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\bib{1966/-afips-29}
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\bib{1968/-afips-33}
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\bib{1968/-rc22}
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\paper ALGOL procedures voor het rekenen in dubbele lengte
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\bib{1976/-focs}
\yr 1976
\mr 56:1766
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\bib{1977/-focs}
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\mr 57:18173
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\bib{1979/-focs}
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\mr 82a:68004
\book 20th annual symposium on foundations of computer science
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\bib{1982/-focs}
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\bib{1985/-rennes}
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\bib{1985/-ieee754}
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\bib{1985/-stoc}
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\book Proceedings of the 18th annual ACM symposium on theory of computing
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\bib{1987/-journees}
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\book Journ\'ees arithm\'etiques de Besan\c con
\bookinfo Ast\'erisque 147--148
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\bib{1989/-issac}
\yr 1989
\book International symposium on symbolic and algebraic computation, ISSAC '89, Portland, Oregon, USA, July 17--19, 1989
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\bib{1991/ecma-48}
\yr 1991
\book Standard ECMA--48: control functions for coded character sets
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\bib{1992/-finding-a-balance}
\yr 1992
\book Finding a balance: computer software, intellectual property and the challenge of technological change
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\bib{1995/-sha}
\yr 1995
\book Secure hash standard
\bookinfo Federal Information Processing Standard 180-1
\publ National Institute of Standards and Technology
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\bib{1996/-focs}
\yr 1996
\isbn 0--8186--7594--2
\book 37th annual symposium on foundations of computer science
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\bib{1997/-focs}
\yr 1997
\isbn 0--8186--8197--7
\book 38th annual symposium on foundations of computer science
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\bib{1997/-soda}
\yr 1997
\isbn 0--89871--390--0
\mr 97k:68011
\book Proceedings of the eighth annual ACM-SIAM symposium on discrete algorithms: held in New Orleans, LA, January 5--7, 1997
\publ Association for Computing Machinery
\publaddr New York
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\bib{1998/-stoc}
\yr 1998
\isbn 0--89791--962--9
\mr 2001d:68026
\book Proceedings of the 30th annual ACM symposium on theory of computing
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\bib{1999/-stoc}
\yr 1999
\isbn 1--58113--067--8
\mr 2001f:68004
\book Annual ACM symposium on theory of computing: proceedings of the 31st symposium (STOC '99) held in Atlanta, GA, May 1--4, 1999
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\bib{2000/-dss}
\yr 2000
\book Digital signature standard (DSS)
\bookinfo Federal Information Processing Standard 186-2
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\bib{2000/-stoc}
\yr 2000
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\book Proceedings of the 32nd annual ACM symposium on theory of computing
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\bib{2002/-sha}
\yr 2002
\book Secure hash standard
\bookinfo Federal Information Processing Standard 180-2
\publ National Institute of Standards and Technology
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\bib{2004/-intel-optimization}
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\bib{2004/-amd-25112}
\yr 2004
\book Software optimization guide for AMD Athlon 64 and AMD Opteron processors
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\bib{2005/-freescale-7450}
\yr 2005
\book MPC7450 RISC microprocessor family reference manual
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\bib{1995/abrash}
\yr 1995
\isbn 188357708X
\by Michael Abrash
\book Zen of graphics programming
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\bib{1979/adleman}
\yr 1979
\by Leonard M. Adleman
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\inbook \cite{1979/-focs}
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\bib{1991/adleman}
\yr 1991
\by Leonard M. Adleman
\paper Factoring numbers using singular integers
\inbook \cite{1991/awerbuch}
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Some wild speculation on NFS performance in practice: ``Where is the crossover? A naive approach to this question is to ignore the o(1)'s ... 123 decimal digits. However, this may be far too optimistic because it appears that the o(1)'s actually favor the old algorithms. ... It seems possible that the new algorithms may begin to overtake the old ones only on numbers of about 330 decimal digits or so [because at that point QS needs smoothness of numbers] between 165 and 200 decimal digits [while NFS needs smoothness of numbers] of about 188 decimal digits.'' One of the reasons that these figures are bogus is that the 188-digit numbers are chosen to factor into at least two pieces.

