Welcome to the resource topic for 2019/538
Title:
On Perfect Endomorphic Ciphers
Authors: Nikolay Shenets
Abstract:It has been 70 years since the publication of the seminal outstanding work of Claude Elwood Shannon, in which he first gave a mathematical definition of the cryptosystem and introduced the concept of perfect ciphers. He also examined the conditions in which such a ciphers exist. Shannon’s results in one form or another are presented in almost all books on cryptography. One of his result deals with so-called endomorphic ciphers in which the cardinalities of the message space \mathcal{M} and the ciphertexts \mathcal{C} are the same. The Vernam cipher (one-time pad) is the most famous representative of such ciphers. Moreover, it’s the only one known to be perfect. Surprisingly, we have found a mistake in the Shannon’s result. Namely, Shannon stated that an endomorphic cipher, in which the keyspace \mathcal{K} has the same cardinality as message space, is perfect if and only if two conditions are satisfied. The first suggests that for any pair plaintext - ciphertext there exists only one key that translates this plaintext into this ciphertext. The second argues that the key distribution must be uniform. We show, that these two conditions are not really enough. We prove in three different ways that the plaintexts must also be equally probable. Moreover, we study the general endomorphic cipher and get the same result. It follows, that in practice perfect endomorphic ciphers do not exist.
ePrint: https://eprint.iacr.org/2019/538
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .