What are Elliptic Curves?
Elliptic Curves
... Acknowledgements I would like to thank all of the wonderful professors I have had at CSUSB. I am grateful for all they have taught me. I would like to thank Professor Chavez for always having an enjoyable class and ...
87
Elliptic curves and Pythagorean triples
... Department of Pure Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran Abstract. The aim of this paper is to study the family of elliptic curves of the form y 2 = x ( x − a 2 )( x − b 2 ) , where ...
9
Explicit isogenies of elliptic curves
... of elliptic curves, isogenies of elliptic curves, modular curves, modular forms and modular func- tions, which will be required in the later ...modular curves, modular functions ...
121
Factoring integers with elliptic curves
... This paper 19 devoted to the deacnption and analysis of a new algonthm to factor positive mtegers It depends on the use of elliptic curves The new m et b öd α obtained from Pollird's p-1[r] ...
19
Requirements for Standard Elliptic Curves
... elliptic curves. A potential compromise is the construction of new curves with similar properties as the Brainpool Curves, ...of curves, one for high-speed software in secure ...
5
Elliptic Curves for Pairing Applications
... Abstract In this paper we address the question of representing the discriminant of an imaginary quadratic field with respect to the basis of a cyclotomic field. This representation allows us to parameterize new families ...
15
An Attack on Disguised Elliptic Curves
... Disguising elliptic curves This proposal consists of taking the Weil restriction of an elliptic curve with respect to F q n /F q and then transforming the group operation equations using a linear ...
8
Disguising tori and elliptic curves
... 6 Conclusions We have given a simple algebraic attack which shows that it is not secure to disguise the torus T 2 . We have then explained why this attack does not seem to apply to disguised elliptic ...
12
How to Hash into Elliptic Curves
... From our encoding, we have defined two constructions, which enable to hash into an elliptic curve. The first construction is provably one-way and the second is provably one-way and collision resistant in the ...
14
Knapsack Cryptosystem on Elliptic Curves
... 4-3-16 Jonan Yonezawa-shi Yamagata, 922-8510 Japan Email: kobayash@yz.yamagata-u.ac.jp Abstract—The LLL algorithm is strong algorithm that de- crypts the additional type Knapsack cryptosystem. However, the LLL algorithm ...
6
Elliptic curves in Huff's model
... system. Elliptic curves can be represented in different ...of elliptic curves have been extensively studied in the last two ...important elliptic curve families include Jacobi ...
19
Huff's Model for Elliptic Curves
... for elliptic curves over finite fields of odd characteristic and a statement of the addition law in these ...all elliptic curves over non-binary finite fields with a subgroup isomorphic to Z ...
17
ELLIPTIC CURVES BJORN POONEN
... 6. The addition law on elliptic curves Let E be an elliptic curve defined over Q. We have seen that a line L with rational slope passing through one rational point on E need not intersect E in ...
7
Elliptic Curves and Diophantine Equations
... Elliptic curves, which are curves of the form y 2 = x 3 +ax+b and related theorems can be used to solve a wide variety of Diophantine equations, equations that only allow integer ...of ...
7
Elliptic curves over C
... an elliptic curve E/ C. This map is parameterized by elliptic functions, specifically the Weier- strass ...of elliptic functions in Section ...construct elliptic curves with desired ...
11
On Indifferentiable Deterministic Hashing into Elliptic Curves
... Nafissatou Diarra 1 , Djiby Sow 1,∗ , Ahmed Youssef Ould Cheikh Khlil 1 1 Laboratoire d’Alg` ebre, de Cryptographie, de G´ eom´ etrie Alg´ ebrique et Aplications (LAC- GAA, Cheikh Anta Diop University, Dakar, Senegal ...
29
Periods of Tribonacci sequences and elliptic curves
... A b s t r ac t . We will study the periods of Tribonacci sequences associated to elliptic curves. This work is motivated by a paper of Coleman et al. who did it for classical Fibonacci sequences. We are ...
17
Generating more MNT elliptic curves
... of elliptic curves of prime order with embedding degree 3, 4, or ...Such curves are important for the real- isation of pairing-based cryptosystems on ordinary (non-supersingular) elliptic ...
10
Elliptic Curves with Low Embedding Degree
... In this case either − s or − 4s is the fundamental discriminant of the complex multiplication field of the corresponding elliptic curve. Accordingly, for positive real numbers x, y and z we denote by Q k (x, y, z) ...
13
A taxonomy of pairing-friendly elliptic curves
... pairing-friendly elliptic curves with ρ ≤ 2 for every embedding degree k ≤ 1000 that is not divisible by ...pairing-friendly curves (our Definition ...that curves with k > 1000 will be ...
53