\bib{1994/adleman-ffs}
\yr 1994
\mr 96d:11135
\by Leonard M. Adleman
\paper The function field sieve
\inbook \cite{1994/adleman-ants}
\pages 108--121
\seenewer \cite{1999/adleman}
\url http://cr.yp.to/\allowbreak bib/\allowbreak entries.html#\allowbreak 1994/adleman-ffs
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\bib{1993/adleman}
\yr 1993
\mr 94e:11140
\by Leonard M. Adleman
\by Jonathan DeMarrais
\paper A subexponential algorithm for discrete logarithms over all finite fields
\jour Mathematics of Computation
\issn 0025--5718
\vol 61
\pages 1--15
\seeolder \cite{1994/adleman-subexp}
\endref

\bib{1994/adleman-subexp}
\yr 1994
\mr 95d:94013
\by Leonard M. Adleman
\by Jonathan DeMarrais
\paper A subexponential algorithm for discrete logarithms over all finite fields
\inbook \cite{1994/stinson-book}
\pages 147--158
\seenewer \cite{1993/adleman}
\endref

It is possible to improve the running time in several ways. Sparse matrix methods can be used to find some dependencies[Wi]. A better bound on q in Algorithm I can be argued heuristically. Smoothness of norms can be tested using the `elliptic curve methods' [Le]. The integer factoring done in various parts can probably be avoided if necessary or `L[1/3]' methods can be used (e.g. [AH, LLMP]). The use of Algorithm II can perhaps be avoided altogether by adopting [sic] Algorithm I to a more general setting. Alternatively the `L[1/3,c]' method of Coppersmith [Co] might be adapted for the case n >= p.

