A Multivariate Public Key Cryptosystem (MPKC) for Digital Image and Video Encryption Based on Multiple Permutation Polynomials over Finite Fields with a Novel Approach for Secure Key Transmission

The revolutionary idea of a public key cryptosystem has transformed today’s communication system and has added a remarkable contribution to the world of cryptography. The Multivariate Public Key Cryptosystems (MPKCs) are the cryptosystems whose public keys are a set of multivariate polynomials [1]. MPKCs usually have a set of quadratic polynomials over a finite field as its public map. The NP-hardness of the solution of non-linear equations over a finite field is a major security assumption associated with them. MPKCs can prove to be even stronger than quantum computers of the future [2]. This paper presents a novel technique for the encryption of digital images and videos by using multiple multivariate permutation polynomials over finite fields. The strength of any cryptographic scheme is its key. In a polynomial-based encryption scheme, coefficients are used for encryption and hence, they need to be transmitted securely. A new approach for the secure key transmission has been discussed in the paper. It increases the level of complexity to identify the relation between the two keys and makes it almost impossible to crack the private key i.e. the shared secret between communicating parties. The objective of the work reported in this paper is to enhance the strength of the image encryption (the security level) by using multivariate permutation polynomials whose coefficients are unique and transmitting them in a secure manner.