-
1
-
-
0018724062
-
A subexponential algorithm for the discrete logarithm problem with applications to cryptography
-
L., M. Adleman. A subexponential algorithm for the discrete logarithm problem with applications to cryptography. In 20th Annual Symposium on Foundations of Computer Science, pages 55-60, 1979.
-
(1979)
20Th Annual Symposium on Foundations of Computer Science
, pp. 55-60
-
-
Adleman, L.M.1
-
5
-
-
0001671902
-
On distinguishing prime numbers from composite numbers
-
L., M. Adleman, C., Pomerance, and R., S. Rumely. On distinguishing prime numbers from composite numbers. Annals of Mathematics, 117:173-206, 1983.
-
(1983)
Annals of Mathematics
, vol.117
, pp. 173-206
-
-
Adleman, L.M.1
Pomerance, C.2
Rumely, R.S.3
-
6
-
-
0012527140
-
-
M., Agrawal, N., Kayal and N., Saxena., PRIMES is in P. Manuscript, www.cse.iitk.ac.in/news/primality.html, 2002.
-
(2002)
PRIMES is in P. Manuscript
-
-
Agrawal, M.1
Kayal, N.2
Saxena, N.3
-
7
-
-
0001725847
-
There are infintely many carmichael numbers
-
W., Alford, A., Granville, and C., Pomerance. There are infintely many Carmichael numbers. Annals of Mathematics, 140:703-722, 1994.
-
(1994)
Annals of Mathematics
, vol.140
, pp. 703-722
-
-
Alford, W.1
Granville, A.2
Pomerance, C.3
-
9
-
-
0023985412
-
How to generate factored random numbers
-
E., Bach. How to generate factored random numbers. SIAM Journal on Computing, 17:179-193, 1988.
-
(1988)
SIAM Journal on Computing
, vol.17
, pp. 179-193
-
-
Bach, E.1
-
10
-
-
84966198660
-
Explicit bounds for primality testing and related problems
-
E., Bach. Explicit bounds for primality testing and related problems. Mathematics of Computation, 55:355-380, 1990.
-
(1990)
Mathematics of Computation
, vol.55
, pp. 355-380
-
-
Bach, E.1
-
11
-
-
0032073302
-
Efficient prediction of marsaglia-zaman random number generators
-
E., Bach. Efficient prediction of Marsaglia-Zaman random number generators. IEEE Transactions on Information Theory, IT-44:1253-1257, 1998.
-
(1998)
IEEE Transactions on Information Theory
, vol.IT44
, pp. 1253-1257
-
-
Bach, E.1
-
16
-
-
84968518238
-
Factoring polynomials over large finite fields
-
E., R. Berlekamp. Factoring polynomials over large finite fields. Mathematics of Computation, 24(111):713-735, 1970.
-
(1970)
Mathematics of Computation
, vol.24
, Issue.111
, pp. 713-735
-
-
Berlekamp, E.R.1
-
17
-
-
0022716288
-
A simple unpredictable pseudo-random number generator
-
L., Blum, M., Blum, and M., Shub. A simple unpredictable pseudo-random number generator. SIAM Journal on Computing, 15:364-383, 1986.
-
(1986)
SIAM Journal on Computing
, vol.15
, pp. 364-383
-
-
Blum, L.1
Blum, M.2
Shub, M.3
-
19
-
-
0034226114
-
Cryptanalysis of rsa with private key d less than n0 292
-
D., Boneh and G., Durfee. Cryptanalysis of RSA with private key d less than N0 292. IEEE Transactions on Information Theory, iT-46:1339-1349, 2000.
-
(2000)
IEEE Transactions on Information Theory
, vol.iT46
, pp. 1339-1349
-
-
Boneh, D.1
Durfee, G.2
-
20
-
-
0018019849
-
Fast algorithms for manipulating formal power series
-
R., P. Brent and H., T. Kung. Fast algorithms for manipulating formal power series. Journal of the ACM, 25:581-595, 1978.
