A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Function Field Sieve Method for Discrete Logarithms over Finite Fields

1999
*
Information and Computation
*

We present a

doi:10.1006/inco.1998.2761
fatcat:56hsxeqbuzdufeuygqqnwqqzwe
*function**field**sieve**method**for**discrete**logarithms**over**finite**fields*. This*method*is an analog of the number*field**sieve**method*originally developed*for*factoring integers. ... It is asymptotically faster than the previously known algorithms when applied to*finite**fields*F p n , where p 6 n. ... As noted in [23] that, while the number*field**sieve**method*works well*for**finite**fields*F p n , where n< <(log p) 1Â2 , the*function**field**sieve**method*works well*for**finite**fields*F p n , where log ...##
###
Function Field Sieve in Characteristic Three
[chapter]

2004
*
Lecture Notes in Computer Science
*

In this paper we investigate the efficiency of the

doi:10.1007/978-3-540-24847-7_16
fatcat:nmqkq72njbhovfn53wye5cq3gy
*function**field**sieve*to compute*discrete**logarithms*in the*finite**fields*F3n . ... This allows us to represent the*function**field**over*different base*fields*. Practical experiments appear to show that a*function**field**over*F3 gives the best results. ... The same cannot be said*for**discrete**logarithm*algorithms*over**finite**fields*. Such algorithms depend quite closely on the characteristic. ...##
###
The Function Field Sieve Is Quite Special
[chapter]

2002
*
Lecture Notes in Computer Science
*

In this paper, we describe improvements to the

doi:10.1007/3-540-45455-1_34
fatcat:46ofpwonlzblxc2b2fuhhkowca
*function**field**sieve*(FFS)*for*the*discrete**logarithm*problem in Fpn , when p is small. ... We demonstrate the efficiency of the algorithm by successfully computing*discrete**logarithms*in a large*finite**field*of characteristic two, namely F 2 521 . ... Conclusion In this paper, we described improvements to the*function**field**sieve**for*the*discrete**logarithm*problem. ...##
###
An experiment of number field sieve for discrete logarithm problem over $\text{GF}(p^n)$

2014
*
JSIAM Letters
*

At CRYPTO 2006, Joux et al. proposed the number

doi:10.14495/jsiaml.6.53
fatcat:gcdtnywmffc7pa4j4ab2uxmt2m
*field**sieve**over*GF(p n ), but the number*field**sieve*needs multi-dimensional*sieving*. ...*sieving*. ... The security of pairing-based cryptography using the BN curves is based on the hardness of the*discrete**logarithm*problem (DLP)*over**finite**fields*GF(p 12 ). ...##
###
Page 10 of Mathematical Reviews Vol. , Issue 2001C
[page]

2001
*
Mathematical Reviews
*

The authors present a new version of the

*function**field**sieve*algorithm*for*computing*discrete**logarithms*in*finite**fields*. ... ., Providence, RI, 1999. 2001¢:11136b 11Y16 68P25 94A60 Adleman, Leonard M. (1-SCA-C; Los Angeles, CA); Huang, Ming-Deh A. (1-SCA-C; Los Angeles, CA)*Function**field**sieve**method**for**discrete**logarithms*...##
###
Page 6869 of Mathematical Reviews Vol. , Issue 2000j
[page]

2000
*
Mathematical Reviews
*

The author adapts the number

*field**sieve*factoring algorithm to the problem of finding*discrete**logarithms*in a*finite**field*with q = p” elements. ... 6869*discrete**logarithms*in the group of rational points on the Jaco- bians of large genus hyperbolic curves*over*a*field*GF(q), logg < (2g + 1)'-**for*each 0 <e <1, is proposed. ...##
###
The Past, Evolving Present, and Future of the Discrete Logarithm
[chapter]

2014
*
Open Problems in Mathematics and Computational Science
*

In particular, this is the case

doi:10.1007/978-3-319-10683-0_2
fatcat:ykp3rhh2lnhn5ml4otrrfszoii
*for*the multiplicative groups of*finite**fields*with medium to large characteristic and*for*the additive group of a general elliptic curve. ... The first practical public key cryptosystem ever published, the Diffie-Hellman key exchange algorithm, relies*for*its security on the assumption that*discrete**logarithms*are hard to compute. ...*Discrete**Logarithm*in*Finite**Fields*A Short History The earliest*methods*introduced to compute*discrete**logarithms*are generic. ...##
###
Page 3499 of Mathematical Reviews Vol. , Issue 87g
[page]

