On Black-Box Ring Extraction and Integer Factorization

Kristina Altmann; Tibor Jager; Andy Rupp

Paper 2008/156

On Black-Box Ring Extraction and Integer Factorization

Kristina Altmann, Tibor Jager, and Andy Rupp

Abstract

The black-box extraction problem over rings has (at least) two important interpretations in cryptography: An efficient algorithm for this problem implies (i) the equivalence of computing discrete logarithms and solving the Diffie-Hellman problem and (ii) the in-existence of secure ring-homomorphic encryption schemes. In the special case of a finite field, Boneh/Lipton and Maurer/Raub showed that there exist algorithms solving the black-box extraction problem in subexponential time. It is unknown whether there exist more efficient algorithms. In this work we consider the black-box extraction problem over finite rings of characteristic $n$, where $n$ has at least two different prime factors. We provide a polynomial-time reduction from factoring $n$ to the black-box extraction problem for a large class of finite commutative unitary rings. Under the factoring assumption, this implies the in-existence of certain efficient generic reductions from computing discrete logarithms to the Diffie-Hellman problem on the one side, and might be an indicator that secure ring-homomorphic encryption schemes exist on the other side.

Note: This is an extended version of the paper with the same title that appeared in the proceedings of ICALP 2008.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Black Box Extraction Problem Integer Factorization Homomorphic Encryption
Contact author(s): tibor jager @ rub de
History: 2008-07-06: last of 2 revisions; 2008-04-08: received; See all versions
Short URL: https://ia.cr/2008/156
License: CC BY

BibTeX

@misc{cryptoeprint:2008/156,
      author = {Kristina Altmann and Tibor Jager and Andy Rupp},
      title = {On Black-Box Ring Extraction and Integer Factorization},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/156},
      year = {2008},
      url = {https://eprint.iacr.org/2008/156}
}