A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve

1993
*
SIAM Journal on Discrete Mathematics
*

*GF*(

*p*) with heuristic expected running time Lp[1/3; 3 2/3 ]. ... Recently, several algorithms using number field sieves have been given to factor a number n

*in*heuristic expected time

*In*this paper we present an algorithm to solve the

*discrete*

*logarithm*problem for ... Thanks also to Andrew Odlyzko for several email discussions about

*discrete*

*logarithms*, and Hendrik Lenstra for helpful comments. ...

##
###
Computing Individual Discrete Logarithms Faster in $${{\mathrm{GF}}}(p^n)$$ with the NFS-DL Algorithm
[chapter]

2015
*
Lecture Notes in Computer Science
*

The Number Field Sieve (NFS) algorithm is the best known method to compute

doi:10.1007/978-3-662-48797-6_7
fatcat:guobsnva6jdv3ah75ss5wta2b4
*discrete**logarithms*(DL)*in*finite fields F_p^n, with*p*medium to large and n ≥ 1 small. ... If one can write the target preimage as a product of elements of known (virtual)*logarithm*, then one can deduce the*discrete**logarithm*of the target. ... Let n > 1 and s ∈ F **p*n a random element (not*in*a proper subfield of F*p*n ). We want to compute its*discrete**logarithm*modulo ℓ, where ℓ | Φ n (*p*), with Φ n the n-th cyclotomic polynomial. ...##
###
Discrete Logarithm in GF(2809) with FFS
[chapter]

2014
*
Lecture Notes in Computer Science
*

The year 2013 has seen several major complexity advances for the

doi:10.1007/978-3-642-54631-0_13
fatcat:u6gyopw6lzapnli3ixnwhdqlfq
*discrete**logarithm*problem*in*multiplicative groups of smallcharacteristic finite fields. ... This article presents the state of the art with regard to the FFS algorithm, and reports data from a record-sized*discrete**logarithm*computation*in*a prime-degree extension field. ... It brings important data, however, towards the assessment of the feasibility limit of*discrete**logarithms**in**GF*(2*p*) for prime extension degrees*p*. ...##
###
Solving a 676-Bit Discrete Logarithm Problem in GF(36n)

2012
*
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
*

Taking into account the Menezes-Okamoto-Vanstone (MOV) attack, the

doi:10.1587/transfun.e95.a.204
fatcat:6irl5wow35h6dbb7z25lfpwebq
*discrete**logarithm*problem (DLP)*in**GF*(3 6n ) becomes a concern for the security of cryptosystems using ηT pairings*in*this case. ... Therefore, we first fulfill such an implementation and we successfully set a new record for solving the DLP*in**GF*(3 6n ), the DLP*in**GF*(3 6·71 ) of 676bit size. ...*discrete**logarithm*. 1. ...##
###
Solving a 676-Bit Discrete Logarithm Problem in GF(36n )
[chapter]

2010
*
Lecture Notes in Computer Science
*

Taking into account the Menezes-Okamoto-Vanstone (MOV) attack, the

doi:10.1007/978-3-642-13013-7_21
fatcat:lxybufswe5hnfbayukaxndjl7i
*discrete**logarithm*problem (DLP)*in**GF*(3 6n ) becomes a concern for the security of cryptosystems using ηT pairings*in*this case. ... Therefore, we first fulfill such an implementation and we successfully set a new record for solving the DLP*in**GF*(3 6n ), the DLP*in**GF*(3 6·71 ) of 676bit size. ...*discrete**logarithm*. 1. ...##
###
Processing, Lecture notes in Computer Science

1993
*
АНО НПО «Профессионал», 2005.-480 с. 2. Gordon D. Discrete Logarithms in GF(p) using the Number Field Sieve //SIAM Journal on Discrete Mathematics
*
unpublished

α : n=38 416 для δ=0,005,

fatcat:rzfbwzd3irdvlkjdseu2cifkjm
*p*α =0,95. ... В табл. 1 содержатся полученные оценки*p*(A 1 ,c) и*p*(A 2 ,c) для кода C 1 с указанием приведенных в теореме 1 границ областей компрометации. ...##
###
Collision Search for Elliptic Curve Discrete Logarithm over GF(2 m ) with FPGA
[chapter]

*
Lecture Notes in Computer Science
*

Indeed, no sub-exponential algorithms are known to solve the underlying hard problem: the Elliptic Curve

doi:10.1007/978-3-540-74735-2_26
fatcat:yzgvk7kc35flbnel7rw6h7yxnu
*Discrete**Logarithm*. ...*In*this last decade, Elliptic Curve Cryptography (ECC) has gained increasing acceptance*in*the industry and the academic community and has been the subject of several standards. ... The underlying hard problem of ECC is the intractability of the Elliptic Curve*Discrete**Logarithm*Problem (ECDLP). Let E (F) be an elliptic curve over a finite field F and let*P*be a point of E (F). ...##
###
An experiment of number field sieve for discrete logarithm problem over $\text{GF}(p^n)$