-
(1978)
Journal of the ACM
, vol.25
, pp. 581-595
-
-
Brent, R.P.1
Kung, H.T.2
-
21
-
-
0013415910
-
Factoring integers with the number field sieve
-
A. K. Lenstra and H. W. Lenstra, Jr., editors, Springer-Verlag
-
J., P. Buhler, H., W. Lenstra Jr and C., Pomerance. Factoring integers with the number field sieve. In A. K. Lenstra and H. W. Lenstra, Jr., editors, The Development of the Number Field Sieve, pages 50-94. Springer-Verlag, 1993.
-
(1993)
The Development of the Number Field Sieve
, pp. 50-94
-
-
Buhler, J.P.1
Lenstra, H.W.2
Pomerance, C.3
-
22
-
-
84976007230
-
The distribution of quadratic residues and non-residues
-
D., A. Burgess. The distribution of quadratic residues and non-residues. Math- ematika, 4:106-112, 1957.
-
(1957)
Math- Ematika
, vol.4
, pp. 106-112
-
-
Burgess, D.A.1
-
23
-
-
0002768224
-
On a problem of oppenheim concerning ‘factorisatio numerorum’
-
E., Canfield, P., Erdos, and C., Pomerance. On a problem of Oppenheim concerning ‘Factorisatio Numerorum’. Journal of Number Theory, 17:1-28, 1983.
-
(1983)
Journal of Number Theory
, vol.17
, pp. 1-28
-
-
Canfield, E.1
Erdos, P.2
Pomerance, C.3
-
24
-
-
34249916280
-
On fast multiplication of polynomials over arbitrary rings
-
D., G. Cantor and E., Kaltofen. On fast multiplication of polynomials over arbitrary rings. Acta Informatica, 28:693-701, 1991.
-
(1991)
Acta Informatica
, vol.28
, pp. 693-701
-
-
Cantor, D.G.1
Kaltofen, E.2
-
27
-
-
0027610980
-
Modifications to the number field sieve
-
D., Coppersmith. Modifications to the number field sieve. Journal of Cryptology, 6:169-180, 1993.
-
(1993)
Journal of Cryptology
, vol.6
, pp. 169-180
-
-
Coppersmith, D.1
-
29
-
-
0004116989
-
-
MIT Press, second edition
-
T., H. Cormen, C., E. Leiserson, R., L. Rivest, and C., Stein. Introduction to Algorithms. MIT Press, second edition, 2001.
-
(2001)
Introduction to Algorithms
-
-
Cormen, T.H.1
Leiserson, C.E.2
Rivest, R.L.3
Stein, C.4
-
32
-
-
84966230027
-
Average case error estimates for the strong probable prime test
-
I., Damgard, P., Landrock, and C., Pomerance. Average case error estimates for the strong probable prime test. Mathematics of Computation, 61:177-194, 1993.
-
(1993)
Mathematics of Computation
, vol.61
, pp. 177-194
-
-
Damgard, I.1
Landrock, P.2
Pomerance, C.3
-
34
-
-
84966249438
-
Asymptotocally fast factorization of integers
-
J., Dixon. Asymptotocally fast factorization of integers. Mathematics of Computation, 36:255-260, 1981.
-
(1981)
Mathematics of Computation
, vol.36
, pp. 255-260
-
-
Dixon, J.1
-
35
-
-
0023346708
-
On the equivalence between berlekamp’s and euclid’s algorithms
-
J., L. Dornstetter. On the equivalence between Berlekamp’s and Euclid’s algorithms. IEEE Transactions on Information Theory, IT-33:428-431, 1987.
-
(1987)
IEEE Transactions on Information Theory
, vol.IT33
, pp. 428-431
-
-
Dornstetter, J.L.1
-
36
-
-
0013506173
-
Theoreme de brun-titchmarsh; application au theoreme de ferma
-
E., Fouvry. Theoreme de Brun-Titchmarsh; application au theoreme de Fermat. Inventiones Mathematicae, 79:383-407, 1985.
-
(1985)
Inventiones Mathematicae
, vol.79
, pp. 383-407
-
-
Fouvry, E.1
-
38
-
-
0001605828
-
Computing frobenius maps and factoring polynomials
-
J., von zur Gathen and V., Shoup. Computing Frobenius maps and factoring polynomials. Computational Complexity, 2:187-224, 1992.
