[PDF] Top 20 Generic Hardness of the Multiple Discrete Logarithm Problem
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Generic Hardness of the Multiple Discrete Logarithm Problem
... better generic algorithm for ...a generic algorithm solving ...precise generic hardness of MDL is not ...a generic algorithm solving n DL instances within O( √ p), independent of n, is ... See full document
18
A New Signature Scheme Define over a Class of Non-Abelian Group
... the hardness of some mathematical problems in a large and finite abelian group (more precisely, finite cyclic groups) (Fiat et ...and discrete logarithm problems (Rivest et ... See full document
8
On the discrete logarithm problem in finite fields of fixed characteristic
... to c = 3 1/3 ≈ 1.44 [37] and to c = 2 1/3 ≈ 1.26 [30], the latter using a clever method to amplify one relation into many others. Note that we mention the medium characteristic developments because they can be applied to ... See full document
20
Aggregation of Gamma-Signatures and Applications to Bitcoin
... 16], multiple signers sign the same message, and more importantly they need inter- active ...the discrete logarithm problem is hard [8, 47], in the plain public-key model where no trusted ... See full document
22
Recent progress on the elliptic curve discrete logarithm problem
... the generic Gr¨ obner basis is much more costly than a single standard ...a generic Gr¨ obner basis opens the way to sieving, as demonstrated by Joux and Vitse [76], which can have a huge practical ...the ... See full document
26
Modified Baby Step Giant Step Algorithm to Solve Elliptic Curve Discrete Logarithm Problem (ECDLP)
... known generic algorithms to find discrete log while the Index Calculus algorithm [9] is a powerful non-generic ...computes discrete logarithms in a cyclic group G of order N in deterministic ... See full document
5
A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem
... A algorithm that we developed, uses Gaussian elimination algorithm multiple times to solve Problem L. In particular we use the row operations from the Gaussian elimination algorithm. Abusing our notations ... See full document
12
Quantum algorithm for the discrete logarithm problem for matrices over finite group rings
... the discrete logarithm problem in matrices over finite group ...The hardness of this problem was recently employed in the design of a key-exchange protocol proposed by ... See full document
8
Connecting Legendre with Kummer and Edwards
... For the twisted Edwards curves which are obtained from Legendre curves using a birational equivalence, the hardness of the discrete logarithm problem is preserved. For these twisted Edwa[r] ... See full document
25
The Discrete-Logarithm Problem with Preprocessing
... Generic Multiple-Discrete-Log ...the discrete-log problem, and algorithms for the multiple-discrete-log problem—in which the task is to compute many discrete ... See full document
51
Tight Reductions for Diffie-Hellman Variants in the Algebraic Group Model
... Fuchsbauer, Kiltz, and Loss (Crypto’18) gave a simple and clean definition of an alge- braic group model (AGM) that lies in between the standard model and the generic group model (GGM). Specifically, an algebraic ... See full document
31
A Digital Signature Scheme for Long-Term Security
... In this paper we defined a signature system based on two difficult arithmetic prob- lems. In the framework chosen, these problems have similar resistance to known attacks. We explained how to implement in practice all ... See full document
10
PERFORMANCE OF COOPERATIVE COMMUNICATION SYSTEM WITH NETWORK CODING USING SOFTWARE DEFINED RADIO
... Now, we are going to describe the new cryptosystem, which adapts to use with elliptic curves. Suppose Alice wants to send a secret message to Bob. Alice and Bob choose an elliptic curve , defined over a finite field , so ... See full document
7
A New Index Calculus Algorithm for the Elliptic Curve Discrete Logarithm Problem and Summation Polynomial Evaluation
... curve discrete logarithm problem, and several recent papers have explored their ...Curve Discrete Logarithm Problem that makes use of a technique for fast evaluation of the sum- ... See full document
21
An Encryption and Decryption More Secure Elgamal Cryptosystem
... In our system we overcome the problem that arises in the previous system and it has also less time complexity and it is more powerful than the existing system. In our system we enforce Chinese Remainder Theorem ... See full document
9
On Discrete Logarithm Problem based on Algebraic Varieties over Finite Field and Public Key Cryptosystem
... In this chapter, we propose new DLPs for exponential subfield as a base field and extension of this base field by the product operators over finite fields whic[r] ... See full document
8
A Digital Signature Scheme Based on Pell Equation
... normal discrete logarithm problem (DLP) and the integer factorization problem (IFP), the elliptic curve discrete logarithm problem (ECDLP) has no sub exponential-time ... See full document
5
An Efficient ID based Proxy Signcryption Scheme without Bilinear Pairings
... The paper is organized as follow. In the next section, the hard computational problems are discussed. Section 3 introduces the syntax of a generic identity-based proxy signcryption scheme (ID-PSC). Section 4 ... See full document
6
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
A Riddle Wrapped in an Enigma
... For many years it has been known [55] that both the integer factorization problem, upon which RSA is based, and the elliptic curve discrete logarithm problem (ECDLP), upon which ECC is b[r] ... See full document
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