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Smoothness testing of polynomials over finite fields
1. | Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4 |
2. | Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada |
References:
[1] |
gf2x, a C/C++ software package containing routines for fast arithmetic in $GF(2)[x]$, (multiplication, ().
|
[2] |
D. Bernstein, How to find smooth parts of integers,, submitted., ().
|
[3] |
J.-F. Biasse and M. Jacobson, Practical improvements to class group and regulator computation of real quadratic fields, in Algorithmic Number Theory (eds. G. Hanrot, F. Morain and E. Thomé), Springer-Verlag, 2010, 50-65.
doi: 10.1007/978-3-642-14518-6_8. |
[4] |
G. Bisson and A. Sutherland, Computing the endomorphism ring of an ordinary elliptic curve over a finite field, J. Number Theory, 113 (2011), 815-831.
doi: 10.1016/j.jnt.2009.11.003. |
[5] |
D. Coppersmith, Fast evaluation of logarithms in fields of characteristic two, IEEE Trans. Inf. Theory, 30 (1984), 587-594.
doi: 10.1109/TIT.1984.1056941. |
[6] |
J. Detrey, P. Gaudry and M. Videau, Relation collection for the function field sieve, in 21st IEEE Int. Symp. Computer Arith. (eds. A. Nannarelli, P.-M. Seidel and P. Tang), IEEE, 2013, 201-210.
doi: 10.1109/ARITH.2013.28. |
[7] |
A. Enge and P. Gaudry, A general framework for subexponential discrete logarithm algorithms, Acta Arith., 102 (2002), 83-103.
doi: 10.4064/aa102-1-6. |
[8] |
M. Jacobson, A. Menezes and A. Stein, Solving elliptic curve discrete logarithm problems using Weil descent, J. Ramanujan Math. Soc., 16 (2001), 231-260. |
[9] |
H. Lenstra, Factoring integers with elliptic curves, Ann. Math., 126 (1987), 649-673.
doi: 10.2307/1971363. |
[10] |
R. Lidl and H. Niederreiter, Introduction to Finite Fields and their Applications, Cambridge Univ. Press, New York, 1986. |
[11] |
A. Odlyzko, Discrete logarithms in finite fields and their cryptographic significance, in Proc. EUROCRYPT 84 Workshop Adv. Cryptology: Theory Appl. Crypt. Techn., Springer-Verlag, New York, 1985, 224-314.
doi: 10.1007/3-540-39757-4_20. |
[12] |
A. Schnhage and V. Strassen, Schnelle Multiplikation grosser Zahlen (in German), Computing, 7 (1971), 281-292. |
[13] |
V. Shoup, NTL: A library for doing number theory,, Software, ().
|
[14] |
M. Velichka, M. Jacobson and A. Stein, Computing discrete logarithms in the jacobian of high-genus hyperelliptic curves over even characteristic finite fields, Math. Comp., 83 (2014), 935-963.
doi: 10.1090/S0025-5718-2013-02748-2. |
[15] |
J. von zur Gathen and V. Shoup, Computing Frobenius maps and factoring polynomials, Comp. Complexity, 2 (1992), 187-224.
doi: 10.1007/BF01272074. |
show all references
References:
[1] |
gf2x, a C/C++ software package containing routines for fast arithmetic in $GF(2)[x]$, (multiplication, ().
|
[2] |
D. Bernstein, How to find smooth parts of integers,, submitted., ().
|
[3] |
J.-F. Biasse and M. Jacobson, Practical improvements to class group and regulator computation of real quadratic fields, in Algorithmic Number Theory (eds. G. Hanrot, F. Morain and E. Thomé), Springer-Verlag, 2010, 50-65.
doi: 10.1007/978-3-642-14518-6_8. |
[4] |
G. Bisson and A. Sutherland, Computing the endomorphism ring of an ordinary elliptic curve over a finite field, J. Number Theory, 113 (2011), 815-831.
doi: 10.1016/j.jnt.2009.11.003. |
[5] |
D. Coppersmith, Fast evaluation of logarithms in fields of characteristic two, IEEE Trans. Inf. Theory, 30 (1984), 587-594.
doi: 10.1109/TIT.1984.1056941. |
[6] |
J. Detrey, P. Gaudry and M. Videau, Relation collection for the function field sieve, in 21st IEEE Int. Symp. Computer Arith. (eds. A. Nannarelli, P.-M. Seidel and P. Tang), IEEE, 2013, 201-210.
doi: 10.1109/ARITH.2013.28. |
[7] |
A. Enge and P. Gaudry, A general framework for subexponential discrete logarithm algorithms, Acta Arith., 102 (2002), 83-103.
doi: 10.4064/aa102-1-6. |
[8] |
M. Jacobson, A. Menezes and A. Stein, Solving elliptic curve discrete logarithm problems using Weil descent, J. Ramanujan Math. Soc., 16 (2001), 231-260. |
[9] |
H. Lenstra, Factoring integers with elliptic curves, Ann. Math., 126 (1987), 649-673.
doi: 10.2307/1971363. |
[10] |
R. Lidl and H. Niederreiter, Introduction to Finite Fields and their Applications, Cambridge Univ. Press, New York, 1986. |
[11] |
A. Odlyzko, Discrete logarithms in finite fields and their cryptographic significance, in Proc. EUROCRYPT 84 Workshop Adv. Cryptology: Theory Appl. Crypt. Techn., Springer-Verlag, New York, 1985, 224-314.
doi: 10.1007/3-540-39757-4_20. |
[12] |
A. Schnhage and V. Strassen, Schnelle Multiplikation grosser Zahlen (in German), Computing, 7 (1971), 281-292. |
[13] |
V. Shoup, NTL: A library for doing number theory,, Software, ().
|
[14] |
M. Velichka, M. Jacobson and A. Stein, Computing discrete logarithms in the jacobian of high-genus hyperelliptic curves over even characteristic finite fields, Math. Comp., 83 (2014), 935-963.
doi: 10.1090/S0025-5718-2013-02748-2. |
[15] |
J. von zur Gathen and V. Shoup, Computing Frobenius maps and factoring polynomials, Comp. Complexity, 2 (1992), 187-224.
doi: 10.1007/BF01272074. |
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