Post-quantum digital signature scheme based on multivariate cubic problem. (August 2020) - Kundu, Nibedita; Debnath, Sumit Kumar; Mishra, Dheerendra; Choudhury, Tanmay
Abstract: Today, with the advent of internet technology, we are looking for e-mechanisms such as e-voting, e-commerce, e-learning, etc., where electronic information are transferred between the entities via the public network. However, e-mechanisms require the support of integrity, authenticity and non-repudiability of the transmitted electronic information. The digital signature is a technique that allows users to attain these parameters during the transmission of information via the public channel. The existing number-theoretic assumption based digital signature schemes is vulnerable to quantum attacks due to the development in a quantum computer. Thus, there is a necessity of quantum computer resistant digital signature scheme, i.e., post-quantum digital signature. Multivariate Public Key Cryptography (MPKC) is one of the most promising candidates of post-quantum cryptography as the MPKC based constructions are computationally fast and need only modest computational resources. In the literature, there are few multivariate digital signature schemes based on Multivariate Quadratic (MQ) problem. However, the design of efficient constructions of digital signature schemes based on higher degree ( > 2) multivariate polynomials is still an open problem. Generally, the question relating to the multivariate polynomials of degree  > 2 is expected to be equally or harder than the quadratic one. In this paper, we have designed a digital signature framework based on Multivariate Cubic (MC) problem to address the issue. The signature size in our scheme is less than all the existing MPKC based signature schemes under the same security assumptions.