In cryptography

Cryptography

Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

, the strong RSA assumption states that the RSA problem

RSA problem

In cryptography, the RSA problem summarizes the task of performing an RSA private-key operation given only the public key. The RSA algorithm raises a message to an exponent, modulo a composite number N whose factors are not known. As such, the task can be neatly described as finding the eth roots...

 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

Digital signature

A digital signature or digital signature scheme is a mathematical scheme for demonstrating the authenticity of a digital message or document. A valid digital signature gives a recipient reason to believe that the message was created by a known sender, and that it was not altered in transit...

 schemes provably secure

Provable security

In cryptography, a system has provable security if its security requirements can be stated formally in an adversarial model, as opposed to heuristically, with clear assumptions that the adversary has access to the system as well as enough computational resources...

 against existential forgery without resorting to the random oracle model.