\bib{1994/adleman-largegenus}
\yr 1994
\mr 96b:11078
\by Leonard M. Adleman
\by Jonathan DeMarrais
\by Ming-Deh Huang
\paper A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields
\inbook \cite{1994/adleman-ants}
\seenewer \cite{1999/adleman-largegenus}
\pages 28--40
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\bib{1994/adleman-ants}
\yr 1994
\isbn 3--540--58691--1
\mr 95j:11119
\editor Leonard M. Adleman
\editor Ming-Deh Huang
\book Algorithmic number theory: first international symposium, ANTS-I, Ithaca, NY, USA, May 6--9, 1994, proceedings
\series Lecture Notes in Computer Science
\seriesvol 877
\publ Springer-Verlag
\publaddr Berlin
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\bib{1999/adleman}
\yr 1999
\by Leonard M. Adleman
\by Ming-Deh Huang
\paper Function field sieve method for discrete logarithms over finite fields
\jour Information and Computation
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\vol 151
\pages 5--16
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\bib{1992/adleman}
\yr 1992
\isbn 3--540--55308--8
\mr 93g:11128
\by Leonard M. Adleman
\by Ming-Deh A. Huang
\book Primality testing and abelian varieties over finite fields
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\publ Springer-Verlag
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\bib{1977/adleman}
\yr 1977
\mr 58:19339
\by Leonard M. Adleman
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\bib{1994/adleman-problems}
\yr 1994
\by Leonard M. Adleman
\by Kevin S. McCurley
\paper Open problems in number theoretic complexity, II
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\bib{1983/adleman}
\yr 1983
\mr 84e:10008
\by Leonard M. Adleman
\by Carl Pomerance
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\vol 117
\pages 173--206
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\bib{2004/adoba}
\yr 2004
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\by Joshua Tseng
\by Jesse Walker
\by Venkat Rangan
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\bib{1997/afanassiev}
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\bib{1977/agarwal}
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\bib{preprint/agashe}
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\bib{2002/agrawal}
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\bib{1973/aho-stoc5}
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\bib{1975/aho}
\yr 1975
\mr 51:7393
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\bib{1974/aho}
\yr 1974
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\book The design and analysis of computer algorithms
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\bib{1993/aiello}
\yr 1993
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\bib{2001/akishita-simultaneous}
\yr 2001
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\bib{1988/alexi}
\yr 1988
\mr 89j:11120
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\by Benny Chor
\by Oded Goldreich
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\bib{1994/alford}
\yr 1994
\mr 95k:11114
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\by Andrew Granville
\by Carl Pomerance
\paper There are infinitely many Carmichael numbers
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\vol 139
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\url http://cr.yp.to/\allowbreak bib/\allowbreak entries.html#\allowbreak 1994/alford
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\bib{1995/alford}
\yr 1995
\mr 96k:11152
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\bib{2000/allan}
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\bib{2001/alster-pkccnt}
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\mr 2002h:94001
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\bib{1994/anderson-book}
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\mr 97b:94004
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\bib{1976/anderssen-book}
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\bib{1994/andrews}
\yr 1994
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\yr 1952
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\bib{2005/antipa-accelerated}
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\bib{2003/antipa}
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\yr 1970
\mr 40:4241
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\bib{1968/apostolatos}
\yr 1968
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\bib{1970/arlazarov}
\yr 1970
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\bib{1994/artin-book}
\yr 1994
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\mr 95i:00037
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\book Duration and change
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\bib{1966/artjuhov}
\yr 1966
\mr 35:4153
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\paper Certain criteria for primality of numbers connected with the little Fermat theorem
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\bib{1996/asano}
\yr 1996
\isbn 3--540--62048--6
\mr 98k:68001
\editor Tetsuo Asano
\editor Yoshihide Igarashi
\editor Hiroshi Nagamochi
\editor Satoru Miyano
\editor Subhash Suri
\book Algorithms and computation: Papers from the 7th international symposium (ISAAC '96) held in Osaka, December 16--18, 1996
\series Lecture Notes in Computer Science
\seriesvol 1178
\publ Springer-Verlag
\publaddr Berlin
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\bib{1993/ashby}
\yr 1993
\editor Victoria Ashby
\book First ACM conference on computer and communications security
\publ Association for Computing Machinery
\publaddr New York
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\bib{1996/atici}
\yr 1996
\mr 98g:94021
\by Mustafa Atici
\by Douglas R. Stinson
\paper Universal hashing and multiple authentication
\inbook \cite{1996/koblitz}
\pages 15--30
\url http://link.springer.de/link/service/series/0558/bibs/1109/11090016.htm
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\bib{1965/atkin}
\yr 1965
\mr 34:2547
\by A. O. L. Atkin
\paper On pseudo-squares
\jour Proceedings of the London Mathematical Society, Third Series
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\vol 14a
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\bib{1998/atkin}
\yr 1998
\mr 98k:11183
\by A. O. L. Atkin
\paper Intelligent primality test offer
\inbook \cite{1998/buell}
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\bib{2004/atkin-primesieves}
\yr 2004
\by A. O. L. Atkin
\by Daniel J. Bernstein
\paper Prime sieves using binary quadratic forms
\jour Mathematics of Computation
\issn 0025--5718
\vol 73
\pages 1023--1030
\url http://cr.yp.to/papers.html#primesieves
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\bib{1982/atkin}
\yr 1982
\mr 84d:10013
\by A. O. L. Atkin
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\paper On a primality test of Solovay and Strassen
\jour SIAM Journal on Computing
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\vol 11
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\bib{1993/atkin-ecpp}
\yr 1993
\mr 93m:11136
\by A. O. L. Atkin
\by Francois Morain
\paper Elliptic curves and primality proving
\jour Mathematics of Computation
\issn 0025--5718
\vol 61
\pages 29--68
\url http://www.lix.polytechnique.fr/~morain/Articles/articles.english.html
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\bib{1993/atkin}
\yr 1993
\mr 93k:11115
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\paper Finding suitable curves for the elliptic curve method of factorization
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\bib{1995/atkins}
\yr 1995
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\bib{2000/augot}
\yr 2000
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\bib{1983/auslander}
\yr 1983
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\bib{2004/avanzi-aspects}
\yr 2004
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\paper Aspects of hyperelliptic curves over large prime fields in software implementations
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\yr 2005
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\bib{1991/awerbuch}
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\bib{1984/bach}
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\bib{1986/bach}
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\bib{1996/bach-semismooth}
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\bib{1989/bach}
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\bib{1996/bach-book}
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\bib{1993/bach-powers}
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\bib{2000/bellare-book}
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\mr 2002c:94002  
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\bib{1996/bellare-hmac}
\yr 1996
\by Mihir Bellare
\by Ran Canetti
\by Hugo Krawczyk
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\bib{1996/bellare-hmac-draft}
\yr 1996
\by Mihir Bellare
\by Ran Canetti
\by Hugo Krawczyk
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\pages 16--30
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\bib{1996/bellare-cascade}
\yr 1996
\by Mihir Bellare
\by Ran Canetti
\by Hugo Krawczyk
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\seeolder \cite{1996/bellare-cascade-draft}
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\bib{1996/bellare-cascade-draft}
\yr 1996
\by Mihir Bellare
\by Ran Canetti
\by Hugo Krawczyk
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\bib{2000/bellare-modes}
\yr 2000
\by Mihir Bellare
\by Anand Desai
\by Eron Jokipii
\by Phillip Rogaway
\paper A concrete security treatment of symmetric encryption: analysis of the DES modes of operation
\url http://www.cs.ucdavis.edu/~rogaway/papers/sym-enc-abstract.html
\endref

\bib{1994/bellare-incremental}
\yr 1994
\by Mihir Bellare
\by Oded Goldreich
\by Shafi Goldwasser
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\pages 216--233
\url http://www-cse.ucsd.edu/~mihir/papers/incremental.html
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\bib{2004/bellare-verification}
\yr 2004
\by Mihir Bellare
\by Oded Goldreich
\by Anton Mityagin
\paper The power of verification queries in message authentication and authenticated encryption
\url http://eprint.iacr.org/2004/309
\endref

\bib{1995/bellare-xor}
\yr 1995
\by Mihir Bellare
\by Roch Gu\'erin
\by Phillip Rogaway
\paper XOR MACs: new methods for message authentication using finite pseudorandom functions
\url http://www-cse.ucsd.edu/~mihir/papers/xormacs.html
\seeolder \cite{1995/bellare-xor-draft}
\endref

