A Digital Signature Scheme Secure Against Adaptive Chosen - Message Attacks * ( Revision March 23 , 1995 )

Shafi Goldwasser∗∗ Silvio Micali∗∗ Ronald L. Rivest ∗∗ Abstract We present a digital signature scheme based on the computational difficulty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosen-message attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a way that depends on the signatures of previously chosen messages) can not later forge the signature of even a single additional message. This may be somewhat surprising, since the properties of having forgery being equivalent to factoring and being invulnerable to an adaptive chosen-message attack were considered in the folklore to be contradictory. More generally, we show how to construct a signature scheme with such properties based on the existence of a “claw-free” pair of permutations – a potentially weaker assumption than the intractibility of integer factorization. The new scheme is potentially practical: signing and verifying signatures are reasonably fast, and signatures are compact.