-
(1992)
Computational Complexity
, vol.2
, pp. 187-224
-
-
Von Zur Gathen, J.1
Shoup, V.2
-
40
-
-
0000303380
-
Discrete logarithms in gf(p) using the number field sieve
-
D., M. Gordon. Discrete logarithms in GF(p) using the number field sieve. SIAM Journal on Discrete Mathematics, 6:124-138, 1993.
-
(1993)
SIAM Journal on Discrete Mathematics
, vol.6
, pp. 124-138
-
-
Gordon, D.M.1
-
41
-
-
0017302550
-
Very simple method to find the minimal polynomial of an arbitrary non-zero element of a finite field
-
J., Gordon. Very simple method to find the minimal polynomial of an arbitrary non-zero element of a finite field. Electronic Letters, 12:663-664, 1976.
-
(1976)
Electronic Letters
, vol.12
, pp. 663-664
-
-
Gordon, J.1
-
43
-
-
33646862107
-
Some problems of partito numerorum. III. On the expression of a number as a sum of primes
-
G., H. Hardy and J., E. Littlewood. Some problems of partito numerorum. III. On the expression of a number as a sum of primes. Acta Mathematica, 44:1-70, 1923.
-
(1923)
Acta Mathematica
, vol.44
, pp. 1-70
-
-
Hardy, G.H.1
Littlewood, J.E.2
-
45
-
-
84963042409
-
Zero-free regions for dirichlet l-functions and the least prime in an arithmetic progression
-
D., Heath-Brown. Zero-free regions for Dirichlet L-functions and the least prime in an arithmetic progression. Proceedings of the London Mathematical Society, 64:265-338, 1992.
-
(1992)
Proceedings of the London Mathematical Society
, vol.64
, pp. 265-338
-
-
Heath-Brown, D.1
-
46
-
-
0024866111
-
Pseudo-random number generation from any one-way function
-
R., Impagliazzo, L., Levin, and M., Luby. Pseudo-random number generation from any one-way function. In 21st Annual ACM Symposium on Theory of Computing, pages 12-24, 1989.
-
(1989)
21St Annual ACM Symposium on Theory of Computing
, pp. 12-24
-
-
Impagliazzo, R.1
Levin, L.2
Luby, M.3
-
48
-
-
0040404412
-
On the error term in the linear sieve
-
H., Iwaniec. On the error term in the linear sieve. Acta Arithmetica, 19:1-30, 1971.
-
(1971)
Acta Arithmetica
, vol.19
, pp. 1-30
-
-
Iwaniec, H.1
-
49
-
-
0001453406
-
On the problem of jacobsthal
-
H., Iwaniec. On the problem of Jacobsthal. Demonstratio Mathematica, 11:225-231, 1978.
-
(1978)
Demonstratio Mathematica
, vol.11
, pp. 225-231
-
-
Iwaniec, H.1
-
52
-
-
0001464763
-
Multiplication of multidigit numbers on automata
-
A., A. Karatsuba and Y., Of man. Multiplication of multidigit numbers on automata. Soviet Physics Doklady, 7:595-596, 1963.
-
(1963)
Soviet Physics Doklady
, vol.7
, pp. 595-596
-
-
Karatsuba, A.A.1
Ofman, Y.2
-
53
-
-
84968468626
-
The probability that a random probable prime is composite
-
S., H. Kim and C., Pomerance. The probability that a random probable prime is composite. Mathematics of Computation, 53(188):721-741, 1989.
-
(1989)
Mathematics of Computation
, vol.53
, Issue.188
, pp. 721-741
-
-
Kim, S.H.1
Pomerance, C.2
-
57
-
-
0001258323
-
Factoring integers with elliptic curves
-
H.Jrx, W. Lenstra. Factoring integers with elliptic curves. Annals of Mathematics, 126:649-673, 1987.
-
(1987)
Annals of Mathematics
, vol.126
, pp. 649-673
-
-
Lenstra, H.J.W.1
-
58
-
-
84968513551
-
A rigorous time bound for factoring integers
-
H., W. Lenstra Jr and C., Pomerance. A rigorous time bound for factoring integers. Journal of the AMS’, 4:483-516, 1992.
