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Fast Scalar Multiplication for Elliptic Curves over Prime Fields by Efficiently Computable Formulas
twisted Edwards curves Edwards curves scalar multiplication
2018/11/6
This paper addresses fast scalar multiplication for elliptic curves over finite fields. In the first part of the paper, we obtain several efficiently computable formulas for basic elliptic curves arit...
Fast Scalar Multiplication for Elliptic Curves over Binary Fields by Efficiently Computable Formulas
binary elliptic curves point multiplication lambda coordinates
2017/9/7
This paper considers efficient scalar multiplication of elliptic curves over binary fields with a twofold purpose. Firstly, we derive the most efficient 3P3P formula in λλ-projective coordinates and 5...
Privacy-Free Garbled Circuits for Formulas: Size Zero and Information-Theoretic
Garbled Circuits Privacy-free Formula
2017/6/15
Garbled circuits are of central importance in cryptography, finding widespread application in secure computation, zero-knowledge (ZK) protocols, and verifiable outsourcing of computation to name a few...
Implementing Complete Formulas on Weierstrass Curves in Hardware
Elliptic curve cryptography FPGA Weierstrass curves
2016/12/12
This work revisits the recent complete addition formulas for prime order elliptic curves of Renes, Costello and Batina in light of parallelization. We introduce the first hardware implementation of th...
Garbling Scheme for Formulas with Constant Size of Garbled Gates
garbled circuits constant size of garbled gates correlation robustness
2016/6/6
We provide a garbling scheme which creates garbled circuits
of a very small constant size (four bits per gate) for circuits with fanout
one (formulas). For arbitrary fan-out, we additionally need on...
Complete addition formulas for prime order elliptic curves
public-key cryptography elliptic curves short Weierstrass form
2015/12/21
An elliptic curve addition law is said to be complete if it correctly computes the
sum of any two points in the elliptic curve group. One of the main reasons for the increased
popularity of Edwards ...
Analogues of Velu's formulas for Isogenies on Alternate Models of Elliptic Curves
Elliptic curves Isogenies Edwards Curves Huff curves
2012/3/27
Isogenies of elliptic curves have been well-studied, in part because there are several cryptographic applications. Using Velu's formula, isogenies can be evaluated explicitly given their kernel. Howev...
Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation
Explicit Formulas Real Hyperelliptic Curves Affine Representation
2011/3/11
We present a complete set of efficient explicit formulas for arithmetic
in the degree 0 divisor class group of a genus two real hyperelliptic curve
givenin affine coordinates. In addition to formula...
Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation
foundations / hyperelliptic curve, reduced divisor, infrastructure and distance Cantor’s algorithm explicit formulas efficient implementation cryptographic key exchange
2012/3/29
We present a complete set of efficient explicit formulas for arithmetic in the degree 0 divisor class group of a genus two real hyperelliptic curve given in affine coordinates. In addition to formulas...
Faster Explicit Formulas for Computing Pairings over Ordinary Curves
Efficient software implementation explicit formulas bilinear pairings
2010/10/20
We describe efficient formulas for computing pairings on ordinary elliptic curves over prime fields. First, we generalize lazy reduction techniques, previously considered only for arithmetic in quadra...
R. Feng, and H. Wu recently established a certain mean-value formula
for the x-coordinates of the n-division points on an elliptic curve given in
Weierstrass form (A mean value formula for elliptic ...
Efficient Quintuple Formulas for Elliptic Curves and Efficient Scalar Multiplication Using Multibase Number Representation
Elliptic Curve Cryptosystems Scalar Multiplication Quintupling Efficient Curve Arithmetic
2008/9/17
In the current work we propose two efficient formulas for computing the 5-fold (5P) of an elliptic curve point P. One formula is for curves over finite fields of even characteristic and the other is f...
Somos Sequence Near-Addition Formulas and Modular Theta Functions
Somos Sequence Near-Addition Formulas Modular Theta Functions
2008/9/9
We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions.