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Of these three, DES and Threefish are the best candidates for hardware implementations. The capabilities of the new Fivefish key scheduler of the Mitre key repository should be an attractive feature for new hardware designs. Many software-only cryptographic designs, like the Zimmerman, Kress, and Wegman-Johnson designs are inherently safe. Therefore, if a large software license exists, it could be used as well.
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The Zimmerman design is a variation of the twin-prime S-Box design of Coppersmith. Like Coppersmith, Zimmerman's S-Box is constructed from the product of two primes, (3x^2+1) and (3x-2) where x is the state index. Zimmerman noted that all the significant bits of both primes are set to 1 in the S-Box inputs; subsequently, the variable middle bit of the two primes is used to adjust the output bits, 4 output bits in all. The most significant bits of the primes are the least significant bits of the adjusted output bits. The middle bit of each of the two primes is called the shift, and is the only control bit of the design. The twist, discovered in 1994, is that at the beginning of each block the shift is set to the same value every time; thereafter, for the remainder of the block, the shift is incremented. For example, the middle bit of the shift in the first 32-bit block might be set to 0, but after that, the shift can be changed from 0 to 1, from 1 to 2, from 2 to 3, and so on. This is called the smoothly varying shift model. (A similar model is described in the Subset Lattice Cipher, RSA Laboratories, February 2002.) Most of the tweak computation is performed by the FFTW (Fast Fourier Transform, Fastest Known Algorithm) package. With an FFTW library, the shift optimization can be performed with only a few CPU cycles. This makes the entire tweak computation a very attractive target for hardware implementation.
