Asymptotic secrecy of the information protection by the usage of simple integer splitting method

Abstract

The integer splitting method is a special method that is used to encrypt the text. In this method, each text character is represented as an integer in accordance with the selected code table after that this integer is replaced on the base of another number with a sequence of k integers (k-splitting level) and this is performed by the usage of modular arithmetic. This article studies the property of asymptotic secrecy of the simple integer splitting method when it is used in the field of cryptography; the research is conducted from the point view of the hacker. The purpose of using integer splitting method is to increase the level of security and provide the ability to control the degree of protection of information. So a lemma was proven in this article and as a conclusion we can notice that the more usage of the splitting level leads to the more level of safety and protection of information.

The quantitative comparison between the integer splitting cipher and the traditional gamma cipher

“…Of all the attempts to restore the plaintext M , only one case will give a meaningful plaintext that matches what is encrypted by the sender. This is a situation where the selected keys on the attacker's side match the same keys that were used by the sender during the encryption process of the plaintext [6,8]. So, this leads to the fact that the number of correct extractions of a meaningful text, which meets the plaintext, is equal to one.…”

“…As discussed previously, only one case will produce a meaningful plaintext that matches what is encrypted by the sender. This is a case when the selected gammas on the attacker's side match the same gammas that are used by the sender's side when encrypting the plaintext [6,8]. So…”