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Given a CM sextic field K, we give an explicit method for finding and constructing all genus 3 hyperelliptic curves whose Jacobians have complex multiplication by the maximal order of this field. Our ...
Generating Pairing-friendly Parameters for the CM Construction of Genus 2 Curves over Prime Fields
hyperelliptic curve cryprography pairing-friendly parameters
2010/10/20
We present two contributions in this paper. First, we give a quantitative analysis of the scarcity of pairing-friendly genus 2 curves, assuming the Riemann Hypothesis. This result is an improvement re...
Secure and Efficient HB-CM Entity Authentication Protocol
HB-CM Entity Authentication Protocol HB-CM− protocol GRS attack
2009/9/27
The simple, computationally efficient LPN-based HB-like entity
authentication protocols have attracted a great deal of attention in
the past few years due to the broad application prospect in low-co...
Secure and Efficient HB-CM Entity Authentication Protocol
Secure Efficient HB-CM Entity Authentication Protocol
2009/9/22
The simple, computationally efficient LPN-based HB-like entity
authentication protocols have attracted a great deal of attention in
the past few years due to the broad application prospect in low-co...
We present an algorithm for constructing cryptographic hyperelliptic
curves of genus 2 and p-rank 1, using the CM method. We
also present an algorithm for constructing such curves that, in addition,...
CHOOSING THE CORRECT ELLIPTIC CURVE IN THE CM METHOD
elliptic curves CM method point-counting
2008/8/19
We give easy ways to distinguish between the twists of an ordinary
elliptic curve E over Fp in order to identify one with p + 1 − 2U points, when
p = U2 + dV 2 with 2U, 2V 2 Z and E is constr...