On Using Expansions to the Base of -2

This short note investigates the effects of using expansions to the base of -2. The main applications we have in mind are cryptographic protocols, where the crucial operation is computation of scalar multiples. For the recently proposed groups arising from Picard curves this leads to a saving of at least 7% for the computation of an m-fold. For more general non-hyperelliptic genus 3 curves we expect a larger speed-up.Comment: 5 page

Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes

We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate by projecting to the x-line or Kummer surface, where we can exploit faster and more uniform pseudomultiplication, before recovering the proper "signed" output back on the curve or Jacobian. This extends the work of L{\'o}pez and Dahab, Okeya and Sakurai, and Brier and Joye to genus 2, and also to two-dimensional scalar multiplication. Our results show that many existing fast pseudomultiplication implementations (hitherto limited to applications in Diffie--Hellman key exchange) can be wrapped with simple and efficient pre-and post-computations to yield competitive full scalar multiplication algorithms, ready for use in more general discrete logarithm-based cryptosystems, including signature schemes. This is especially interesting for genus 2, where Kummer surfaces can outperform comparable elliptic curve systems. As an example, we construct an instance of the Schnorr signature scheme driven by Kummer surface arithmetic

A Survey Report On Elliptic Curve Cryptography

The paper presents an extensive and careful study of elliptic curve cryptography (ECC) and its applications. This paper also discuss the arithmetic involved in elliptic curve  and how these curve operations is crucial in determining the performance of cryptographic systems. It also presents  different forms of elliptic curve in various coordinate system , specifying which is most widely used and why. It also explains how isogenenies between elliptic curve  provides the secure ECC. Exentended form of elliptic curve i.e hyperelliptic curve has been presented here with its pros and cons. Performance of ECC and HEC is also discussed based on scalar multiplication and DLP. Keywords: Elliptic curve cryptography (ECC), isogenies, hyperelliptic curve (HEC) , Discrete Logarithm Problem (DLP), Integer  Factorization , Binary Field, Prime FieldDOI:http://dx.doi.org/10.11591/ijece.v1i2.8

Proxy Blind Signature using Hyperelliptic Curve Cryptography

Blind signature is the concept to ensure anonymity of e-coins. Untracebility and unlinkability are two main properties of real coins and should also be mimicked electronically. A user has to fulll above two properties of blind signature for permission to spend an e-coin. During the last few years, asymmetric cryptosystems based on curve based cryptographiy have become very popular, especially for embedded applications. Elliptic curves(EC) are a special case of hyperelliptic curves (HEC). HEC operand size is only a fraction of the EC operand size. HEC cryptography needs a group order of size at least 2160. In particular, for a curve of genus two eld Fq with p 280 is needeed. Therefore, the eld arithmetic has to be performed using 80-bit long operands. Which is much better than the RSA using 1024 bit key length. The hyperelliptic curve is best suited for the resource constraint environments. It uses lesser key and provides more secure transmisstion of data

1. Kryptotag - Workshop über Kryptographie

Der Report enthält eine Sammlung aller Beiträge der Teilnehmer des 1. Kryptotages am 1. Dezember 2004 in Mannheim