Abstract
This paper describes an algorithm for secure transmission of information via open communication channels based on the discrete logarithm problem. The proposed algorithm also provides sender identification (digital signature). It is twice as fast as the RSA algorithm and requires fifty per cent fewer exponentiations than the ElGamal cryptosystems. In addition, the algorithm requires twice less bandwidth than the ElGamal algorithm. Numerical examples illustrate all steps of the proposed algorithm: system design (selection of private and public keys), encryption, transmission of information, decryption and information recovery.
Highlights
This paper describes a protocol for secure transmission of information that resembles the RSA algorithm [1].the crypto-immunity of the proposed protocol is not based on computational complexity of integer factorization
This paper describes an algorithm for secure transmission of information via open communication channels based on the discrete logarithm problem
Hardness of its cryptanalysis is based on the computational complexity of a discrete logarithm problem (DLP) [2,3] if the base g is a generator in modular arithmetic with prime modulus p
Summary
This paper describes a protocol for secure transmission of information that resembles the RSA algorithm [1]. The crypto-immunity of the proposed protocol is not based on computational complexity of integer factorization. Hardness of its cryptanalysis is based on the computational complexity of a discrete logarithm problem (DLP) [2,3] if the base g is a generator in modular arithmetic with prime modulus p. Definition1.1: A prime integer p is called a safe prime if q : p 1 2. Are examples of safe primes: 44618543, 64542503, 171534179, 1111127819, 2176078679, 2382062063. As it is demonstrated in [4], if p is a safe prime, the computation of a generator g is a computationally fast procedure
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