On the equivalence of RSA and factoring regarding generic ring algorithms

Authors:
Gregor Leander;Andy Rupp
Affiliations:
Horst-Görtz Institute for IT-Security, Ruhr-University Bochum, Germany;Horst-Görtz Institute for IT-Security, Ruhr-University Bochum, Germany
Venue:
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Year:
2006

Citing 3
Cited 5

A method for obtaining digital signatures and public-key cryptosystems

Communications of the ACM
Generic Lower Bounds for Root Extraction and Signature Schemes in General Groups

EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Lower bounds for discrete logarithms and related problems

EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques

On Black-Box Ring Extraction and Integer Factorization

ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
On the Equivalence of Generic Group Models

ProvSec '08 Proceedings of the 2nd International Conference on Provable Security
Breaking RSA Generically Is Equivalent to Factoring

EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
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
Solving systems of modular equations in one variable: how many RSA-encrypted messages does eve need to know?

PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography

Quantified Score

Hi-index	0.00

Visualization

Abstract

To prove or disprove the computational equivalence of solving the RSA problem and factoring integers is a longstanding open problem in cryptography. This paper provides some evidence towards the validity of this equivalence. We show that any efficient generic ring algorithm which solves the (flexible) low-exponent RSA problem can be converted into an efficient factoring algorithm. Thus, the low-exponent RSA problem is intractable w.r.t. generic ring algorithms provided that factoring is hard.