\bib{1995/bellare-xor-draft}
\yr 1995
\by Mihir Bellare
\by Roch Gu\'erin
\by Phillip Rogaway
\paper XOR MACs: new methods for message authentication using finite pseudorandom functions
\inbook \cite{1995/coppersmith-book}
\pages 15--28
\seenewer \cite{1995/bellare-xor}
\endref

\bib{1994/bellare-cbc-draft}
\yr 1994
\by Mihir Bellare
\by Joe Kilian
\by Phillip Rogaway
\paper The security of cipher block chaining
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\pages 341--358
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\bib{2000/bellare-cbc}
\yr 2000
\by Mihir Bellare
\by Joe Kilian
\by Phillip Rogaway
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\jour Journal of Computer and System Sciences
\issn 0022--0000
\vol 61
\pages 362--399
\url http://www-cse.ucsd.edu/~mihir/papers/cbc.html
\seeolder \cite{1994/bellare-cbc-draft}
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\bib{2000/bellare-backwards}
\yr 2000
\by Mihir Bellare
\by Ted Krovetz
\by Phillip Rogaway
\paper Luby-Rackoff backwards: increasing security by making block ciphers non-invertible
\url http://www.cs.ucdavis.edu/~krovetz/
\endref

\bib{1993/bellare}
\yr 1993
\by Mihir Bellare
\by Phillip Rogaway
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\bib{1996/bellare-sigs}
\yr 1996
\by Mihir Bellare
\by Phillip Rogaway
\paper The exact security of digital signatures: how to sign with RSA and Rabin
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\seeolder \cite{1996/bellare-sigs-draft}
\endref

\bib{1996/bellare-sigs-draft}
\yr 1996
\by Mihir Bellare
\by Phillip Rogaway
\paper The exact security of digital signatures: how to sign with RSA and Rabin
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\pages 399--416
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\bib{2004/bellare-chap4}
\yr 2004
\by Mihir Bellare
\by Phillip Rogaway
\paper Introduction to modern cryptography, chapter 4: symmetric encryption
\url http://www-cse.ucsd.edu/users/mihir/cse207/m-se.pdf
\endref

\bib{2004/bellare-games}
\yr 2004
\by Mihir Bellare
\by Phillip Rogaway
\paper The game-playing technique
\url http://eprint.iacr.org/2004/331
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\bib{2005/bellare-chap5}
\yr 2005
\by Mihir Bellare
\by Phillip Rogaway
\paper Introduction to modern cryptography, chapter 5: symmetric encryption
\url http://www.cse.ucsd.edu/users/mihir/cse107/
\endref

\bib{1990/bender}
\yr 1990
\mr 91d:11154
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\bib{1999/bender}
\yr 1999
\mr 2000i:65064
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\by E. Rodney Canfield
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\vol 31
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\bib{1998/bender}
\yr 1998
\mr 99c:11156
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\bib{1986/bengelloun}
\yr 1986
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\bib{2002/bennett}
\yr 2002
\isbn 1--56881--126--8
\mr 2003h:11004
\editor M. A. Bennett
\editor B. C. Berndt
\editor N. Boston
\editor H. G. Diamond
\editor A. J. Hildebrand
\editor W. Philipp
\book Number theory for the millennium. I: papers from the conference held at the University of Illinois at Urbana-Champaign, Urbana, IL, May 21--26, 2000
\publ A. K. Peters
\publaddr Natick, Massachusetts
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\bib{2005/bentahar-equivalence}
\yr 2005
\by Kamel Bentahar
\paper The equivalence between the DHP and DLP for elliptic curves used in practical applications, revisited
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\bib{1994/bergeron}
\yr 1994
\mr 95m:11144
\by Fran\c cois Bergeron
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\by Sre\v cko Brlek
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\issn 1246--7405
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\bib{1989/bergeron}
\yr 1989
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\bib{1968/bergland-real}
\yr 1968
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\paper A fast Fourier transform algorithm for real-valued series
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\bib{1968/bergland-8}
\yr 1968
\mr 37:2485
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\paper A fast Fourier transform algorithm using base $8$ iterations
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\bib{1967/berlekamp}
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\bib{1968/berlekamp}
\yr 1968
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\book Algebraic coding theory
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\bib{1970/berlekamp}
\yr 1970
\mr 43:1948
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\bib{1975/benderskii}
\yr 1975
\mr 52:12397
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\bib{1996/berndt}
\yr 1996
\isbn 0--8176--3933--0
\mr 97c:11001
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\by Harold G. Diamond
\by Adolf J. Hildebrand
\book Analytic number theory, volume 2
\publ Birkhauser
\publaddr Boston
\endref

