[PDF] Top 20 The Discrete-Logarithm Problem with Preprocessing

... Acknowledgements. We would like to thank Dan Boneh for encouraging us to undertake this project and for his advice along the way. We thank Omer Reingold, David Wu, and Benedikt Bünz for fruitful discussions during the ... See full document

... In 1985, ElGamal [6] proposed a public key cryptosystem and a digital signature scheme based on the difficulty of solving the Discrete Logarithm Problem in the multiplicative group of an appropriate ... See full document

... 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

... An encryption scheme based on the integration of Enhanced RSA and Elgamal algorithm is introduced. Enhanced RSA algorithm is based on Integer Factorization Problem (IFP). On the other hand, Elgamal algorithm is ... See full document

... the discrete logarithm problem over finite ...Curve Discrete Logarithm Problem (ECDLP) with a reduced computational complexity compared to other schemes in ... See full document

... the discrete logarithm problem on this group, we have to define a hash function into the group G, namely a map to point ...This problem was studied by various authors giving their own method, ... See full document

... 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

... 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

... 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

... A signature scheme consists of three algorithms, which are, the key generation, signing and verification algorithms used for verifying the authenticity of digital messages or documents. Most existing signature schemes ... See full document

... This paper has described a tight security reduction for a generalised KCDSA scheme with Randomized Hashing to the discrete logarithm problem. Thus security parameters for the two problems can be ... See full document

... 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 best use when ... See full document

... In 2004, Semaev [11] showed that solving PDP in an elliptic curve group is equivalent to solving a particular system of multivariate non-linear system of equations derived from the so called Semaev summation polynomials. ... See full document

... Digital signatures that are used to achieve the integrity along with the authentication could be classified into various types. PKI based, ID based, certificate based and certificateless digital signatures are the most ... See full document

... The L(1/3) subexponential complexity of the function field sieve was first improved by Joux [18] to L(1/4 + o(1)), and then by G¨ olo˘ glu, Granger, McGuire, and Zumbr¨ agel [10] to L(1/4). Shortly thereafter, B˘ ... See full document

... 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

... this problem, we ran another set of experiments. For α = 0.01 and β = 0.001 we re-ran the simulations, but with the threshold now set to C = 2.5. The success probability for this new set of tests was 0.195, which ... See full document

... 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

... Diffie-Hellman Problem in the Generic Group Model. The discrete logarithm (DL) as- sumption and the computational Diffie-Hellman (CDH) assumption including its variants have been devoted to constructing ... See full document

... The word cryptography is derived from the Greek words Crypto meaning cover and grafia meaning writing defining it as covered writing. In image cryptography the information is hidden exclusively in images. Cryptography is ... See full document