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

Diana Maimut; George Teseleanu

Paper 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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. SECITC 2020
Keywords: public key encryption quadratic residuosity squared Jacobi symbol gap $2^k$-residuosity provable security biometric authentication protocol
Contact author(s): george teseleanu @ yahoo com
maimut diana @ gmail com
History: 2022-03-15: last of 3 revisions; 2020-11-10: received; See all versions
Short URL: https://ia.cr/2020/1399
License: CC BY

BibTeX

@misc{cryptoeprint:2020/1399,
      author = {Diana Maimut and George Teseleanu},
      title = {A New Generalisation of the Goldwasser-Micali Cryptosystem Based on the Gap $2^k$-Residuosity Assumption},
      howpublished = {Cryptology ePrint Archive, Paper 2020/1399},
      year = {2020},
      note = {\url{https://eprint.iacr.org/2020/1399}},
      url = {https://eprint.iacr.org/2020/1399}
}