Methods of digital signature truncation for El-Gamal-type signatures and for DSTU 4145-2002.

Abstract

Digital signature truncation is important for implementing cryptographic systems for low-resource devices, particularly in systems where signatures are stored for a long term but are checked relatively infrequently. Among such systems we can mention hardware audit logs or secure document repositories. Signature truncation can also be used in cases where memory is limited to represent or store the signature itself (for example, in QR codes). Signature truncation methods for ECDSA and EdDSA standards were proposed in public sources. This paper proposes a method of truncation of digital signatures for the classical El-Gamal scheme and some of its generalizations, which are based on modular arithmetic. The proposed methods do not require any alternations in the signing procedure, and are therefore applicable to arbitrary existing implementations of the El-Gamal scheme; the restoration of a digital signature occurs at the expense of an increase in computational costs on the part of the party verifying the signature. A digital signature truncation method for the national standard DSTU 4145-2002 is also proposed; this method takes into account the properties of the arithmetic of elliptic curves, on which the standard is based. The proposed methods make it possible to effectively implement the truncation of signatures of the El-Gamal type (especially noticeable for DSTU 4145-2002 signatures), discarding up to 32 bits of signature, but the complexity of the verification increases rapidly with the increase in the discarded part of the signature. However, for selected limits of the length of the discarded part, the proposed algorithms have a relatively efficient implementation and therefore can be used to reduce the length of signatures in protocols for low-resource devices.