-
(1992)
Journal of the AMS’
, vol.4
, pp. 483-516
-
-
Lenstra, H.W.1
Pomerance, C.2
-
60
-
-
84937740421
-
Shift-register synthesis and bch coding
-
J., Massey. Shift-register synthesis and BCH coding. IEEE Transactions on Information Theory, IT-15:122-127, 1969.
-
(1969)
IEEE Transactions on Information Theory
, vol.IT15
, pp. 122-127
-
-
Massey, J.1
-
61
-
-
0029325653
-
Fast generation of prime numbers and secure public-key cryptographic parameters
-
U., Maurer. Fast generation of prime numbers and secure public-key cryptographic parameters. Journal of Cryptology, 8:123-155, 1995.
-
(1995)
Journal of Cryptology
, vol.8
, pp. 123-155
-
-
Maurer, U.1
-
64
-
-
84966216677
-
Continued fractions and linear recurrences
-
W., Mills. Continued fractions and linear recurrences. Mathematics of Computation, 29:173-180, 1975.
-
(1975)
Mathematics of Computation
, vol.29
, pp. 173-180
-
-
Mills, W.1
-
66
-
-
84966219731
-
A method of factoring and the factorization of f7
-
M., Morrison and J., Brillhart. A method of factoring and the factorization of F7. Mathematics of Computation, 29:183-205, 1975.
-
(1975)
Mathematics of Computation
, vol.29
, pp. 183-205
-
-
Morrison, M.1
Brillhart, J.2
-
67
-
-
0010227312
-
Complexity of a determinate algorithm for the discrete logarithm
-
Translated from, Matem- aticheskie Zametki, 55(2):91-101, 1994
-
V., I. Nechaev. Complexity of a determinate algorithm for the discrete logarithm. Mathematical Notes, 55(2):165-172, 1994. Translated from Matem- aticheskie Zametki, 55(2):91-101, 1994.
-
(1994)
Mathematical Notes
, vol.55
, Issue.2
, pp. 165-172
-
-
Nechaev, V.I.1
-
69
-
-
0000442252
-
Versions effectives du theorème de chebotarev sous l’hypothese de riemann generalisee
-
J., Oesterle. Versions effectives du theorème de Chebotarev sous l’hypothese de Riemann generalisee. Astérisque, 61:165-167, 1979.
-
(1979)
Astérisque
, vol.61
, pp. 165-167
-
-
Oesterle, J.1
-
71
-
-
84919085619
-
An improved algorithm for computing logarithms over gf(p) and its cryptographic significance
-
S., Pohlig and M., Hellman. An improved algorithm for computing logarithms over GF(p) and its cryptographic significance. IEEE Transactions on Information Theory, IT-24:106-110, 1978.
-
(1978)
IEEE Transactions on Information Theory
, vol.IT24
, pp. 106-110
-
-
Pohlig, S.1
Hellman, M.2
-
72
-
-
84966238549
-
Monte carlo methods for index computation mod
-
J., M. Pollard. Monte Carlo methods for index computation mod p. Mathematics of Computation, 32:918-924, 1978.
-
(1978)
P. Mathematics of Computation
, vol.32
, pp. 918-924
-
-
Pollard, J.M.1
-
73
-
-
33645002788
-
Factoring with cubic integers
-
A. K. Lenstra and H. W. Lenstra, Jr., editors, Springer-Verlag
-
J., M. Pollard. Factoring with cubic integers. In A. K. Lenstra and H. W. Lenstra, Jr., editors, The Development of the Number Field Sieve, pages 4-10. Springer-Verlag, 1993.
-
(1993)
The Development of the Number Field Sieve
, pp. 4-10
-
-
Pollard, J.M.1
-
74
-
-
0005599967
-
Analysis and comparison of some integer factoring algorithms
-
H. W. Lenstra, Jr. and R. Tijdeman, editors, Mathematisch Centrum
-
C., Pomerance. Analysis and comparison of some integer factoring algorithms. In H. W. Lenstra, Jr. and R. Tijdeman, editors, Computational Methods in Number Theory, Part I, pages 89-139. Mathematisch Centrum, 1982.
