Paper 2023/1202 Original: eprint.iacr.org/2023/1202 ↗

Extension of Shannon's theory of ciphers based on Latin rectangles

Abstract

The paper extends Shannon's classical theory of ciphers. Here ciphers are modeled by Latin rectangles and their resistance to brute force attack is assessed through the valence of cryptograms. The valence of a cryptogram is defined as the number of all meaningful messages produced by decrypting the cryptogram with all possible keys. In this paper, the mean cryptogram valence of an arbitrary modern cipher with K keys, N outputs and N inputs, of which M inputs are messages, is derived. Furthermore, the lower bound on the valence of the cryptograms of entire ciphers is derived in this paper. The obtained parameters allow to assess the resistance of cryptograms, resp. ciphers against brute force attack. The model is general, illustrative and uses a simpler mathematical apparatus than existing theory. Therefore, it can also be used as an introduction to the theory of resistance of ciphers to brute force attack.