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

##
###
A Subexponential Algorithm for Discrete Logarithms Over all Finite Fields

1993
*
Mathematics of Computation
*

However, there appears to be no published

doi:10.2307/2152932
fatcat:uxauutc3ljbbhm3zlhuvizz2ve
*subexponential**algorithm**for*computing*discrete**logarithms**over**all**finite**fields*. ... There are numerous*subexponential**algorithms**for*computing*discrete**logarithms**over*certain classes of*finite**fields*. ... Acknowledgments We would like to thank Dennis Estes and Bob Guralnick*for*their help. In an earlier version of this*algorithm*the authors had chosen m = [nx/2¡ . ...##
###
A subexponential algorithm for discrete logarithms over all finite fields

1993
*
Mathematics of Computation
*

However, there appears to be no published

doi:10.1090/s0025-5718-1993-1225541-3
fatcat:ppcwprlr2jh63ecch5dpmpgrd4
*subexponential**algorithm**for*computing*discrete**logarithms**over**all**finite**fields*. ... There are numerous*subexponential**algorithms**for*computing*discrete**logarithms**over*certain classes of*finite**fields*. ... Acknowledgments We would like to thank Dennis Estes and Bob Guralnick*for*their help. In an earlier version of this*algorithm*the authors had chosen m = [nx/2¡ . ...##
###
A Subexponential Algorithm for Discrete Logarithms over All Finite Fields
[chapter]

*
Advances in Cryptology — CRYPTO' 93
*

However, there appears to be no published

doi:10.1007/3-540-48329-2_13
dblp:conf/crypto/AdlemanD93
fatcat:57c26ihcqndhheuhg6rmgmmj4m
*subexponential**algorithm**for*computing*discrete**logarithms**over**all**finite**fields*. ... There are numerous*subexponential**algorithms**for*computing*discrete**logarithms**over*certain classes of*finite**fields*. ... Acknowledgments We would like to thank Dennis Estes and Bob Guralnick*for*their help. In an earlier version of this*algorithm*the authors had chosen m = [nx/2¡ . ...##
###
Discrete logarithms in curves over finite fields
[article]

2007
*
arXiv
*
pre-print

*A*survey on

*algorithms*

*for*computing

*discrete*

*logarithms*in Jacobians of curves

*over*

*finite*

*fields*. ... The first

*subexponential*

*algorithm*

*for*computing

*discrete*

*logarithms*in hyperelliptic curves of large genus defined

*over*

*a*

*finite*

*field*K = F q is due to Adleman, DeMarrais and Huang [3] . ...

*Subexponential*

*algorithms*of complexity L(1/3) Following the progress

*for*factorisation

*algorithms*,

*a*complexity of L(1/3) has also been established

*for*

*discrete*

*logarithm*computations in

*finite*

*fields*...

##
###
A general framework for subexponential discrete logarithm algorithms

2002
*
Acta Arithmetica
*

The first examples of such groups were the multiplicative groups of

doi:10.4064/aa102-1-6
fatcat:x3fkfj6sl5cvng5j5bxrmeu4na
*finite**fields*; it turned out that in this case the*discrete**logarithm*problem can be solved in expected*subexponential*time by so-called ... Other important examples are class groups of number*fields*[24, 6] and Jacobians, i.e. divisor class groups, of elliptic [25, 19] and hyperelliptic [20] curves*over**finite**fields*. ... The results of this article form part of the authors' doctoral theses; we thank our respective supervisors, Dieter Jungnickel and François Morain,*for*their continuous support and useful suggestions. ...##
###
Page 2503 of Mathematical Reviews Vol. , Issue 94e
[page]

1994
*
Mathematical Reviews
*

There are numerous

*subexponential**algorithms**for*the problem*over**fields*of special form. The paper presents*a**subexponential*method*for*computing*discrete**logarithms**over**all**finite**fields*. ...*over**all**finite**fields*. ...##
###
On the Bounded Sum-of-digits Discrete Logarithm Problem in Kummer and Artin-Schreier Extensions
[article]

2003
*
arXiv
*
pre-print

In this paper, we study the

arXiv:math/0311120v1
fatcat:6guf7oj7bjaxli6vercrofc6fy
*discrete**logarithm*problem in the*finite**fields*_q^n where n|q-1. The*field*is called*a*Kummer*field*or*a*Kummer extension of _q. ... Since every*finite**field*has an extension of reasonable degree which is*a*Kummer*field*, our result reveals an unexpected property of the*discrete**logarithm*problem, namely, the bounded sum-of-digits*discrete*... Acknowledgments We thank Professor Pedro Berrizbeitia*for*very helpful discussions. ...##
###
Page 2507 of Mathematical Reviews Vol. , Issue 95d
[page]

1995
*
Mathematical Reviews
*

*subexponential*

*algorithm*

*for*

*discrete*

*logarithms*

*over*

*all*

*finite*

*fields*. ... However, there appears to be no published

*subexponential*algo- rithm

*for*computing

*discrete*

*logarithms*

*over*

*all*

*finite*

*fields*. ...

