Elliptic Curves over Finite Fields
Regular Ternary Algorithm for Scalar Multiplication on Elliptic Curves over Finite Fields of Characteristic Three
... Abstract: In this paper we propose an efficient and regular ternary algorithm for scalar multiplication on elliptic curves over finite fields of characteristic three. This method is ...
7
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
... F p -isogenies. They observed that the graphs G ` ( F p ) have similar ‘volcano’ structures as the ordinary subgraphs of H ` (F p ) [5]. The remainder of the paper is organized as follows. In §2 we provide a concise sum- ...
14
Multiplication in Finite Fields and Elliptic Curves
... kP = P + · · · + P | {z } k times using the group law given by the chord and tangent rules. Specifically, we focus on parallel scalar multiplication of elliptic curve defined over F 2 n and F 3 n . Recent ...
67
A reduction of the space for the parallelized Pollard lambda search on elliptic curves over prime finite fields and on anomalous binary elliptic curves
... [email protected] August 11, 2003 Abstract Let E be an elliptic curve defined over a prime finite field F p by a Weierstrass equation. In this paper we introduce a new partition of E(F p ...
11
Elliptic curves with weak coverings over cubic extensions of finite fields with odd characteristics
... The curves over extension fields could often be desirable in practice for fast and low-cost implementation, especially certain extension fields with good prop- ...extension fields which ...
59
Fast Scalar Multiplication for Elliptic Curves over Prime Fields by Efficiently Computable Formulas
... for elliptic curves over finite ...basic elliptic curves arithmetic in the family of twisted Edwards curves over prime ...
26
On Efficient Pairings on Elliptic Curves over Extension Fields
... of elliptic curve cryptography, three kinds of finite fields have been widely studied, ...friendly curves are usually chosen among ordinary curves over prime fields and ...
17
Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three
... Weierstraß elliptic curves with a point of order 3 and their equivalent Hessian curves over finite fields of characteristic ...ordinary elliptic curves in ...
14
Number of Jacobi quartic curves over finite fields
... Introduction Elliptic curve cryptosystems were proposed by Miller (1986) and by Koblitz (1987) which relies on the difficulty of the elliptic curve discrete logarithmic ...on elliptic curves ...
11
Isomorphism classes of Edwards curves over finite fields
... Y 2 + a 1 XY + a 3 Y = X 3 + a 2 X 2 + a 4 X + a 6 , where the a i are elements in some field F . While other models for elliptic curves have long been known, in the past few years there has been renewed ...
22
On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields
... a finite field, the problem of how best to construct a factor base, and how to express arbitrary elements over such a factor base is well studied [35, 33, ...For finite fields there exists a ...
20
CRYPTOGRAPHIC PROTOCOLS USING ELLIPTIC CURVE OVER FINITE FIELDS
... Keywords: Elliptic Curve Cryptography, public-key, secret key, encryption, decryption ...of elliptic curves by algebraists, algebraic geometers and number theorists dates back to the middle of the ...
6
Efficient Tate Pairing Computation for Supersingular Elliptic Curves over Binary Fields
... the fields with characteristic ...the fields with characteristic ...the finite fields with characteristic ...supersingular elliptic curves defined over the binary field F ...
17
Faster Scalar Multiplication on Ordinary Weierstrass Elliptic Curves over Fields of Characteristic Three
... Abstract. This paper proposes new explicit formulae for the point dou- bling, tripling and addition on ordinary Weierstrass elliptic curves with a point of order 3 over finite fields of ...
18
Generating genus two hyperelliptic curves over large characteristic finite fields
... hyperelliptic curves to be ...to elliptic curves over F q 2 ...random elliptic curve if their group sizes are the ...the elliptic curve case, we can employ early abort strategy ...
16
Modular Elliptic Curves over Quartic CM Fields
... given elliptic curve ...defined over number fields, where we do not know whether all elliptic curves are modular, but where there exist techniques to prove isomorphism of Galois ...
186
Fast Algorithms for Arithmetic on Elliptic Curves Over Prime Fields
... Algorithms 12 and 13 both take d − 1 squarings and H(k) − 1 additions where d is the bit-length of k and H(k) is the Hamming weight (i.e. the number of non-zero digits) of k. H(k) is (d + 1)/2 on average. A more detailed ...
232
Isomorphism Classes of Picard Curves over Finite Fields
... of elliptic and hyperelliptic curves over finite fields has been of interest for construction of cryptosystems based on the discrete logarithm problem, and elliptic curve ...
10
Fast hashing onto elliptic curves over fields of characteristic 3
... supersingular elliptic curves over F 3 m , and it depends on the existence of a hash function that maps arbitrary messages directly onto curve points in such a way that the dis- crete logarithm of ...
11
On Serre's uniformity conjecture for semistable elliptic curves over totally real fields
... 2016 ELLIPTIC CURVES OVER TOTALLY REAL FIELDS SAMUELE ANNI AND SAMIR SIKSEK ...a finite set of non- archimedean places of ...an elliptic curve defined over K, semistable ...
8