
41ece491
b4c332e6
032268d4
c9600acc
ce387e6d
bf6bb16c
6a70fb78
0d03d9c9
d4df39de
e01063da
4736f464
5ad328d8
b347cc96
75bb0fc3
98511bfb
4ffbcc35
b58bcf6a
e11f0abc
bfc5fe4a
a70aec10
ac39570a
3f04442f
6188b153
e0397a2e
5727cb79
9ceb418f
1cacd68d
2ad37c96
0175cb9d
c69dff09
c75b65f0
d9db40d8
ec0e7779
4744ead4
b11c3274
dd24cb9e
7e1c54bd
f01144f9
d2240eb1
9675b3fd
a3ac3755
d47c27af
51c85f4d
56907596
a5bb15e6
580304f0
ca042cf1
011a37ea
8dbfaadb
35ba3e4a
3526ffa0
c37b4d09
bc30Eed9
98a52666
5648f725
ff5e569d
0cedE3d0
7c63b2cf
700b45e1
d5ea50f1
85a92872
af1fbda7
d4234870
a7870bf3
2d3b4d79
42e04198
0cd0ede7
26470db8
f881814c
474d6ad7
7c0c5e5c
d1231959
381b7298
f5d2f4db
ab838653
6e2f1e23
83719c9e
bd91e046
9a56456e
dc39200c
20c8c571
962bda1c
e1e696ff
b141ab08
7cca89b9
1a69e783
02cc4843
a2f7c579
429ef47d
427b169c
5ac9f049
dd8f0f00
5c8165bf
S-Box S2 (Example 2)
1f201094
ef0ba75b
69e3cf7e
393f4380
fe61cf7a
eec5207a
55889c94
72fc0651
ada7ef79
4e1d7235
d55a63ce
de0436ba
99c430ef
5f0c0794
18dcdb7d
a1d6eff3
a0b52f7b
59e83605
ee15b094
e9ffd909
dc440086
ef944459
ba83ccb3
e0c3cdfb
d1da4181
3b092ab1
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