Isogeny based Quantum Resistant Undeniable Blind Signature and Authenticated Encryption Schemes

Abstract

Post-quantum cryptography refers to the study and analysis of cryptographic newlinetechniques that are meant to be secure in the presence of quantum computers. In newlinethe future, digital communication systems need to be secure against an adversary newlinewho has access to quantum hardware. newlineBearing the above need in focus, the research work in this thesis consists of newlinefour contributions in isogeny-based cryptography viz., (i) the undeniable blind newlinesignature scheme, (ii) the authenticated encryption scheme, (iii) an algorithm to newlinesolve generalized root extraction problem and finally (iv) an optimized algorithm newlinefor the undeniable signature scheme proposed by Jao and Soukharev [48]. An newlineabstract of each of these contributions are given below. newlineAn undeniable blind signature scheme (UBSS) based on isogenies between supersingular elliptic curves is proposed. The contribution begins with a formal definition of the notion of an UBSS. A study of its abstract properties and a discussion newlineon its applicability are presented. Based on the generic foundation of UBSS described above, a specific UBSS is constructed. This construction is built upon the newlineundeniable signature scheme proposed by Jao and Soukharev [48]. The proposed newlinescheme is then proved to be quantum secure under certain hardness assumptions. newlineA quantum resistant authenticated encryption scheme is presented. The generic newlineconstruction is based on a suitable modification that combines the classical BellareNamprempre [12] security model for authenticated encryption with Boneh-Zhandry newlineadaptations [15] to provide security in the presence of quantum adversaries. Once newlinethis is formulated, an authenticated encryption scheme based on isogenies between supersingular elliptic curves is presented. This specific scheme has been newlineimplemented for 128-bit security level newline