Strong RSA assumption

In cryptography, the strong RSA assumption states that the RSA problem is intractable even when the solver is allowed to choose the public exponent e (for e ≥ 3). More specifically, given a modulus N of unknown factorization, and a ciphertext C, it is infeasible to find any pair (M, e) such that C ≡ M ^e mod N.

The strong RSA assumption was first used for constructing signature schemes provably secure against existential forgery without resorting to the random oracle model.

References

• Niko Barić and Birgit Pfitzmann. Collision-free accumulators and failstop signature schemes without trees. In Advances in Cryptology— EUROCRYPT ’97, volume 1233 of Lecture Notes in Computer Science, pages 480–494. Springer-Verlag, 1997.
• Eiichiro Fujisaki and Tatsuaki Okamoto. Statistical zero knowledge protocols to prove modular polynomial relations. In Burton S. Kaliski Jr., editor, Proc. CRYPTO ’97, volume 1294 of LNCS, pages 16–30. Springer-Verlag, 1997.
• Ronald Cramer and Victor Shoup. Signature schemes based on the strong RSA assumption. ACM Transactions on Information and System Security, 3(3):161–185, 2000. pdf file
• Ronald L. Rivest and Burt Kaliski. RSA Problem. pdf file