batch verification.pdf
batch verification.pdf
batch verification.pdf
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Introduction<br />
ECDSA Algorithm<br />
A Naive Algorithm for ECDSA Batch Verification<br />
A New Batch-<strong>verification</strong> Algorithm for ECDSA (S1)<br />
A More Efficient Batch-<strong>verification</strong> Algorithm (S2)<br />
Efficient Variants of S1 and S2<br />
Experimental Results<br />
Conclusion<br />
References<br />
ECDSA Parameters<br />
ECDSA Algorithms<br />
◮ Generation of ECDSA signature (r, s) on a message M.<br />
1. k = A randomly chosen element in the range [1, n − 1] (the session<br />
key).<br />
2. R = kP.<br />
3. r = x(R) (the x-coordinate of R) reduced modulo n.<br />
4. s = k −1 (H(M) + dr)(mod n) (where H is a cryptographic hash<br />
function like SHA-1).<br />
◮ Verification of ECDSA signature (r, s) on a message M.<br />
1. w = s −1 (mod n).<br />
2. u = H(M)w (mod n).<br />
3. v = rw (mod n).<br />
4. R = uP + vQ.<br />
5. Accept the signature if and only if x(R) = r (mod n).<br />
Sabyasachi Karati<br />
Batch Verification of ECDSA Signatures AfricaCrypt 2012 Ifrane, Morocco