Journal of Cryptology
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Speeding up the Arithmetic on Koblitz Curves of Genus Two
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
Supersingular Curves in Cryptography
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
ISC '01 Proceedings of the 4th International Conference on Information Security
An algorithm for solving the discrete log problem on hyperelliptic curves
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Finite Fields and Their Applications
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
IEEE Transactions on Computers
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Effects of Optimizations for Software Implementations of Small Binary Field Arithmetic
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
A new scalar multiplication method suitable for hyperelliptic curve cryptosystems
ICACT'09 Proceedings of the 11th international conference on Advanced Communication Technology - Volume 3
Delaying and merging operations in scalar multiplication: applications to curve-based cryptosystems
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Efficient divisor class halving on genus two curves
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Towards minimizing memory requirement for implementation of hyperelliptic curve cryptosystems
ISPEC'07 Proceedings of the 3rd international conference on Information security practice and experience
Another look at square roots (and other less common operations) in fields of even characteristic
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
The 2-adic CM method for genus 2 curves with application to cryptography
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Superscalar coprocessor for high-speed curve-based cryptography
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
A complete divisor class halving algorithm for hyperelliptic curve cryptosystems of genus two
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Efficient doubling on genus 3 curves over binary fields
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
New families of hyperelliptic curves with efficient gallant-lambert-vanstone method
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
SPA resistant left-to-right integer recodings
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Halving for the 2-Sylow subgroup of genus 2 curves over binary fields
Finite Fields and Their Applications
Algebraic curves and cryptography
Finite Fields and Their Applications
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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In most algorithms involving elliptic and hyperelliptic curves, the costliest part consists in computing multiples of ideal classes. This paper investigates how to compute faster doubling over fields of characteristic two. We derive explicit doubling formulae making strong use of the defining equation of the curve. We analyze how many field operations are needed depending on the curve making clear how much generality one loses by the respective choices. Note, that none of the proposed types is known to be weak – one only could be suspicious because of the more special types. Our results allow to choose curves from a large enough variety which have extremely fast doubling needing only half the time of an addition. Combined with a sliding window method this leads to fast computation of scalar multiples. We also speed up the general case.