-
5
-
-
0010703519
-
Factoring a binary polynomial of degree over one million
-
OLAF BONORDEN, JOACHIM VON ZUR GATHEN, JÜRGEN GERHARD, OLAF MÜLLER & MICHAEL NÖCKER (2001). Factoring a binary polynomial of degree over one million. ACM SIGSAM Bulletin 35(1), 16-18. http://www-math.upb.de/~aggathen/Publications/bongat01.ps.gz.
-
(2001)
ACM SIGSAM Bulletin
, vol.35
, Issue.1
, pp. 16-18
-
-
Bonorden, O.1
Von zur Gathen, J.2
Gerhard, J.3
Müller, O.4
Nöcker, M.5
-
7
-
-
2942698062
-
A fast algorithm for testing reducibility of trinomials mod 2 and some new primitive trinomials of degree 3021377
-
To appear
-
RICHARD P. BRENT, SAMULI LARVALA & PAUL ZIMMERMANN (2002) A fast algorithm for testing reducibility of trinomials mod 2 and some new primitive trinomials of degree 3021377. Mathematics of Computation To appear.
-
(2002)
Mathematics of Computation
-
-
Brent, R.P.1
Larvala, S.2
Zimmermann, P.3
-
8
-
-
85027967075
-
Fast exponentiation with precomputation
-
Balatonfüred, Hungary, R. RUEPPEL, editor, number 658 in Lecture Notes in Computer Science. Springer-Verlag, Berlin. ISSN 0302-9743. MR 94e:94002
-
ERNEST F. BRICKELL, DANIEL M. GORDON, KEVIN S. MCCURLEY & DAVID B. WILSON (1992) Fast Exponentiation with Precomputation. In Advances in Cryptology: Proceedings of EUROCRYPT 1992, Balatonfüred, Hungary, R. RUEPPEL, editor, number 658 in Lecture Notes in Computer Science, 200-207. Springer-Verlag, Berlin. ISSN 0302-9743. MR 94e:94002
-
(1992)
Advances in Cryptology: Proceedings of EUROCRYPT 1992
, pp. 200-207
-
-
Brickell, E.F.1
Gordon, D.M.2
McCurley, K.S.3
Wilson, D.B.4
-
9
-
-
0038076370
-
-
Number 22 in Contemporary Mathematics. American Mathematical Society, Providence RI, third edition. MR 90d:11009
-
n ± 1, b = 2,3,5,6,7,10,11,12 up to High Powers. Number 22 in Contemporary Mathematics. American Mathematical Society, Providence RI, third edition. MR 90d:11009
-
(2001)
n ± 1, b = 2,3,5,6,7,10,11,12 Up to High Powers
-
-
Brillhart, J.1
Lehmer, D.H.2
Selfridge, J.L.3
Tuckerman, B.4
Wagstaff Jr., S.S.5
-
10
-
-
0010656780
-
On arithmetical algorithms over finite fields
-
MR 90f:11100
-
DAVID G. CANTOR (1989) On Arithmetical Algorithms over Finite Fields. Journal of Combinatorial Theory, Series A 50, 285-300. MR 90f:11100
-
(1989)
Journal of Combinatorial Theory, Series A
, vol.50
, pp. 285-300
-
-
Cantor, D.G.1
-
11
-
-
84966220369
-
A new algorithm for factoring polynomials over finite fields
-
MR 82e:12020
-
DAVID G. CANTOR & HANS ZASSENHAUS (1981) A New Algorithm for Factoring Polynomials Over Finite Fields. Mathematics of Computation 36(154), 587-592. MR 82e:12020
-
(1981)
Mathematics of Computation
, vol.36
, Issue.154
, pp. 587-592
-
-
Cantor, D.G.1
Zassenhaus, H.2
-
13
-
-
0009399673
-
Computing sequences with addition chains
-
MR 82h:68064
-
PETER DOWNEY, BENTON LEONG & RAVI SETHI (1981) Computing Sequences with Addition Chains. SIAM Journal on Computing 10(3), 638-646. MR 82h:68064
-
(1981)
SIAM Journal on Computing
, vol.10
, Issue.3
, pp. 638-646
-
-
Downey, P.1
Leong, B.2
Sethi, R.3
-
15
-
-
0033477786
-
Normal bases via general Gauß periods
-
MR 99c:11148
-