-
(1982)
Computational Methods in Number Theory, Part I
, pp. 89-139
-
-
Pomerance, C.1
-
78
-
-
0017930809
-
A method for obtaining digital signatures and public-key cryptosystems
-
R., L. Rivest, A., Shamir, and L., M. Adleman. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21(2):120-126, 1978.
-
(1978)
Communications of the ACM
, vol.21
, Issue.2
, pp. 120-126
-
-
Rivest, R.L.1
Shamir, A.2
Adleman, L.M.3
-
79
-
-
84972540003
-
Approximate formulas for some functions of prime numbers
-
J., Rosser and L., Schoenfeld. Approximate formulas for some functions of prime numbers. Illinois Journal of Mathematics, 6:64-94, 1962.
-
(1962)
Illinois Journal of Mathematics
, vol.6
, pp. 64-94
-
-
Rosser, J.1
Schoenfeld, L.2
-
80
-
-
84958036387
-
Discrete logarithms: The effectiveness of the index calculus method
-
O., Schirokauer, D., Weber, and T., Denny. Discrete logarithms: the effectiveness of the index calculus method. In Proc. 2nd International Symposium on Algorithmic Number Theory (ANTS-II), pages 337-361, 1996.
-
(1996)
Proc. 2Nd International Symposium on Algorithmic Number Theory (ANTS-II)
, pp. 337-361
-
-
Schirokauer, O.1
Weber, D.2
Denny, T.3
-
81
-
-
0015197550
-
Schnelle berechnung von kettenbruchentwicklungen
-
A., Schonhage. Schnelle Berechnung von Kettenbruchentwicklungen. Acta Informatica, 1:139-144, 1971.
-
(1971)
Acta Informatica
, vol.1
, pp. 139-144
-
-
Schonhage, A.1
-
82
-
-
34250459760
-
Schnelle multiplikation grosser zahlen
-
A., Schonhage and V., Strassen. Schnelle Multiplikation grosser Zahlen. Computing, 7:281-282, 1971.
-
(1971)
Computing
, vol.7
, pp. 281-282
-
-
Schonhage, A.1
Strassen, V.2
-
83
-
-
70350122357
-
Construction of irreducible polynomials over finite fields with linearly independent roots
-
Russian; English translation in, Math. USSR-Sbornik, 63(2):507-519, 1989
-
I., A. Semaev. Construction of irreducible polynomials over finite fields with linearly independent roots. Mat. S’bornik, 135:520-532, 1988. In Russian; English translation in Math. USSR-Sbornik, 63(2):507-519, 1989.
-
(1988)
Mat. S’Bornik
, vol.135
, pp. 520-532
-
-
Semaev, I.A.1
-
84
-
-
0038982373
-
Factoring numbers in 0(log n) arithmetic steps
-
A., Shamir. Factoring numbers in 0(log n) arithmetic steps. Information Processing Letters, 8:28-31, 1979.
-
(1979)
Information Processing Letters
, vol.8
, pp. 28-31
-
-
Shamir, A.1
-
85
-
-
0018545449
-
How to share a secret
-
A., Shamir. How to share a secret. Communications of the ACM, 22:612-613, 1979.
-
(1979)
Communications of the ACM
, vol.22
, pp. 612-613
-
-
Shamir, A.1
-
86
-
-
0000211152
-
Class number, a theory of factorization, and genera
-
D., Shanks. Class number, a theory of factorization, and genera. In Proceedings of Symposia in Pure Mathematics, volume 20, pages 415-440, 1969.
-
(1969)
Proceedings of Symposia in Pure Mathematics
, vol.20
, pp. 415-440
-
-
Shanks, D.1
-
87
-
-
85115374351
-
Algorithms for quantum computation: Discrete logarithms and factoring
-
P., Shor. Algorithms for quantum computation: discrete logarithms and factoring. In 35th Annual Symposium on Foundations of Computer Science, pages 124-134, 1994.
-
(1994)
35Th Annual Symposium on Foundations of Computer Science
, pp. 124-134
-
-
Shor, P.1
-
88
-
-
0032628303
-
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
-
P., Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Review, 41:303-332, 1999.
-
(1999)
SIAM Review
, vol.41
, pp. 303-332
-
-
Shor, P.1
-
89
-
-
84966245630
-
New algorithms for finding irreducible polynomials over finite fields
-
V., Shoup. New algorithms for finding irreducible polynomials over finite fields. Mathematics of Computation, 54(189):435-447, 1990.
