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If there is no better way to break GOST other than brute force, it is a very secure algorithm. GOST has a 256-bit key—longer if you count the secret S-boxes. Against differential and linear cryptanalysis, GOST is probably stronger than DES. Although the random S-boxes in GOST are probably weaker than the fixed S-boxes in DES, their secrecy adds to GOST’s resistance against differential and linear attacks. Also, both of these attacks depend on the number of rounds: the more rounds, the more difficult the attack. GOST has twice as many rounds as DES; this alone probably makes both differential and linear cryptanalysis infeasible.
The other parts of GOST are either on par or worse than DES. GOST doesn’t have the same expansion permutation that DES has. Deleting this permutation from DES weakens it by reducing the avalanche effect; it is reasonable to believe that GOST is weaker for not having it. GOST’s use of addition instead is no less secure than DES’s XOR.
The greatest difference between them seems to be GOST’s cyclic shift instead of a permutation. The DES permutation increases the avalanche effect. In GOST a change in one input bit affects one S-box in one round, which then affects two S-boxes in the next round, three the round after that, and so on. GOST requires 8 rounds before a single change in an input affects every output bit; DES only requires 5 rounds. This is certainly a weakness. But remember: GOST has 32 rounds to DES’s 16.
GOST’s designers tried to achieve a balance between efficiency and security. They modified DES’s basic design to create an algorithm that is better suited for software implementation. They seem to have been less sure of their algorithm’s security, and have tried to compensate by making the key length very large, keeping the S-boxes secret, and doubling the number of iterations. Whether their efforts have resulted in an algorithm more secure than DES remains to be seen.
CAST was designed in Canada by Carlisle Adams and Stafford Tavares [10,7]. They claim that the name refers to their design procedure and should conjure up images of randomness, but note the authors’ initials. The example CAST algorithm uses a 64-bit block size and a 64-bit key.
The structure of CAST should be familiar. The algorithm uses six S-boxes with an 8-bit input and a 32-bit output. Construction of these S-boxes is implementation-dependent and complicated; see the references for details.
To encrypt, first divide the plaintext block into a left half and a right half. The algorithm has 8 rounds. In each round the right half is combined with some key material using function f and then XORed with the left half to form the new right half. The original right half (before the round) becomes the new left half. After 8 rounds (don’t switch the left and right halves after the eighth round), the two halves are concatenated to form the ciphertext.
Function f is simple:
Alternatively, the 32-bit input can be XORed with 32 bits of key, divided into four 8-bit quarters, processed through the S-boxes, and then XORed together [7]. N rounds of this appears to be as secure as N + 2 rounds of the other option.
The 16-bit subkey for each round is easily calculated from the 64-bit key. If k_{1}, k_{2},..., k_{8} are the 8 bytes of the key, then the subkeys for each round are:
Round 1: | k_{1}, k_{2} | |
Round 2: | k_{3}, k_{4} | |
Round 3: | k_{5}, k_{6} | |
Round 4: | k_{7}, k_{8} | |
Round 5: | k_{4}, k_{3} | |
Round 6: | k_{2}, k_{1} | |
Round 7: | k_{8}, k_{7} | |
Round 8: | k_{6}, k_{5} |
The strength of this algorithm lies in its S-boxes. CAST does not have fixed S-boxes; new ones are constructed for each application. Design criteria are in [10]; bent functions are the S-box columns, selected for a number of desirable S-box properties (see Section 14.10). Once a set of S-boxes has been constructed for a given implementation of CAST, they are fixed for all time. The S-boxes are implementation-dependent, but not key-dependent.
It was shown in [10] that CAST is resistant to differential cryptanalysis and in [728] that CAST is resistant to linear cryptanalysis. There is no known way to break CAST other than brute force.
Northern Telecom is using CAST in their Entrust security software package for Macintoshes, PCs, and UNIX workstations. The particular S-boxes they chose are not public. The Canadian government is evaluating CAST as a new encryption standard. CAST is patent-pending.
Blowfish is an algorithm of my own design, intended for implementation on large microprocessors [1388,1389]. The algorithm is unpatented, and the C code in the back of this book is in the public domain. I designed Blowfish to meet the following design criteria.
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