\bib{1987/bernstein}
\yr 1987
\by Daniel J. Bernstein
\paper New fast algorithms for $\pi$ and $e$
\paperinfo paper for the Westinghouse competition, distributed widely at the Ramanujan Centenary Conference
\url http://cr.yp.to/\allowbreak bib/\allowbreak entries.html#\allowbreak 1987/bernstein
\endref

\bib{1994/bernstein}
\yr 1994
\by Daniel J. Bernstein
\paper A non-iterative $2$-adic statement of the $3N+1$ conjecture
\jour Proceedings of the American Mathematical Society
\issn 0002--9939
\vol 121
\pages 405--408
\url http://cr.yp.to/papers.html
\endref

\bib{1995/bernstein-thesis}
\yr 1995
\by Daniel J. Bernstein
\book Detecting perfect powers in essentially linear time, and other studies in computational number theory
\phdthesis
\publ University of California at Berkeley
\endref

\bib{1995/bernstein-mmecrt}
\yr 1995
\by Daniel J. Bernstein
\paper Multidigit modular multiplication with the explicit Chinese remainder theorem
\inbook \cite{1995/bernstein-thesis}
\url http://cr.yp.to/papers.html
\endref

\bib{1995/bernstein-mlnfs}
\yr 1995
\by Daniel J. Bernstein
\paper The multiple-lattice number field sieve
\inbook \cite{1995/bernstein-thesis}
\url http://cr.yp.to/papers.html
\endref

\bib{1996/bernstein-fiall}
\yr 1996
\by Daniel J. Bernstein
\paper Fast ideal arithmetic via lazy localization
\inbook \cite{1996/cohen}
\pages 27--34
\url http://cr.yp.to/papers.html
\endref

\bib{1998/bernstein-compose}
\yr 1998
\by Daniel J. Bernstein
\paper Composing power series over a finite ring in essentially linear time
\jour Journal of Symbolic Computation
\issn 0747--7171
\vol 26
\pages 339--341
\url http://cr.yp.to/papers.html
\endref

\bib{1998/bernstein-powers}
\yr 1998
\mr 98j:11121
\by Daniel J. Bernstein
\paper Detecting perfect powers in essentially linear time
\jour Mathematics of Computation
\issn 0025--5718
\vol 67
\pages 1253--1283
\url http://cr.yp.to/papers.html
\endref

\bib{1999/bernstein-hash127-abs}
\yr 1999
\by Daniel J. Bernstein
\paper Guaranteed message authentication faster than MD5 (abstract)
\url http://cr.yp.to/papers.html#hash127-abs
\endref

\bib{1999/bernstein-stretch}
\yr 1999
\by Daniel J. Bernstein
\paper How to stretch random functions: the security of protected counter sums
\jour Journal of Cryptology
\issn 0933--2790
\vol 12
\pages 185--192
\url http://cr.yp.to/papers.html
\endref

\bib{2001/bernstein-schimmler}
\yr 2001
\by Daniel J. Bernstein
\paper An introduction to Schimmler sorting
\url http://cr.yp.to/talks.html#2001.05.14
\endref

\bib{2001/bernstein-nfscircuit}
\yr 2001
\by Daniel J. Bernstein
\paper Circuits for integer factorization: a proposal
\url http://cr.yp.to/papers.html
\endref

\bib{2001/bernstein-sortedsums}
\yr 2001
\by Daniel J. Bernstein
\paper Enumerating solutions to $p(a)+q(b)=r(c)+s(d)$
\jour Mathematics of Computation
\issn 0025--5718
\vol 70
\pages 389--394
\url http://cr.yp.to/papers.html
\endref

\bib{2001/bernstein-nsa}
\yr 2001
\by Daniel J. Bernstein
\paper The NSA sieving circuit
\url http://cr.yp.to/talks.html#2001.05.07
\endref

\bib{2002/bernstein-psi}
\yr 2002
\by Daniel J. Bernstein
\paper Arbitrarily tight bounds on the distribution of smooth integers
\inbook \cite{2002/bennett}
\pages 49--66
\url http://cr.yp.to/papers.html#psi
\endref

\bib{2004/bernstein-cachetiming}
\yr 2004
\by Daniel J. Bernstein
\paper Cache-timing attacks on AES
\url http://cr.yp.to/papers.html#cachetiming
\id cd9faae9bd5308c440df50fc26a517b4
\endref

\bib{2004/bernstein-focus}
\yr 2004
\by Daniel J. Bernstein
\paper Doubly focused enumeration of locally square polynomial values
\inbook \cite{2004/vanderpoorten}
\pages 69--76
\url http://\allowbreak cr.yp.to/papers.html#focus
\id b4795a4f12863c26de5b7afe9296ffd8
\endref

\bib{2005/bernstein-dcba}
\yr 2005
\by Daniel J. Bernstein
\paper Factoring into coprimes in essentially linear time
\jour Journal of Algorithms
\issn 0196--6774
\vol 54
\pages 1--30
\url http://cr.yp.to/papers.html#dcba
\id f32943f0bb67a9317d4021513f9eee5a
\endref

