Speeding-up verification of digital signatures

• Published in: Journal of computer and system sciences Vol. 116; pp. 22 - 39
• Main Authors: Taleb, Abdul Rahman, Vergnaud, Damien
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.03.2021; Elsevier
• Subjects: Computer Science; Cryptography and Security; Digital signatures; ECDSA signatures; GPV signatures; Probabilistic verification; Public-key cryptography; RSA signatures; GPV signatures; Probabilistic verification; Public-key cryptography; Digital signatures; ECDSA signatures; RSA signatures; Probabilistic Verification; Public-Key Cryptography; Digital Signatures; RSA Signatures; ECDSA Signatures; GPV Signatures
• ISSN: 0022-0000; 1090-2724
• DOI: 10.1016/j.jcss.2020.08.005

In 2003, Fischlin introduced the concept of progressive verification in cryptography to relate the error probability of a cryptographic verification procedure to its running time. It ensures that the verifier confidence in the validity of a verification procedure grows with the work it invests in the computation. Le, Kelkar and Kate recently revisited this approach for digital signatures and proposed a similar framework under the name of flexible signatures. We propose efficient probabilistic verification procedures for popular signature schemes in which the error probability of a verifier decreases exponentially with the verifier running time. We propose theoretical schemes for the RSA and ECDSA signatures based on some elegant idea proposed by Bernstein in 2000 and some additional tricks. We also present a general practical method, that makes use of efficient error-correcting codes, for signature schemes for which verification involves a matrix/vector multiplication.