SANDRA FEISEL, JOACHIM VON ZUR GATHEN & M. AMIN SHOKROLLAHI (1999) Normal bases via general Gauß periods. Mathematics of Computation 68(225), 271-290. http://www.ams.org/Journal-getitem?pii=S0025-5718-99-00988-6. MR 99c:11148
-
(1999)
Mathematics of Computation
, vol.68
, Issue.225
, pp. 271-290
-
-
Feisel, S.1
Von zur Gathen, J.2
Amin Shokrollahi, M.3
-
16
-
-
0001057132
-
Optimal normal bases
-
MR 93j:12003
-
S. GAO & H. W. LENSTRA, JR. (1992) Optimal normal bases. Designs, Codes, and Cryptography 2, 315-323. MR 93j:12003
-
(1992)
Designs, Codes, and Cryptography
, vol.2
, pp. 315-323
-
-
Gao, S.1
Lenstra Jr., H.W.2
-
17
-
-
0000185837
-
Algorithms for exponentiation in finite fields
-
MR 2002e:68152a
-
SHUHONG GAO, JOACHIM VON ZUR GATHEN, DANIEL PANARIO & VICTOR SHOUP (2000) Algorithms for Exponentiation in Finite Fields. Journal of Symbolic Computation 29(6), 879-889. http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0309. MR 2002e:68152a
-
(2000)
Journal of Symbolic Computation
, vol.29
, Issue.6
, pp. 879-889
-
-
Gao, S.1
Von zur Gathen, J.2
Panario, D.3
Shoup, V.4
-
18
-
-
0003555072
-
Efficient and optimal exponentiation in finite fields
-
MR 94a:68061
-
JOACHIM VON ZUR GATHEN (1991) Efficient and optimal exponentiation in finite fields. Computational Complexity 1, 360-394. MR 94a:68061
-
(1991)
Computational Complexity
, vol.1
, pp. 360-394
-
-
Von zur Gathen, J.1
-
20
-
-
0004257127
-
-
Cambridge University Press, Cambridge, UK, 1st edition. ISBN 0-521-64176-4. Second edition 2003. MR 2000j:68205
-
JOACHIM VON ZUR GATHEN & JÜRGEN GERHARD (1999) Modern Computer Algebra. Cambridge University Press, Cambridge, UK, 1st edition. ISBN 0-521-64176-4. http://www-math.upb.de/~aggathen/mca/. Second edition 2003. MR 2000j:68205
-
(1999)
Modern Computer Algebra
-
-
Von zur Gathen, J.1
Gerhard, J.2
-
23
-
-
84957797971
-
Exponentiation in finite fields: Theory and practice
-
TEO MORA & HAROLD MATTSON, editors, number 1255 in Lecture Notes in Computer Science. Springer-Verlag. ISSN 0302-9743. MR 99c:68123
-
JOACHIM VON ZUR GATHEN & MICHAEL NÖCKER (1997) Exponentiation in Finite Fields: Theory and Practice. In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: AAECC-12, Toulouse, France, TEO MORA & HAROLD MATTSON, editors, number 1255 in Lecture Notes in Computer Science, 88-113. Springer-Verlag. ISSN 0302-9743. MR 99c:68123
-
(1997)
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: AAECC-12, Toulouse, France
, pp. 88-113
-
-
Von zur Gathen, J.1
Nöcker, M.2
-
24
-
-
2942681029
-
Computing special powers in finite fields: Extended abstract
-
Vancouver, Canada, SAM DOOLEY, editor. ACM Press. MR 2002a:00022
-
JOACHIM VON ZUR GATHEN & MICHAEL NOCKER (1999) Computing Special Powers in Finite Fields: Extended Abstract. In Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation ISSAC '99, Vancouver, Canada, SAM DOOLEY, editor, 83-90. ACM Press, http://doi.acm.org/10.1145/309831.309869. MR 2002a:00022
-
(1999)
Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation ISSAC '99
, pp. 83-90
-
-
Von zur Gathen, J.1
Nocker, M.2
-
25
-
-
2942664838
-
Polynomial and normal bases for finite fields
-
To appear
-
JOACHIM VON ZUR GATHEN & MICHAEL NÖCKER (2003) Polynomial and normal bases for finite fields. Journal of Cryptology. To appear.
-
(2003)
Journal of Cryptology
-
-
Von zur Gathen, J.1
Nöcker, M.2
-
27
-
-
0010745457
-
Factoring polynomials over finite fields: A survey
-
MR 2001k:11253
-
JOACHIM VON ZUR GATHEN & DANIEL PANARIO (2001) Factoring Polynomials Over Finite Fields: A Survey. Journal of Symbolic Computation 81(1-2), 3-17. http://www.idealibrary.com/links/doi/10.1006/jsco.1999.1002. MR 2001k:11253
-
(2001)
Journal of Symbolic Computation
, vol.81
, Issue.1-2
, pp. 3-17
-
-
Von zur Gathen, J.1
Panario, D.2
-
29
-
-
0001605828
-
Computing frobenius maps and factoring polynomials
-
MR 94d:12011
-
JOACHIM VON ZUR GATHEN & VICTOR SHOUP (1992) Computing Frobenius maps and factoring polynomials. Computational Complexity 2, 187-224. MR 94d:12011
-
(1992)
Computational Complexity
, vol.2
, pp. 187-224
-
-
Von zur Gathen, J.1
Shoup, V.2
-
30
-
-
0003439018
-
-
Gerh. Fleischer Iun., Leipzig. English translation by ARTHUR A. CLARKE, Springer-Verlag, New York, 1986. MR 87f:01105
-
CARL FRIEDRICH GAUSS (1801) Disquisitiones Arithmeticae. Gerh. Fleischer Iun., Leipzig. English translation by ARTHUR A. CLARKE, Springer-Verlag, New York, 1986. MR 87f:01105
-
(1801)
Disquisitiones Arithmeticae
-
-
Gauss, C.F.1
-
31
-
-
0010935817
-
Periodische Dezimalbrüche - Was nicht jeder darüber weiß
-
A. BEUTELSPACHER, editor. Vieweg
-
KURT GIRSTMAIR (1995) Periodische Dezimalbrüche - was nicht jeder darüber weiß. In Jahrbuch Überblicke Mathematik 1995, A. BEUTELSPACHER, editor, 163-179. Vieweg.
-
(1995)
Jahrbuch Überblicke Mathematik 1995
, pp. 163-179
-
-
Girstmair, K.1
-
32
-
-
0000490812
-
A survey of fast exponentiation methods
-
MR 99g:94014
-
DANIEL M. GORDON (1998) A Survey of Fast Exponentiation Methods. Journal of Algorithms 27, 129-146. MR 99g:94014
-
(1998)
Journal of Algorithms
, vol.27
, pp. 129-146
-
-
Gordon, D.M.1
-
37
-
-
0005395785
-
-
A. KARATSUBA & YU. OFMAN (1962) Doklady Akademiǐ Nauk SSSR 145, 293-294. Multiplication of multidigit numbers on automata, Soviet Physics-Doklady 7 (1963), 595-596.
-
(1962)
Doklady Akademiǐ Nauk SSSR
, vol.145
, pp. 293-294
-
-
Karatsuba, A.1
Ofman, Yu.2
-
38
-
-
0001464763
-
Multiplication of multidigit numbers on automata
-
A. KARATSUBA & YU. OFMAN (1962) Doklady Akademiǐ Nauk SSSR 145, 293-294. Multiplication of multidigit numbers on automata, Soviet Physics-Doklady 7 (1963), 595-596.
-
(1963)
Soviet Physics-doklady
, vol.7
, pp. 595-596
-
-
-
39
-
-
0012096216
-
Evaluation of polynomials by computer
-
MR 27:970
-
DONALD E. KNUTH (1962) Evaluation of Polynomials By Computer. Communications of the ACM 5(1), 595-599. MR 27:970
-
(1962)
Communications of the ACM
, vol.5
, Issue.1
, pp. 595-599
-
-
Knuth, D.E.1
-
40
-
-
0003657590
-
-
Addison-Wesley, Reading MA, 3rd edition. First edition 1969. MR 4:3531
-
DONALD E. KNUTH (1998) The Art of Computer Programming, vol. 2, Seminumerical Algorithms. Addison-Wesley, Reading MA, 3rd edition. First edition 1969. MR 4:3531
-
(1998)
The Art of Computer Programming, Vol. 2, Seminumerical Algorithms
, vol.2
-
-
Knuth, D.E.1
-
41
-
-
0002989263
-
Euclid's algorithm for large numbers
-
D. H. LEHMER (1938) Euclid's algorithm for large numbers. The American Mathematical Monthly 45, 227-233.
-
(1938)
The American Mathematical Monthly
, vol.45
, pp. 227-233
-
-
Lehmer, D.H.1
-
42
-
-
0004129394
-
-
Kluwer Academic Publishers, Norwell MA
-
ALFRED J. MENEZES, IAN F. BLAKE, XUHONG GAO, RONALD C. MULLIN, SCOTT A. VANSTONE & TOMIK YAGHOOBIAN (1993) Applications of finite fields. Kluwer Academic Publishers, Norwell MA.
