In this paper is demonstrated a method for reduction of integer factorization problem to an analysis of a sequence of modular elliptic equations. As a result, the paper provides a non-deterministic algorithm that comp...In this paper is demonstrated a method for reduction of integer factorization problem to an analysis of a sequence of modular elliptic equations. As a result, the paper provides a non-deterministic algorithm that computes a factor of a semi-prime integer n=pq, where prime factors p and q are unknown. The proposed algorithm is based on counting points on a sequence of at least four elliptic curves y2=x(x2+b2)(modn) , where b is a control parameter. Although in the worst case, for some n the number of required values of parameter b that must be considered (the number of basic steps of the algorithm) substantially exceeds four, hundreds of computer experiments indicate that the average number of the basic steps does not exceed six. These experiments also confirm all important facts discussed in this paper.展开更多
A hybrid cryptographic system providing digital authentication is described and analyzed in this paper. The proposed cryptosystem incorporates three features: complexity of the discrete logarithm problem, complexity o...A hybrid cryptographic system providing digital authentication is described and analyzed in this paper. The proposed cryptosystem incorporates three features: complexity of the discrete logarithm problem, complexity of integer factorization of a product of two large primes and a combination of symmetric and asymmetric keys. In order to make the cryptosystem less vulnerable to cryptanalytic attacks a concept of digital entanglements is introduced. As a result, the proposed cryptographic system has four layers (entanglement-encryption- decryption-disentanglement). It is shown that in certain instances the proposed communication cryptocol is many times faster than the RSA cryptosystem. Examples provided in the paper illustrate details of the proposed authentication cryptocol.展开更多
文摘In this paper is demonstrated a method for reduction of integer factorization problem to an analysis of a sequence of modular elliptic equations. As a result, the paper provides a non-deterministic algorithm that computes a factor of a semi-prime integer n=pq, where prime factors p and q are unknown. The proposed algorithm is based on counting points on a sequence of at least four elliptic curves y2=x(x2+b2)(modn) , where b is a control parameter. Although in the worst case, for some n the number of required values of parameter b that must be considered (the number of basic steps of the algorithm) substantially exceeds four, hundreds of computer experiments indicate that the average number of the basic steps does not exceed six. These experiments also confirm all important facts discussed in this paper.
文摘A hybrid cryptographic system providing digital authentication is described and analyzed in this paper. The proposed cryptosystem incorporates three features: complexity of the discrete logarithm problem, complexity of integer factorization of a product of two large primes and a combination of symmetric and asymmetric keys. In order to make the cryptosystem less vulnerable to cryptanalytic attacks a concept of digital entanglements is introduced. As a result, the proposed cryptographic system has four layers (entanglement-encryption- decryption-disentanglement). It is shown that in certain instances the proposed communication cryptocol is many times faster than the RSA cryptosystem. Examples provided in the paper illustrate details of the proposed authentication cryptocol.
