Diffie-Hillman is as Strong as Discrete Log for Certain Primes
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Algorithms
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Algorithms for Black-Box Fields and their Application to Cryptography (Extended Abstract)
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Discrete Logarithms and Factoring
Discrete Logarithms and Factoring
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Black-box extension fields and the inexistence of field-homomorphic one-way permutations
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
On the equivalence of RSA and factoring regarding generic ring algorithms
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Automorphisms of finite rings and applications to complexity of problems
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Abstract models of computation in cryptography
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
On the Equivalence of Generic Group Models
ProvSec '08 Proceedings of the 2nd International Conference on Provable Security
On the Analysis of Cryptographic Assumptions in the Generic Ring Model
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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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 [1] and Maurer/ Raub [2] show 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 nhas at least two different prime factors. We provide a polynomial-time reduction from factoring nto 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.