A new distributed primality test for shared RSA keys using quadratic fields

Ingrid Biehl, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


In the generation method for RSA-moduli proposed by Boneh and Franklin in [BF97] the partial signing servers generate random shares pi, qi and compute as candidate for an RSA-modulus n = pq where p = (Ʃ pi) and q = (Ʃ qi). Then they perform a time-consuming distributed primality test which simultaneously checks the primality both of p and q by computing g(p−1)(q−1) = 1 mod n. The primality test proposed in [BF97] cannot be generalized to products of more than two primes. A more complicated one for products of three primes was presented in [BH98]. In this paper we propose a new distributed primality test, which can independently prove the primality of p or q for the public modulus n = pq and can be easily generalized to products of arbitrarily many factors, i.e., the Multi-Prime RSA of PKCS #1 v2.0 Amendment 1.0 [PKCS]. The proposed scheme can be applied in parallel for each factor p and q. We use properties of the group Cl(−8n2), which is the class group of the quadratic field with discriminant −8n2. As it is the case with the Boneh-Franklin protocol our protocol is (formula presented)-private, i.e. less than (formula presented) colluding servers cannot learn any information about the primes of the generated modulus. The security of the proposed scheme is based on the intractability of the discrete logarithm problem in Cl(−8n2) and on the intractability of a new number theoretic problem which seems to be intractable too.

Original languageEnglish
Title of host publicationInformation Security and Privacy - 7th Australasian Conference, ACISP 2002, Proceedings
EditorsLynn Batten, Jennifer Seberry
PublisherSpringer Verlag
Number of pages16
ISBN (Print)3540438610, 9783540438618
Publication statusPublished - 2002
Externally publishedYes
Event7th Australasian Conference on Information Security and Privacy, ACISP 2002 - Melbourne, Australia
Duration: Jul 3 2002Jul 5 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other7th Australasian Conference on Information Security and Privacy, ACISP 2002

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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