Attacks on the Random Gamming Code

Abstract

In 1917, Hilbert Vernam patented a top-secret encryption scheme, which at first was called a one-time notepad and later a Vernam cipher. At the time that Vernam proposed this scheme, there was no evidence that it was completely secret, since, in fact, at that time yet there was no idea what the perfect secret of the cipher was. However, about 25 years later, Claude Shannon introduced the definition of perfect secrecy (perfect cipher) and demonstrated that the random gamming cipher reaches this level of security. Cryptographers believe that there are no effective attacks for attacks of random gamming. In particular, there are no effective attacks for the Vernam cipher.Objective: to justify the fallacy of this proposition to build effective attacks.Methods: analysis of the relationship between the cipher key and the received encrypted text.Results: an attack on the plaintext of a random gamming cipher based on a given encrypted text was developed. In addition, there was a suggestion for another attack on the plaintext contents based on the encrypted text. For all attacks, parameters of their complexity are calculated. These results are new. Previously, an attack on the random gamma code was unavailable. The results disprove the opinion that there are no attacks on this cipher.Practical relevance: firstly, it has become possible to carry out attacks on the random gamming code. Secondly, when using this cipher, it is necessary to strictly limit the length of the message.Discussion: the idea that there is an effective attack on a random gamming cipher arose in 2002, due to the possibility of introducing a similar concept, in which in a definition of the perfect cipher the plaintext is changed for a key. The first idea in creating attacks is that when the key is long its elements are repeated. The second idea is that attacks on two plaintexts are encrypted with one key. And the main idea was that it is necessary to improve the mathematical model of the Shannon code. Therein, when interpreting the concept of the perfect cipher, we should talk about the cipher model perfection.The publication place: in the Yandex search engine a query "Perfect ciphers" resulted in 22 million links, on a query "schemes perfectly secret" there were 43 million links. Yandex on the query "random gamming code" gave 13 million results.