1987
*
Mathematical Reviews
*

The

*method*described in the article is developed di- rectly*for**finite**fields*in contrast to the known*methods*which are*finite*-*field*adaptations of the*methods**for*solving systems*over*the reals. N. ... The authors present several related*methods*(of the Western- Miller family) of finding*discrete**logarithms*in a*field*GF(p), p prime. ...##
###
The Multiple Number Field Sieve with Conjugation and Generalized Joux-Lercier Methods
[chapter]

2015
*
Lecture Notes in Computer Science
*

In this paper, we propose two variants of the Number

doi:10.1007/978-3-662-46800-5_7
fatcat:g4g7zib4zzcsdanng5h4hxnouy
*Field**Sieve*(NFS) to compute*discrete**logarithms*in medium characteristic*finite**fields*. ... selections*for*the classical Number*Field**Sieve*. ... Acknowledgment I would like to sincerely thank Taechan Kim*for*his careful proofreading. ...##
###
Page 10 of Mathematical Reviews Vol. , Issue 2004a
[page]

2004
*
Mathematical Reviews
*

The

*function**field**sieve*of Adleman and Huang can be used to find*discrete**logarithms*in the*field*F, with g elements, where ¢ = p" and p is small in the sense that p< n'/°. ... This results in a*discrete**logarithm*algorithm whose conjectured complexity is the same as the*function**field**sieve*—L,[1/3, (32/9)'/* + o(1)] l—a where L,[a, c] = exp(c log“ (log(q)) log log’ ~“ )—which ...##
###
Indiscreet logarithms in finite fields of small characteristic
[article]

2016
*
arXiv
*
pre-print

the state-of-the-art algorithms

arXiv:1604.03837v1
fatcat:tafikapvajb57kwzxixbkfdc2u
*for*computing*discrete**logarithms*in all*finite**fields*. ... Recently, several striking advances have taken place regarding the*discrete**logarithm*problem (DLP) in*finite**fields*of small characteristic, despite progress having remained essentially static*for*nearly ... Inspired by the number*field**sieve*, the*function**field**sieve*was developed*for*computing*discrete**logarithms*in small (fixed) characteristic [Adl94, AH99, JL02, JL06] . ...##
###
Indiscreet logarithms in finite fields of small characteristic

2018
*
Advances in Mathematics of Communications
*

the state-of-the-art algorithms

doi:10.3934/amc.2018017
fatcat:fly5nkijurfsjiio7snqaw23qy
*for*computing*discrete**logarithms*in all*finite**fields*. ... Recently, several striking advances have taken place regarding the*discrete**logarithm*problem (DLP) in*finite**fields*of small characteristic, despite progress having remained essentially static*for*nearly ... Inspired by the number*field**sieve*, the*function**field**sieve*was developed*for*computing*discrete**logarithms*in small (fixed) characteristic [Adl94, AH99, JL02, JL06] . ...##
###
A unified polynomial selection method for the (tower) number field sieve algorithm

2019
*
Advances in Mathematics of Communications
*

to the

doi:10.3934/amc.2019028
fatcat:w7bandnngjhtfipis2zpgd42je
*discrete**logarithm*problem*over**finite**fields*. ... This line of work has led to new asymptotic complexities*for*various cases of the*discrete**logarithm*problem*over**finite**fields*. ... Acknowledgment We thank the reviewers*for*carefully reading the paper and providing comments which have helped in improving the work. ...##
###
Page 1110 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

., 877, Springer, Berlin, 1994; MR 96d:11135]

*for*computing*discrete**logarithms*in the multiplicative group of a*finite**field*. ... In fact, the number*field**sieve*has this complex- ity*for*small n relative to p, and the*function**field**sieve*has this complexity*for*large relative to p; roughly speaking, no algo- rithm of complexity ...##
###
Page 7668 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

The

*discrete**logarithm*algorithms mentioned include Shanks’ baby-step-giant-step*method*, the Silver-Pohlig-Hellman*method*, Adleman’s index calculus, Gordon’s number*field**sieve*and the Xendi calculus*for*...*For*a*function*f defined*over*Z/p! ...
« Previous

*Showing results 1 — 15 out of 2,285 results*