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Introduction ECDSA Algorithm A Naive Algorithm for ECDSA Batch Verification A New Batch-verification Algorithm for ECDSA (S1) A More Efficient Batch-verification Algorithm (S2) Efficient Variants of S1 and S2 Experimental Results Conclusion References ECDSA Batch Verification Algorithm N 1. Compute w i = s −1 i (mod n) for all i = 1, 2, . . . , t. 2. Compute u i = H(M i )w i (mod n) for all i = 1, 2, . . . , t. 3. Compute v i = r i w i (mod n) for all i = 1, 2, . . . , t. 4. Compute R ′ = ( ∑ t i=1 u i)P + ∑ t i=1 v iQ i ∈ E(F q ). Club together the points Q i from same signers during the computation of R ′ . For example, if all the signatures belong to the same signer, compute R ′ as ( ∑ t i=1 u i)P + ( ∑ t i=1 v i)Q. 5. For each i = 1, 2, . . . , t, if ri 3 + ar i + b is neither zero nor a quadratic residue modulo q, reject the i-th signature, and remove it from the batch. 6. For i = 1, . . . , t, compute the square roots of ri 3 + ar i + b modulo q. 7. For each square root y i of ri 3 + ar i + b for all i = 1, 2, . . . , t,if R ′ = ∑ t i=1 (r i, y i ), accept all the signatures. 8. Reject all the signatures. Sabyasachi Karati Batch Verification of ECDSA Signatures AfricaCrypt 2012 Ifrane, Morocco
Introduction ECDSA Algorithm A Naive Algorithm for ECDSA Batch Verification A New Batch-verification Algorithm for ECDSA (S1) A More Efficient Batch-verification Algorithm (S2) Efficient Variants of S1 and S2 Experimental Results Conclusion References ECDSA Batch Verification Algorithm N ′ ◮ A single extra bit of information in an ECDSA signature can remove the ambiguity. ◮ Avoid the Θ(2 t ) overhead. ◮ This updated (and efficient) version of the naive algorithm will henceforth be denoted by Algorithm N ′ . Sabyasachi Karati Batch Verification of ECDSA Signatures AfricaCrypt 2012 Ifrane, Morocco
Page 1 and 2: Introduction ECDSA Algorithm A Naiv
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Page 25 and 26: Algorithm S1 ′ Introduction ECDSA
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