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Algorithm S2 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 Analysis of Algorithm S2 ◮ It was designed in order to avoid the linearization stage (O(m 2 t) field operations) and the Gaussian-elimination stage of Algorithm S1. ◮ Determine each y i correctly up to multiplication by ±1. ◮ Multivariate equation (linear in y i ) can be written as uy i + v = 0 (where u, v are polynomials in y 1 , . . . , y i−1 , y i+1 , . . . , y t ). ◮ Multiplying this equation by uy i − v so that ±y i satisfy u 2 yi 2 − v 2 = ui 2(r i 3 + ar i + b) − vi 2 = 0 [∵ yi 2 = ri 3 + ar i + b]. ◮ Like Algorithm S1, symbolically compute R = ∑ t i=1 R i = (R x , R y ) to arrive the multivariate equation R x − α = 0. ◮ First eliminate y 1 , and use substitution given by Eqn (3) for i = 2, 3, . . . , t to arrive at a linear multivariate equation in y 2 , y 3 , . . . , y t . ◮ Eliminate y i for i = 2, 3, . . . , t, using the same method. ◮ If the polynomial reduces to zero, accepts 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 Analysis of Algorithm S2 Analysis of Algorithm S2 1. Running Time: The time complexity of Algorithm S2 is O(mt 2 ) field operations, which is significantly better than the O(m 3 ) operations needed by Algorithm S1. Moreover, Algorithm S2 outperforms Algorithm N for a wide range of t and q. 2. Security Analysis: It was proved that Algorithm S2 is as secure as ECDSA* batch verification. Sabyasachi Karati Batch Verification of ECDSA Signatures AfricaCrypt 2012 Ifrane, Morocco
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