Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting

Carmit Hazay, Gert Læssøe Mikkelsen, Tal Rabin, Tomas Toft, Angelo Agatino Nicolosi

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first non-generic fully simulatable protocol for distributively generating an RSA composite with security against malicious behavior. Our second contribution is a complete Paillier (in: EUROCRYPT, pp 223–238, 1999) threshold encryption scheme in the two-party setting with security against malicious attacks. We further describe how to extend our protocols to the multiparty setting with dishonest majority. Our RSA key generation protocol is comprised of the following subprotocols: (i) a distributed protocol for generation of an RSA composite and (ii) a biprimality test for verifying the validity of the generated composite. Our Paillier threshold encryption scheme uses the RSA composite for the public key and is comprised of the following subprotocols: (i) a distributed generation of the corresponding secret key shares and (ii) a distributed decryption protocol for decrypting according to Paillier.

Original languageEnglish
Pages (from-to)265-323
Number of pages59
JournalJournal of Cryptology
Volume32
Issue number2
DOIs
StatePublished - 15 Apr 2019

Bibliographical note

Publisher Copyright:
© 2018, International Association for Cryptologic Research.

Keywords

  • Paillier
  • RSA generation
  • Secure two-party computation
  • Threshold encryption scheme

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