## Cryptology ePrint Archive: Report 2020/1399

A New Generalisation of the Goldwasser-Micali Cryptosystem Based on the Gap $2^k$-Residuosity Assumption

Diana Maimut and George Teseleanu

Abstract: We present a novel public key encryption scheme that enables users to exchange many bits messages by means of \emph{at least} two large prime numbers in a Goldwasser-Micali manner. Our cryptosystem is in fact a generalization of the Joye-Libert scheme (being itself an abstraction of the first probabilistic encryption scheme). We prove the security of the proposed cryptosystem in the standard model (based on the gap $2^k$-residuosity assumption) and report complexity related facts. We also describe an application of our scheme to biometric authentication and discuss the security of our suggested protocol. Last but not least, we indicate several promising research directions.

Category / Keywords: public-key cryptography / public key encryption, quadratic residuosity, squared Jacobi symbol, gap $2^k$-residuosity, provable security, biometric authentication protocol

Original Publication (in the same form): SECITC 2020

Date: received 10 Nov 2020, last revised 10 Nov 2020

Contact author: george teseleanu at yahoo com, maimut diana@gmail com

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2020/1399

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