Results 21 to 30 of about 136,439 (162)
Compact elliptic curve representations
Journal of Mathematical Cryptology, 2011 Let y2 = x3 + ax + b be an elliptic curve over 𝔽p, p being a prime number greater than 3, and consider a, b ∈ [1, p]. In this paper, we study elliptic curve isomorphisms, with a view towards reduction in the size of elliptic curves coefficients. We first
Ciet Mathieu +2 more
doaj +1 more source
Complete classification of torsion of elliptic curves over quadratic cyclotomic fields [PDF]
, 2010 In a previous paper, the author examined the possible torsions of an elliptic curve over the quadratic fields $\mathbb Q(i)$ and $\mathbb Q(\sqrt{-3})$.
Najman, Filip
core +2 more sources
Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform
Sensors, 2020 We implement elliptic curve cryptography on the MSP430 which is a commonly used microcontroller in wireless sensor network nodes. We use the number theoretic transform to perform finite field multiplication and squaring as required in elliptic curve ...
Utku Gulen, Selcuk Baktir
doaj +1 more source
Nonlinearities in Elliptic Curve Authentication
Entropy, 2014 In order to construct the border solutions for nonsupersingular elliptic curve equations, some common used models need to be adapted from linear treated cases for use in particular nonlinear cases.
Ramzi Alsaedi +2 more
doaj +1 more source
Torsion points with multiplicatively dependent coordinates on elliptic curves
, 2020 In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations.
Barroero, Fabrizio, Sha, Min
core +1 more source
On the de Rham and p-adic realizations of the Elliptic Polylogarithm for CM elliptic curves [PDF]
, 2008 In this paper, we give an explicit description of the de Rham and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good reduction at p, then ...
Bannai, Kenichi +2 more
core +2 more sources
Efficient Unified Arithmetic for Hardware Cryptography [PDF]
, 2008 The basic arithmetic operations (i.e. addition, multiplication, and inversion) in finite fields, GF(q), where q = pk and p is a prime integer, have several applications in cryptography, such as RSA algorithm, Diffie-Hellman key exchange algorithm [1 ...
Koc, Cetin Kaya +3 more
core +2 more sources
On tea, donuts and non-commutative geometry [PDF]
Surveys in Mathematics and its Applications, 2018 As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theorem.
Igor V. Nikolaev
doaj
A Novel Scheme of Image Encryption Based on Elliptic Curves Isomorphism and Substitution Boxes
IEEE Access, 2021 In this manuscript, we propose an image encryption technique by using isomorphic elliptic curves which are proved to be effective against side-channel attacks and have efficient key size as compared to other public-key structures.
Ijaz Khalid +4 more
doaj +1 more source
Regulators of rank one quadratic twists [PDF]
, 2008 We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists of a fixed elliptic curve. In particular, we formulate some conjectures on the average size of these regulators.
Delaunay, Christophe +1 more
core +6 more sources