Welcome to the resource topic for 2005/276
Title:
Use of Sparse and/or Complex Exponents in Batch Verification of Exponentiations
Authors: Jung Hee Cheon, Dong Hoon Lee
Abstract:Modular exponentiation in an abelian group is one of the most
frequently used mathematical primitives in modern cryptography.
{\em Batch verification} is to verify many exponentiations
simultaneously. We propose two fast batch verification algorithms.
The first one makes use of exponents with small weight, called
{\em sparse exponents}, which is asymptotically 10 times faster
than the individual verification and twice faster than the
previous works without security loss. The second one is applied
only to elliptic curves defined over small finite fields. Using
sparse Frobenius expansion with small integer coefficients, we
propose a complex exponent test which is four times faster than
the previous works. For example, each exponentiation in one batch
requires asymptotically 9 elliptic curve additions in some
elliptic curves for 2^{80} security.
ePrint: https://eprint.iacr.org/2005/276
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