Paper 2020/389

A Unary Cipher with Advantages over the Vernam Cipher

Gideon Samid

Abstract

Vernam cipher offers mathematical security because every possible message of same length as the encrypted message can be decrypted from the given ciphertext. This irreducible equivocation is the basis of the celebrated Vernam's One Time Pad cipher. A comparable equivocation can be achieved by first encoding a message in a smart unary way where bit identity carries no content information. Instead, content is expressed by bit count, using bit identities only to mark where one countable string begins and another ends. The resultant encoded expression, albeit, larger, undergoes a single round of transposition. It turns out that the thoroughly transposed bits can be reassembled to construct any content that can be originally expressed in a bit string of some finite size. This includes the full range of bit size up to an arbitrary limit. By transposing n bits, with a key in the form of a single positive integer, k, of a limited range, one can include the key for the next message in the present message, and maintain a limited but persistent level of equivocation. A repeat use of the same transposition key will deteriorate the initial mathematical secrecy, but the rate of deterioration is subject to user's control. This Transposition Encoding Unary cipher may be positioned as a Vernam alternative, also serving as a mathematical secrecy reference to computationally secure ciphers.

Note: This "security through equivocation" cipher is in line with formerly published ciphers: BitFlip, and BitLoop, and is based largely on US patent 10,608,814.