\bib{2005/bernstein-poly1305}
\yr 2005
\by Daniel J. Bernstein
\paper The Poly1305-AES message-authentication code
\inbook \cite{2005/gilbert-fse2005}
\pages 32--49
\url http://cr.yp.to/papers.html#poly1305
\id 0018d9551b5546d97c340e0dd8cb5750
\endref

\bib{preprint/bernstein-sigs}
\by Daniel J. Bernstein
\paper A secure public-key signature system with extremely fast verification
\paperinfo accepted by {\it Journal of Cryptology}, but withdrawn to be incorporated into author's {\it High-speed cryptography} book
\url http://cr.yp.to/papers.html#sigs
\endref

\bib{preprint/bernstein-unipat}
\by Daniel J. Bernstein
\paper A simple universal pattern-matching automaton
\paperinfo submitted for publication
\url http://cr.yp.to/papers.html
\endref

\bib{preprint/bernstein-logfloor}
\by Daniel J. Bernstein
\paper Computing logarithm floors in essentially linear time
\url http://cr.yp.to/\allowbreak papers.html#\allowbreak logfloor
\id 97bbdc1ce6aff974c789eab21b9cfba1
\endref

\bib{preprint/bernstein-logagm}
\by Daniel J. Bernstein
\paper Computing logarithm intervals with the arithmetic-geometric-mean iteration
\url http://cr.yp.to/\allowbreak papers.html#\allowbreak logagm
\id 8f92b1e3ec7918d37b28b9efcee5e97f
\endref

\bib{preprint/bernstein-prime2004}
\by Daniel J. Bernstein
\paper Distinguishing prime numbers from composite numbers: the state of the art in 2004
\paperinfo submitted
\url http://cr.yp.to/\allowbreak papers.html#\allowbreak prime2004
\id d72f09ae5b05f41a53e2237c53f5f276
\endref

\bib{preprint/bernstein-dcba}
\by Daniel J. Bernstein
\paper Factoring into coprimes in essentially linear time
\paperinfo to appear
\jour Journal of Algorithms
\issn 0196--6774
\url http://cr.yp.to/papers.html
\id f32943f0bb67a9317d4021513f9eee5a
\endref

\bib{preprint/bernstein-multapps}
\by Daniel J. Bernstein
\paper Fast multiplication and its applications
\paperinfo to appear in Buhler-Stevenhagen {\it Algorithmic number theory} book
\url http://\allowbreak cr.yp.to/papers.html#multapps
\id 8758803e61822d485d54251b27b1a20d
\endref

\bib{preprint/bernstein-zmult}
\by Daniel J. Bernstein
\paper Faster multiplication of integers
\paperinfo draft
\endref

\bib{preprint/bernstein-sqroot}
\by Daniel J. Bernstein
\paper Faster square roots in annoying finite fields
\paperinfo to be incorporated into author's {\it High-speed cryptography} book
\url http://cr.yp.to/papers.html#sqroot
\endref

\bib{preprint/bernstein-hash127}
\by Daniel J. Bernstein
\paper Floating-point arithmetic and message authentication
\paperinfo to be incorporated into author's {\it High-speed cryptography} book
\url http://cr.yp.to/papers.html#hash127
\id dabadd3095644704c5cbe9690ea3738e
\endref

\bib{preprint/bernstein-sf}
\by Daniel J. Bernstein
\paper How to find small factors of integers
\paperinfo accepted to Mathematics of Computation; now being revamped
\url http://cr.yp.to/papers.html
\endref

\bib{preprint/bernstein-smoothparts}
\by Daniel J. Bernstein
\paper How to find smooth parts of integers
\paperinfo draft
\url http://cr.yp.to/papers.html#smoothparts
\id 201a045d5bb24f43f0bd0d97fcf5355a
\endref

\bib{preprint/bernstein-m3}
\by Daniel J. Bernstein
\paper Multidigit multiplication for mathematicians
\url http://cr.yp.to/papers.html
\endref

\bib{preprint/bernstein-pippenger}
\by Daniel J. Bernstein
\paper Pippenger's exponentiation algorithm
\paperinfo to be incorporated into author's {\it High-speed cryptography} book
\url http://cr.yp.to/papers.html
\endref

\bib{preprint/bernstein-aks}
\by Daniel J. Bernstein
\paper Proving primality after Agrawal-Kayal-Saxena
\url http://\allowbreak cr.yp.to/\allowbreak papers.html#aks
\endref

\bib{preprint/bernstein-quartic}
\by Daniel J. Bernstein
\paper Proving primality in essentially quartic random time
\paperinfo submitted
\url http://cr.yp.to/papers.html#quartic
\id 43f1d5199196c0593c1e8442af682180
\endref

