Loops whose translations generate the alternating group

The Round Functions of RIJNDAEL Generate the Alternating Group

For the block cipher RIJNDAEL with a block length of 128 bits group theoretic properties of the round functions are derived. Especially it is shown that these round functions generate the alternating group.

The Round Functions of SERPENT Generate the Alternating Group

The results in the paper exclude several thinkable regularities of the SERPENT round functions. Thus they support the statement of the SERPENT authors that this algorithm has strong cryptographic properties.

DES-like functions can generate the alternating group

DES - Like Functions Can Generate the 863 Alternating Group

I N the design of block ciphers,’ it is considered a virtue if the encipherment can perform all the (2”)! permutations on n vectors, where n is large enough to prevent the feasibility of applying the usual techniques for cryptanalyzing a substitution code. However, this is an impractical target since such a system would require a key of length log,(2”)! = n . 2”. Thus, one is inclined to weaken...

The One-Round Functions of the DES Generate the Alternating Group

hi c a d of thc 16 DES rounds we have a permutation of @-bitblocks. According to the corresponding key-block there are 248 possible permutations per round. In this paper we will prove that these permutations generate the alternating group. The main parts of the paper are the proof that the generated group is 3-transitive, and the application of a result from p. J. Cameron based on the classific...