2014
*
JSIAM Letters
*

Using efficient parameters, we have solved the DLP over

doi:10.14495/jsiaml.6.53
fatcat:gcdtnywmffc7pa4j4ab2uxmt2m
*GF*(*p*12 ) of 203 bits*in*about 43 hours using a PC of 16 CPU cores. ... The security of the optimal Ate pairing using the BN curves is based on the hardness of the DLP over*GF*(*p*12 ). ... Finally, we present an example of the*discrete**logarithm*. Let γ = x 2 + x − 7 be a generator of*GF*(*p*12 ) * = (*GF*(*p*)[X]/f 1 (X)) * . ...##
###
EdDSA Over Galois Field GF(p^m) for Multimedia Data

2019
*
Journal of Engineering Research and Reports
*

The operations like addition and multiplication

doi:10.9734/jerr/2019/v4i416911
fatcat:iym7gxsj5rgflf7yufw6evaaii
*in*Galois field are different compared to normal addition and multiplication. ... The finite field*GF*(pm) is an indispensable mathematical tool for some research fields such as information coding, cryptology, theory and application of network coding. ... Creation of signature is deterministic*in*EdDSA and it has higher security due to intractability of some*discrete**logarithm*problems. ...##
###
An FPGA implementation of a GF(p) ALU for encryption processors

2004
*
Microprocessors and microsystems
*

Elliptic Curve Cryptosystems over

doi:10.1016/s0141-9331(04)00018-3
fatcat:z35qlsz4knchrnir3owsxahsby
*GF*(*p*) have received very little attention to date due to the seemingly more attractive finite field*GF*(2 m ). ... However, we present a*GF*(*p*) Arithmetic Logic Unit which can perform 160-bit arithmetic at clock speeds of up to 50MHz. ... Unlike the ordinary*discrete**logarithm*problem, no sub-exponential algorithm is known to date to solve the*discrete**logarithm*problem on a suitably chosen elliptic curve. ...##
###
An FPGA implementation of a GF(p) ALU for encryption processors

2004
*
Microprocessors and microsystems
*

Elliptic Curve Cryptosystems over

doi:10.1016/j.micpro.2004.03.006
fatcat:vev7rkiqdfcqzowyeoxw3i5jsa
*GF*(*p*) have received very little attention to date due to the seemingly more attractive finite field*GF*(2 m ). ... However, we present a*GF*(*p*) Arithmetic Logic Unit which can perform 160-bit arithmetic at clock speeds of up to 50MHz. ... Unlike the ordinary*discrete**logarithm*problem, no sub-exponential algorithm is known to date to solve the*discrete**logarithm*problem on a suitably chosen elliptic curve. ...##
###
On Calculating Square Roots in GF(p)
[article]

2016
*
arXiv
*
pre-print

This article presents a new method for calculating square roots

arXiv:1309.2831v3
fatcat:cbsiksh4pjf23ou6bt5xy6erw4
*in**GF*(*p*) by exponentiating*in**GF*(*p*^3) or equivalently modulo irreducible cubic polynomials. ... This algorithm is*in*some ways similar to the Cipolla-Lehmer algorithm which is based on exponentiating*in**GF*(*p*^2). ... But more importantly it has potential applications concerning the integer factorization problem and the*discrete**logarithm*problem*in**GF*(*p*). ...##
###
XTR Extended to GF(p 6m)
[chapter]

2001
*
Lecture Notes in Computer Science
*

Verheul

doi:10.1007/3-540-45537-x_23
fatcat:chqujmacnrdddchmcjzabxuue4
*in*[2] proposed a very efficient way called XTR*in*which certain subgroup of the Galois field*GF*(*p*6 ) can be represented by elements*in**GF*(*p*2 ). ... At the end of their paper [2], they briefly mentioned on a method of generalizing their idea to the field*GF*(*p*6m ). ... Parameter Selection for Security Consideration Various XTR-based public key systems or key exchange protocols rely their security on the*Discrete**Logarithm*Problem(DLP)*in*the base g ∈*GF*(*p*6m ), where ...##
###
Sparse Hard Sets for P: Resolution of a Conjecture of Hartmanis

1999
*
Journal of computer and system sciences (Print)
*

We further prove that if

doi:10.1006/jcss.1998.1615
fatcat:yyzucqjt3vfe3lechb4zq7fpcm
*P*has a sparse hard set under many-one reductions computable*in*NC 1 , then*P*collapses to NC 1 . ... Building on a recent breakthrough by Ogihara, we resolve a conjecture made by Hartmanis*in*1978 regarding the (non-) existence of sparse sets complete for*P*under logspace many-one reductions. ... Acknowledgments We thank Mitsu Ogihara for showing us his work*in*a Rochester-Bu alo joint complexity ...##
###
Using P systems to Solve the Discrete Logarithm Problem used in Diffie-Hellman Key Exchange Protocol

2009
*
International Journal of Computer Network and Information Security
*

This paper presents a

doi:10.5815/ijcnis.2009.01.04
fatcat:tzod2jtmvvc65lll2m2ls5vrga
*P*system with active membranes and strong priority to solve the*discrete**logarithm*problem used*in*Diffie-Hellman key exchange protocol. ... To the best of our knowledge, it's the first time to solve the problem using*P*systems. Index Terms-*P*systems,*Discrete**Logarithm*Problem, Diffie-Hellman key exchange protocol Manuscript ...*In*this paper, we describe a*P*system with active membranes and strong priority to solve the*discrete**logarithm*problem (DLP). ...
« Previous

*Showing results 1 — 15 out of 9,505 results*