Commutative Ciphers Based on Difficulty of Simultaneous Solving Factorization and Discrete Logarithm Problems
Keywords:
Computer Security, Cryptography, Commutative Encryption, Factorization Problem, Discrete LogarithmAbstract
Purpose: There are well-known public-key cryptoscheme designs whose breaking requires a simultaneous solution of two independent computationally hard problems. This makes the cryptoscheme security higher; however, similar designs for commutative encryption algorithms are unknown. The practical significance of improving security of cryptographic mechanisms in information protection makes it vital to look for breakthrough innovations in solving computationally hard problems. This paper deals with developing commutative ciphers whose breaking requires a simultaneous solution of two independent computationally hard problems. Methods: Splitting the encrypted messages and using one-pad encryption keys. Results: For the first time a message-splitting method was proposed which extends the class of computationally hard problems applicable to commutative encryption design. A new commutative cipher was developed, based on the factoring problem, along with a new commutative cipher based on the difficulty of simultaneously solving both a factoring problem and a discrete logarithm problem in the finite field. The requirements were formulated for the selection of the parameters for the proposed algorithms. Practical relevance: Essential improvement was provided for the commutative encryption security.