2013/03/09 by Boris Ryabko, Ryabko, Boris
Computer Science · Mathematics · #94-XX Information and communication #Benford’s Law and Fraud Detection #Chaos-based Image/Signal Encryption #Computability, Logic, AI Algorithms #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT) #circuits #cs.CR #cs.IT #math.IT #msc:94-XX
paper · pdf · doi:10.48550/arxiv.1303.2219
arxiv created 2013/03/09 · openalex publication_date 2013/03/09 · arxiv updated 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Vernam cipher (or one-time pad) has played an important rule in cryptography because it is a perfect secrecy system. For example, if an English text (presented in binary system) X1 X2 ... is enciphered according to the formula Zi = (Xi + Yi) \mod 2 , where Y1 Y2 ... is a key sequence generated by the Bernoulli source with equal probabilities of 0 and 1, anyone who knows Z1 Z2 ... has no information about X1 X2 ... without the knowledge of the key Y1 Y2 .... (The best strategy is to guess X1 X2 ... not paying attention to Z1 Z2 ... .) But what should one say about secrecy of an analogous method where the key sequence Y1 Y2 ... is generated by the Bernoulli source with a small bias, say, P(0) = 0.49, P(1) = 0.51? To the best of our knowledge, there are no theoretical estimates for the secrecy of such a system, as well as for the general case where X1 X2 ... (the plaintext) and key sequence are described by stationary ergodic processes. We consider the running-key ciphers where the plaintext and the key are generated by stationary ergodic sources and show how to estimate the secrecy of such systems. In particular, it is shown that, in a certain sense, the Vernam cipher is robust to small deviations from randomness.