Securuty of modified digital public-key signature EdDSA

Abstract

The Ukrainian National Standard for Digital Signature DSTU 4145-2002 has been in use about 17 years. During this time, significant changes have occurred in the field of information technology, which directly affect the implementation of the current National Standard for Digital Signature DSTU 4145-2002 and indicate the need for its modernization.

Due to the need to revise and update national digital signature standard DSTU 4145-2002, the authors considered several digital signature constructions. Among the requirements to modern public-key signatures it is worth to highlight at least 128-bit security, fast signing and fast signature verification, fast keys generation, foolproof session keys, collision resistance, secure software implementation, etc. There are a lot of obvious variants in classic and elliptic signature systems, ElGamal, Schnorr`s, ECDSA, etc, which can be used in transitional to post quantum period.

This paper introduces one of possible modifications for signature schemes based on the Edwards-curve Digital Signature Algorithm (EdDSA). The main advantages of the modification proposed in this work are:
1) the signature scheme is secure even if the session key generator fails;
2) signature implementation time does not depend on message length;
3) security against related-key attacks.