Provable security of digital signatures in the tamper-proof device model

Proofs of security for practical signature schemes are known in idealised models only. In the present paper, we consider the tamper-proof device model that does not use ideal primitives. Instead of access to a random oracle each participant is provided with tamper-proof device implementing a private-key cryptosystem. The hash-value of a message to be signed is submitted to the tamper-proof device for encryption and this encrypted value is used in the signature generation algorithm. In this model, we prove, modulo a physical assumption, a necessary and sufficient condition for security of the GOST signature scheme.