\bib{preprint/bernstein-rwtight}
\by Daniel J. Bernstein
\paper Proving tight security for standard Rabin-Williams signatures
\paperinfo to be incorporated into author's {\it High-speed cryptography} book
\url http://cr.yp.to/papers.html#rwtight
\id c30057d690a8fb42af6a5172b5da9006
\endref

\bib{preprint/bernstein-smallheight}
\by Daniel J. Bernstein
\paper Reducing lattice bases to find small-height values of univariate polynomials
\paperinfo to appear in Buhler-Stevenhagen {\it Algorithmic number theory} book
\url http://cr.yp.to/papers.html#smallheight
\id 82f82c041b7e2bdce94a5e1f94511773
\endref

\bib{preprint/bernstein-fastnewton}
\by Daniel J. Bernstein
\paper Removing redundancy in high-precision Newton iteration
\paperinfo draft
\url http://cr.yp.to/papers.html#fastnewton
\id def7f1e35fb654671c6f767b16b93d50
\endref

\bib{preprint/bernstein-scaledmod}
\by Daniel J. Bernstein
\paper Scaled remainder trees
\paperinfo draft
\url http://cr.yp.to/papers.html#scaledmod
\id e2b8da026cf72d01d97e20cf2874f278
\endref

\bib{preprint/bernstein-abccong}
\by Daniel J. Bernstein
\paper Sharper ABC-based bounds for congruent polynomials
\jour Journal de Th\'eorie des Nombres de Bordeaux
\issn 1246--7405
\paperinfo to appear
\url http://cr.yp.to/papers.html#abccong
\id 1d9e079cee20138de8e119a99044baa3
\endref

\bib{preprint/bernstein-cachesieving}
\by Daniel J. Bernstein
\paper Sieving in cache
\paperinfo draft
\url http://cr.yp.to/papers.html#cachesieving
\endref

\bib{preprint/bernstein-securitywcs}
\by Daniel J. Bernstein
\paper Stronger security bounds for Wegman-Carter-Shoup authenticators
\url http://cr.yp.to/papers.html#securitywcs
\id 2d603727f69542f30f7da2832240c1ad
\endref

\bib{preprint/bernstein-c3}
\by Daniel J. Bernstein
\paper The complexity of complex convolution
\paperinfo draft
\endref

\bib{1996/bernstein-3x1conjmap}
\yr 1996
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\by Jeffery C. Lagarias
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\jour Canadian Journal of Mathematics
\issn 0008--414X
\vol 48
\pages 1154--1169
\url http://cr.yp.to/papers.html
\endref

\bib{1993/bernstein}
\yr 1993
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\by Arjen K. Lenstra
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\bib{preprint/bernstein-powers2}
\by Daniel J. Bernstein
\by Hendrik W. Lenstra, Jr.
\by Jonathan Pila
\paper Detecting perfect powers by factoring into coprimes
\url http://cr.yp.to/papers.html#powers2
\id bbd41ce71e527d3c06295aadccf60979
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\bib{preprint/bernstein-meecrt}
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\by Jonathan P. Sorenson
\paper Modular exponentiation via the explicit Chinese remainder theorem
\paperinfo submitted
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\endref

\bib{2002/berrizbeitia}
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\bib{2000/biehl-elliptic}
\yr 2000
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\vol 27
\pages 959--963
\url http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub019.html
\endref

\bib{1974/brent}
\yr 1974
\mr 58:31996
\by Richard P. Brent
\paper The parallel evaluation of general arithmetic expressions
\jour Journal of the ACM
\issn 0004--5411
\vol 21
\pages 201--206
\url http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub022.html
\endref

\bib{1976/brent-elementary}
\yr 1976
\mr 52:16111
\by Richard P. Brent
\paper Fast multiple-precision evaluation of elementary functions
\jour Journal of the ACM
\issn 0004--5411
\vol 23
\pages 242--251
\url http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub034.html
\endref

\bib{1976/brent-zero}
\yr 1976
\mr 54:11843
\by Richard P. Brent
\paper Multiple-precision zero-finding methods and the complexity of elementary function evaluation
\inbook \cite{1976/traub}
\pages 151--176
\url http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub028.html
\endref

\bib{1976/brent-arithmetic}
\yr 1976
\by Richard P. Brent
\paper The complexity of multiple-precision arithmetic
\inbook \cite{1976/anderssen-book}
\url http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub032.html
\pages 126--165
\endref

\bib{1980/brent-cycles}
\yr 1980
\mr 82a:10017
\by Richard P. Brent
\paper An improved Monte Carlo factorization algorithm
\jour BIT
\issn 0006--3835
\vol 20
\pages 176--184
\endref

