Speeding-Up Verification of Digital Signatures

Abdul Rahman Taleb (1, 2) , Damien Vergnaud (3, 2)

1 CryptoExperts
2 ALMASTY - ALgorithms for coMmunicAtion SecuriTY
3 IUF - Institut universitaire de France

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 ver-ifier 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.

Mots clés: Public-Key Cryptography; Digital Signatures; Probabilistic Verification; RSA Signatures; ECDSA Signatures; GPV Signatures

Domaines: Cryptographie et sécurité [cs.CR]

Abdul Rahman Taleb, Damien Vergnaud. Speeding-Up Verification of Digital Signatures. Journal of Computer and System Sciences, 2021, 116, pp.22-39. ⟨10.1016/j.jcss.2020.08.005⟩. ⟨hal-02934136⟩