Biblio

In this work NTRU-like cryptosystem NTRU Prime IIT Ukraine, which is created on the basis of existing cryptographic transformations end-to-end encryption type, is considered. The description of this cryptosystem is given and its analysis is carried out. Also, features of its implementation, comparison of the main characteristics and indicators, as well as the definition of differences from existing NTRU-like cryptographic algorithms are presented. Conclusions are made and recommendations are given.

The importance of the task of countering the means of unauthorized access is to preserve the integrity of restricted access information circulating in computer networks determines the relevance of investigating perspective methods of cryptographic transformations, which are characterized by high speed and reliability of encryption. The methods of information security in the telecommunication system were researched based on integration of encryption processes and noise-immune coding. The method for data encryption based on generic polynomials of cyclic codes, gamut of the dynamic chaos sequence, and timer coding was proposed. The expediency of using timer coding for increasing the cryptographic strength of the encryption system and compensating for the redundancy of the verification elements was substantiated. The method for cryptographic transformation of data based on the gamma sequence was developed, which is formed by combining numbers from different sources of dynamical chaos generators. The efficiency criterion was introduced for the integrated information transformation method.

The modular exponentiation is an important operation for cryptographic transformations in public key cryptosystems like the Rivest, Shamir and Adleman, the Difie and Hellman and the ElGamal schemes. computing ax mod n and axby mod n for very large x,y and n are fundamental to the efficiency of almost all pubic key cryptosystems and digital signature schemes. To achieve high level of security, the word length in the modular exponentiations should be significantly large. The performance of public key cryptography is primarily determined by the implementation efficiency of the modular multiplication and exponentiation. As the words are usually large, and in order to optimize the time taken by these operations, it is essential to minimize the number of modular multiplications. In this paper we are presenting efficient algorithms for computing ax mod n and axbymod n. In this work we propose four algorithms to evaluate modular exponentiation. Bit forwarding (BFW) algorithms to compute ax mod n, and to compute axby mod n two algorithms namely Substitute and reward (SRW), Store and forward(SFW) are proposed. All the proposed algorithms are efficient in terms of time and at the same time demands only minimal additional space to store the pre-computed values. These algorithms are suitable for devices with low computational power and limited storage.