[PDF] Top 20 Recent progress on the elliptic curve discrete logarithm problem
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Recent progress on the elliptic curve discrete logarithm problem
... each discrete logarithm computation, even if several take place in the same ...the discrete logarithms of all the factor base elements with a right-kernel computation is guaranteed only if the matrix ... See full document
26
Solving the Elliptic Curve Discrete Logarithm Problem Using Semaev Polynomials, Weil Descent and Grbner Basis Methods -- an Experimental Study
... an elliptic curve point R can be decomposed into m points of the factor basis if and only if the m + 1-st Semaev polynomial associated with R has a ... See full document
14
CRYPTOGRAPHIC PROTOCOLS USING ELLIPTIC CURVE OVER FINITE FIELDS
... of elliptic curves by algebraists, algebraic geometers and number theorists dates back to the middle of the nineteenth ...century. Elliptic Curve Cryptography (ECC) was discovered in 1985 by Neil ... See full document
6
A PARALLEL PASSWORD-AUTHENTICATED KEY EXCHANGE PROTOCOL FOR WIRELESS ENVIRONMENTS
... the elliptic curve discrete logarithm prob- lem (ECDLP) and has the benefit of the key block size, speed and ...attack problem, so they proposed an improved authenticated key agreement ... See full document
6
On the First Fall Degree of Summation Polynomials
... In recent applications Gr¨ obner basis techniques have become relevant to the solution of the Elliptic Curve Discrete Logarithm Problem ... See full document
12
Harder, Better, Faster, Stronger - Elliptic Curve Discrete Logarithm Computations on FPGAs
... Computing discrete logarithms takes ...compute discrete logarithms of Weierstrass curves defined over binary fields and Koblitz curves us- ing ...a discrete logarithm of the elliptic ... See full document
12
Blockchain as cryptanalytic tool
... Abstract One approach for blockchain based applications to provide a proof-of-work is the computation of hash-values. In our opinion 1 these computations are a waste of energy. It would be highly desirable to find an ... See full document
6
Authenticated Multiple Key Establishment Protocol for Wireless Sensor Networks
... Abstract. The article proposes a provably secure authenticated multiple key estab- lishment protocol for Wireless Sensor Network. Security of the protocol is based on the computational infeasiblity of solving ... See full document
9
PROXY BLIND SIGNATURE BASED ON ECDLP
... (Elliptic Curve Discrete Logarithm Problem) has been proposed, which satisfy the security properties of both the blind signature and the proxy ... See full document
5
Point Decomposition Problem in Binary Elliptic Curves
... The discrete logarithm problem (DLP) in G with respect to a base P ∈ G is the following: Given P and Q = aP ∈ G for some secret integer a, compute ... See full document
13
The Discrete-Logarithm Problem with Preprocessing
... a recent algorithm of Barbulescu et al. [8] computes discrete logarithms in quasi-polynomial ...of elliptic-curve groups, there are non-generic algorithms for the discrete-log ... See full document
51
EFFICIENT MAPPING METHODS FOR ELLIPTIC CURVE CRYPTOSYSTEMS
... using elliptic curves, we need to find a “hard ...mathematical problem for their security ...mathematical problem, the notion of an algorithm is ...mathematical problem on which to base a ... See full document
6
Modified Baby Step Giant Step Algorithm to Solve Elliptic Curve Discrete Logarithm Problem (ECDLP)
... discrete logarithms in elliptic curve groups. This new modified algorithm significantly reduces the number of giant steps performed by factoring the group order N . This modified algorithm finds its ... See full document
5
The Discrete Logarithm Problem in non-representable rings
... For Discrete Logarithm based cryptography, it is desirable to find efficiently implementable groups for which sub-exponential algorithms for the Discrete Logarithm Problem are not ...on ... See full document
10
Using Symmetries in the Index Calculus for Elliptic Curves Discrete Logarithm
... introduced elliptic curve cryptog- raphy based on the DLP in the group formed by rational points of an elliptic curve defined over a finite ...particular problem is denoted ECDLP. More ... See full document
40
Generic Hardness of the Multiple Discrete Logarithm Problem
... cryptographic problem, that is, hardness against such generic algorithms, was studied for many group-based cryptographic ...a problem, at least it serves as a sanity check, in the sense that if a ... See full document
18
On the discrete logarithm problem in finite fields of fixed characteristic
... no progress in either direction; the only development in fixed characteristic being a practical improvement [36], while for so-called medium characteristic fields – those for which the base field cardinality ... See full document
20
Solving the Discrete Logarithm of a 113-bit Koblitz Curve with an FPGA Cluster
... the elliptic curve discrete logarithm problem ...based elliptic curves, done by Monico et ...based elliptic curves, also done by Monico et ... See full document
17
New Random Walk Technique and Collision Detection Algorithm to Improve the Pollard RHO Attack of Solving Discrete Logarithm Problem on Elliptic Curves
... A wide research has been done on cryptanalysis of ECDLP [3]. In 1978 Pollard developed an algorithm using “Monte-Carlo” method to solve ECDLP called Pollard Rho attack which is a random method to compute discrete ... See full document
13
An improved proxy blind signature scheme based on ECDLP
... The first proxy blind signature scheme was introduced by Lin and Jan [4]. Later, there are two new schemes have been proposed, one is Tan’s scheme [5], using schnorr’s blind signature scheme based on discrete ... See full document
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