\bib{1986/brent}
\yr 1986
\by Richard P. Brent
\paper Some integer factorization algorithms using elliptic curves
\jour Australian Computer Science Communications
\issn 0157--3055
\vol 8
\pages 149--163
\endref

\bib{1990/brent}
\yr 1990
\mr 91h:11148
\by Richard P. Brent
\paper Parallel algorithms for integer factorisation
\inbook \cite{1990/loxton}
\pages 26--37
\endref

\bib{1999/brent}
\yr 1999
\mr 99e:11154
\by Richard P. Brent
\paper Factorization of the tenth Fermat number
\jour Mathematics of Computation
\issn 0025--5718
\vol 68
\pages 429--451
\endref

\bib{1980/brent-gcd}
\yr 1980
\mr 82d:65033
\by Richard P. Brent
\by Fred G. Gustavson
\by David Y. Y. Yun
\paper Fast solution of Toeplitz systems of equations and computation of Pad\'e approximants
\jour Journal of Algorithms
\issn 0196--6774
\vol 1
\pages 259--295
\url http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub059.html
\endref

\bib{1978/brent}
\yr 1978
\mr 58:25090
\by Richard P. Brent
\by H. T. Kung
\paper Fast algorithms for manipulating formal power series
\jour Journal of the ACM
\issn 0004--5411
\vol 25
\pages 581--595
\endref

\bib{1980/brent-gamma}
\yr 1980
\mr 82g:10002
\by Richard P. Brent
\by Edwin M. McMillan
\paper Some new algorithms for high-precision computation of Euler's constant
\jour Mathematics of Computation
\issn 0025--5718
\vol 34
\pages 305--312
\url http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub049.html
\endref

\bib{1981/brent}
\yr 1981
\mr 83h:10014
\by Richard P. Brent
\by John M. Pollard
\paper Factorization of the eighth Fermat number
\jour Mathematics of Computation
\issn 0025--5718
\vol 36
\pages 627--630
\endref

\bib{1977/bresenham}
\yr 1977
\by Jack Bresenham
\paper A linear algorithm for incremental digital display of circular arcs
\jour Communications of the ACM
\issn 0001--0782
\vol 20
\pages 100--106
\endref

\bib{1989/bressoud}
\yr 1989
\isbn 0--387--97040--1
\mr 91e:11150
\by David M. Bressoud
\book Factorization and primality testing
\publ Springer-Verlag
\publaddr New York
\endref

\bib{1993/brickell-book}
\yr 1993
\isbn 3--540--57340--2, 0--387--57340--2
\mr 95b:94001
\editor Ernest F. Brickell
\book Advances in cryptology---CRYPTO '92: 12th annual international cryptology conference, Santa Barbara, California, USA, August 16--20, 1992, proceedings
\series Lecture Notes in Computer Science
\seriesvol 740
\publ Springer-Verlag
\publaddr Berlin
\endref

\bib{1993/brickell-exp}
\yr 1993
\by Ernest F. Brickell
\by Daniel M. Gordon
\by Kevin S. McCurley
\by David B. Wilson
\paper Fast exponentiation with precomputation (extended abstract)
\inbook \cite{1993/rueppel}
\pages 200--207  
\seenewer \cite{1995/brickell-exp}
\url http://cr.yp.to/\allowbreak bib/\allowbreak entries.html#\allowbreak 1993/brickell-exp
\endref

\bib{1995/brickell-exp}
\yr 1995
\by Ernest F. Brickell
\by Daniel M. Gordon
\by Kevin S. McCurley
\by David B. Wilson
\paper Fast exponentiation with precomputation: algorithms and lower bounds
\url http://research.microsoft.com/~dbwilson/bgmw/
\seeolder \cite{1993/brickell-exp}
\endref

\bib{1983/brickell-logs}
\yr 1983
\by Ernest F. Brickell
\by J. H. Moore
\paper Some remarks on the Herlestam-Johannesson algorithm for computing logarithms over GF$(2^p)$
\inbook \cite{1983/chaum}
\pages 15--19
\endref

At the 1981 IEEE Symposium on Information Theory, T. Herlestam and R. Johannesson presented a heurestic [sic] method for computing logarithms over GF(2^p). They reported computing logarithms over GF(2^{31}) with surprisingly few iterations and claimed that the running time of their algorithm was polynomial in p.

\bib{1988/brigham}
\yr 1988
\isbn 0--13--307505--2 
\by E. Oran Brigham
\book The fast Fourier transform and its applications
\publ Prentice-Hall
\publaddr Englewood Cliffs, New Jersey
\endref

\bib{1981/brillhart}
\yr 1981
\mr 84f:10009
\by John Brillhart
\paper Fermat's factoring method and its variants
\jour Congressus Numerantium
\issn 0384--9864
\vol 32
\pages 29--48
\endref