Polyalphabetic Euclidean ciphers

摘要

First, we prove a fundamental theorem which describes some properties of elements of Euclidean rings. This theorem allows us to construct an infinite family of cryptosystems, among which there are cryptosystems without repetitions. This means that the encryption algorithm can encrypt any text so that all symbols after encryption are different. Therefore, methods of statistic analysis cannot be used against our cryptosystems even theoretically.