##
###
On the Bounded Sum-of-Digits Discrete Logarithm Problem in Finite Fields

2005
*
SIAM journal on computing (Print)
*

In this paper, we study the bounded sum-of-digits

doi:10.1137/s0097539704446037
fatcat:wxmpgefqkbbg7nnxgxyfmdjeke
*discrete**logarithm*problem in*finite**fields*. Our results concern primarily with*fields*Fqn where n|q − 1. ... We also prove that in the*field*F q q−1 , the bounded sum-of-digits*discrete**logarithm*with respect to g can be computed in random time O(f (w) log 4 (q q−1 )), where f is*a**subexponential*function and ... Acknowledgments We thank Professor Pedro Berrizbeitia*for*very helpful discussions. ...##
###
On the Bounded Sum-of-Digits Discrete Logarithm Problem in Finite Fields
[chapter]

2004
*
Lecture Notes in Computer Science
*

In this paper, we study the bounded sum-of-digits

doi:10.1007/978-3-540-28628-8_12
fatcat:yjt5sj3i7nhppfqgmfbzp4x47e
*discrete**logarithm*problem in*finite**fields*. Our results concern primarily with*fields*Fqn where n|q − 1. ... We also prove that in the*field*F q q−1 , the bounded sum-of-digits*discrete**logarithm*with respect to g can be computed in random time O(f (w) log 4 (q q−1 )), where f is*a**subexponential*function and ... Acknowledgments We thank Professor Pedro Berrizbeitia*for*very helpful discussions. ...##
###
An L (1/3 + ε) Algorithm for the Discrete Logarithm Problem for Low Degree Curves
[chapter]

2007
*
Lecture Notes in Computer Science
*

The

doi:10.1007/978-3-540-72540-4_22
fatcat:3chevkqcn5e5phscimwrveq574
*discrete**logarithm*problem in Jacobians of curves of high genus g*over**finite**fields*_q is known to be computable with*subexponential*complexity L_q^g(1/2, O(1)). ...*For*this family, the group structure can be computed in*subexponential*time of L_q^g(1/3, O(1)), and*a**discrete**logarithm*computation takes*subexponential*time of L_q^g(1/3+ϵ, o(1))*for*any positive ϵ. ... We thank Claus Diem*for*his careful reading of our article and many useful remarks. ...##
###
Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time

2001
*
Mathematics of Computation
*

We provide

doi:10.1090/s0025-5718-01-01363-1
fatcat:lhvat6ftdre4njrnd3wtrgheam
*a**subexponential**algorithm**for*solving the*discrete**logarithm*problem in Jacobians of high-genus hyperelliptic curves*over**finite**fields*. ... Its expected running time*for*instances with genus g and underlying*finite**field*Fq satisfying g ≥ ϑ log q*for**a*positive constant ϑ is given by The*algorithm*works*over*any*finite**field*, and its running ... I thank Alfred Menezes and Scott Vanstone*for*the invitation and their hospitality, and Michael Jacobson, Andreas Stein and Edlyn Teske*for*fruitful discussions. ...##
###
Page 831 of Mathematical Reviews Vol. , Issue 97B
[page]

1997
*
Mathematical Reviews
*

The

*algorithms**for*computing*discrete**logarithms*in F,» run in*subexponential*-time only in the case that m grows and p is fixed. ... Summary: “We present*a**subexponential**algorithm*of the dis- crete*logarithm*in GF(p*), p= 1 mod 3, which runs in time O(exp(24,/log ploglog p)). ...##
###
Page 6868 of Mathematical Reviews Vol. , Issue 2000j
[page]

2000
*
Mathematical Reviews
*

*algorithm*

*for*

*discrete*

*logarithms*

*over*hyperelliptic curves of large genus

*over*GF(q). ... ; La Jolla, CA) New

*algorithms*

*for*generating Conway polynomials

*over*

*finite*

*fields*. ...

##
###
Smooth ideals in hyperelliptic function fields

2001
*
Mathematics of Computation
*

Recently, several

doi:10.1090/s0025-5718-01-01352-7
fatcat:y7dvvxlpand3tpl36v6p3jhylq
*algorithms*have been suggested*for*solving the*discrete**logarithm*problem in the Jacobians of high-genus hyperelliptic curves*over**finite**fields*. ... Some of them have*a*provable*subexponential*running time and are using the fact that smooth reduced ideals are sufficiently dense. We explicitly show how these density results can be derived. ... Most of this contribution is*a*result of*a*research visit of the first author's at the Centre*for*Applied Cryptographic Research. ...
« Previous

*Showing results 1 — 15 out of 1,239 results*