-
(1990)
Mathematics of Computation
, vol.54
, Issue.189
, pp. 435-447
-
-
Shoup, V.1
-
90
-
-
84968515930
-
Searching for primitive roots in finite fields
-
V., Shoup. Searching for primitive roots in finite fields. Mathematics of Computation, 58:369-380, 1992.
-
(1992)
Mathematics of Computation
, vol.58
, pp. 369-380
-
-
Shoup, V.1
-
91
-
-
38149147073
-
Fast construction of irreducible polynomials over finite fields
-
V., Shoup. Fast construction of irreducible polynomials over finite fields. Journal of Symbolic Computation, 17(5):371-391, 1994.
-
(1994)
Journal of Symbolic Computation
, vol.17
, Issue.5
, pp. 371-391
-
-
Shoup, V.1
-
92
-
-
0001465210
-
A new polynomial factorization algorithm and its implementation
-
V., Shoup. A new polynomial factorization algorithm and its implementation. Journal of Symbolic Computation, 20(4):363-397, 1995.
-
(1995)
Journal of Symbolic Computation
, vol.20
, Issue.4
, pp. 363-397
-
-
Shoup, V.1
-
93
-
-
84942550160
-
Lower bounds for discrete logarithms and related problems
-
V., Shoup. Lower bounds for discrete logarithms and related problems. In Advances in Cryptology-Eurocrypt ’97, pages 256-266, 1997.
-
(1997)
Advances in Cryptology-Eurocrypt ’97
, pp. 256-266
-
-
Shoup, V.1
-
95
-
-
0000585372
-
Computational problems associated with racah algebra
-
J., Stein. Computational problems associated with Racah algebra. Journal of Computational Physics, 1:397-405, 1967.
-
(1967)
Journal of Computational Physics
, vol.1
, pp. 397-405
-
-
Stein, J.1
-
97
-
-
0002965602
-
P-adic reconstruction of rational numbers
-
P., Wang, M., Guy, and J., Davenport. p-adic reconstruction of rational numbers. SIGSAM Bulletin, 16:2-3, 1982
-
(1982)
SIGSAM Bulletin
, vol.16
, pp. 2-3
-
-
Wang, P.1
Guy, M.2
Davenport, J.3
-
98
-
-
0010665260
-
On the least primitive root of a prime
-
Y., Wang. On the least primitive root of a prime. Scientia Sinica, 10(1):1-14, 1961.
-
(1961)
Scientia Sinica
, vol.10
, Issue.1
, pp. 1-14
-
-
Wang, Y.1
-
99
-
-
0019572642
-
New hash functions and their use in authentication and set equality
-
M., N. Wegman and J., L. Carter. New hash functions and their use in authentication and set equality. Journal of Computer and System Sciences, 22:265-279, 1981.
-
(1981)
Journal of Computer and System Sciences
, vol.22
, pp. 265-279
-
-
Wegman, M.N.1
Carter, J.L.2
-
100
-
-
0001026996
-
(1 + i)-ary gcd computation in z[i] as an analogue to the binary gcd algorithm
-
A., Weilert. (1 + i)-ary GCD computation in Z[i] as an analogue to the binary GCD algorithm. Journal of Symbolic Computation, 30:605-617, 2000.
-
(2000)
Journal of Symbolic Computation
, vol.30
, pp. 605-617
-
-
Weilert, A.1
-
103
-
-
0022583143
-
Solving sparse linear systems over finite fields
-
D., Wiedemann. Solving sparse linear systems over finite fields. IEEE Transactions on Information Theory, IT-32:54-62, 1986.
-
(1986)
IEEE Transactions on Information Theory
, vol.IT32
, pp. 54-62
-
-
Wiedemann, D.1
-
104
-
-
0025430939
-
Cryptanalysis of short rsa secret exponents
-
M., Wiener. Cryptanalysis of short RSA secret exponents. IEEE Transactions on Information Theory, IT-44:553-558, 1990.
-
(1990)
IEEE Transactions on Information Theory
, vol.IT44
, pp. 553-558
-
-
Wiener, M.1
|