-
(1993)
Applications of Finite Fields
-
-
Menezes, A.J.1
Blake, I.F.2
Gao, X.3
Mullin, R.C.4
Vanstone, S.A.5
Yaghoobian, T.6
-
44
-
-
0347853530
-
On the evaluation of powers and monomials
-
MR 82c:10064
-
NICHOLAS PIPPENGER (1980) On the evaluation of powers and monomials. SIAM Journal on Computing 9(2), 230-250. MR 82c:10064
-
(1980)
SIAM Journal on Computing
, vol.9
, Issue.2
, pp. 230-250
-
-
Pippenger, N.1
-
45
-
-
0001262977
-
Probabilistic algorithms in finite fields
-
MR 81g:12002
-
MICHAEL O. RABIN (1980) Probabilistic algorithms in finite fields. SIAM Journal on Computing 9(2), 273-280. MR 81g:12002
-
(1980)
SIAM Journal on Computing
, vol.9
, Issue.2
, pp. 273-280
-
-
Rabin, M.O.1
-
47
-
-
0015197550
-
Schnelle Berechnung von Kettenbruchentwicklungen
-
A. SCHÖNHAGE (1971) Schnelle Berechnung von Kettenbruchentwicklungen. Acta Informatica 1, 139-144.
-
(1971)
Acta Informatica
, vol.1
, pp. 139-144
-
-
Schönhage, A.1
-
48
-
-
0012680953
-
A lower bound for the length of addition chains
-
MR 57:18229
-
A. SCHÖNHAGE (1975) A lower bound for the length of addition chains. Theoretical Computer Science 1, 1-12. MR 57:18229
-
(1975)
Theoretical Computer Science
, vol.1
, pp. 1-12
-
-
Schönhage, A.1
-
49
-
-
0000256895
-
Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2
-
MR 55:9604
-
A. SCHÖNHAGE (1977) Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2. Acta Informatica 7, 395-398. MR 55:9604
-
(1977)
Acta Informatica
, vol.7
, pp. 395-398
-
-
Schönhage, A.1
-
50
-
-
34250459760
-
Schnelle Multiplikation großer Zahlen
-
MR 45:1431
-
ARNOLD SCHÖNHAGE & VOLKER STRASSEN (1971) Schnelle Multiplikation großer Zahlen. Computing 7, 281-292. MR 45:1431
-
(1971)
Computing
, vol.7
, pp. 281-292
-
-
Schönhage, A.1
Strassen, V.2
-
52
-
-
0001977576
-
The computational complexity of continued fractions
-
MR 84b:12004
-
VOLKER STRASSEN (1983) The computational complexity of continued fractions. SIAM Journal on Computing 12(1), 1-27. MR 84b:12004
-
(1983)
SIAM Journal on Computing
, vol.12
, Issue.1
, pp. 1-27
-
-
Strassen, V.1
-
54
-
-
0040557251
-
Zur Arithmetik in endlichen Körpern
-
MR 94g:11114
-
ALFRED WASSERMANN (1993) Zur Arithmetik in endlichen Körpern. Bayreuther Math. Schriften 44, 147-251. MR 94g:11114
-
(1993)
Bayreuther Math. Schriften
, vol.44
, pp. 147-251
-
-
Wassermann, A.1
-
55
-
-
2942682200
-
A fast algorithm for multiplicative inverses based on the normal basis representation
-
DAZHUAN XU (1990) A fast algorithm for multiplicative inverses based on the normal basis representation. Journal of Nanjing Aeronautical Institute (English edition) 7(1), 121-124.
-
(1990)
Journal of Nanjing Aeronautical Institute (English Edition)
, vol.7
, Issue.1
, pp. 121-124
-
-
Xu, D.1
-
56
-
-
0346395014
-
On the evaluation of powers
-
MR 52:16128
-
ANDREW CHI-CHIH YAO (1976) On the Evaluation of Powers. SIAM Journal on Computing 5(1), 100-103. MR 52:16128
-
(1976)
SIAM Journal on Computing
, vol.5
, Issue.1
, pp. 100-103
-
-
Yao, A.C.-C.1
|