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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 Algorithm S1 ′ Algorithm S2 ′ ◮ Replace the starting equation φ = R x − α of Algorithm S2 ′ with ◮ Then repeatedly eliminate y 1 , y 2 , . . . , y t . φ = x(R (1) ) − x(R (2) ). (13) ◮ Initial expression of φ contains much less number of monomials than in the original Algorithm S2. ◮ Elimination of y 1 makes φ almost full through introduction of many new monomials in φ. ◮ The theoretical running time of S2 ′ , same as that of S2, is Θ(mt 2 ) field operations. ◮ Still, the effects of our heuristic are clearly noticeable in practical implementations. ◮ Call this efficient variant of S2 as S2 ′ . 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 Experimental Results ◮ Implemented using the GP/PARI calculator. ◮ Choice of this implementation platform is dictated by 1. the symbolic-computation facilities. 2. an easy user interface ◮ All experiments are carried out in ◮ a 2.33 MHz Xeon server. ◮ Mandriva Linux Version 2010.1. ◮ The GNU C compiler 4.4.3 is used for compiling the GP/PARI calculator. Sabyasachi Karati Batch Verification of ECDSA Signatures AfricaCrypt 2012 Ifrane, Morocco
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