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.
Category / Keywords: public-key cryptography / Black Box Extraction Problem, Integer Factorization, Homomorphic Encryption Date: received 7 Apr 2008, last revised 6 Jul 2008 Contact author: tibor jager at rub de Available formats: PDF | BibTeX Citation Note: This is an extended version of the paper with the same title that appeared in the proceedings of ICALP 2008.
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