Design of lattice‐based ElGamal encryption and signature schemes using SIS problem

Abstract

AbstractThe emerging technologies like quantum computing and cloud computing have a complex computing power and can break the security of the classical cryptographic constructions (like ElGamal's cryptosystem). Thus, we were motivated to work on hard lattice problems, which are more complex and can resist these new modern technologies. In this proposal, we present a lattice‐based version of discrete logarithm problem‐based ElGamal public‐key encryption and signature schemes that exhibit strong security features and efficient implementation. The security of these presented schemes is based on the worst‐case hardness of approximating a small integer vector in their corresponding lattice. Furthermore, this proposed work illustrates a security proof of the proposed schemes and shows that the presented schemes are well protected in the modern computing environment. The performance analysis and comparison with classical ElGamal schemes and recent lattice‐based schemes are also made, and it is seen that the proposed schemes achieve better performance.