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

Public-key cryptography

Algorithms

Integer Factorization	Benaloh Blum–Goldwasser Cayley–Purser Damgård–Jurik GMR Goldwasser–Micali Paillier Rabin RSA Okamoto–Uchiyama Schmidt–Samoa

Discrete logarithm	Cramer–Shoup DH DSA ECDH ECDSA EdDSA EKE ElGamal signature scheme MQV Schnorr SPEKE SRP STS

Others	AE CEILIDH EPOC HFE IES Lamport McEliece Merkle–Hellman Naccache–Stern Naccache–Stern knapsack cryptosystem NTRUEncrypt NTRUSign Three-pass protocol XTR

Theory

Standardization

Topics

Cryptography

History of cryptography Cryptanalysis Outline of cryptography

Symmetric-key algorithm Block cipher Stream cipher Public-key cryptography Cryptographic hash function Message authentication code Random numbers Steganography

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