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On the multiple threshold decoding of LDPC codes over GF(q)
AFSRs synthesis with the extended Euclidean rational approximation algorithm
1. | Department of Computer Science, William Paterson University of New Jersey, Wayne, NJ 07470 USA |
2. | Department of Computer Science, University of Kentucky, Lexington, KY 40506, USA |
Pseudo-random sequence generators are widely used in many areas, such as stream ciphers, radar systems, Monte-Carlo simulations and multiple access systems. Generalization of linear feedback shift registers (LFSRs) and feedback with carry shift registers (FCSRs), algebraic feedback shift registers (AFSRs) [
References:
[1] |
F. Arnault, T. P. Berger and A. Necer,
Feedback with carry shift registers synthesis with the Euclidean algorithm, IEEE Trans. Inform. Theory, 50 (2004), 910-917.
doi: 10.1109/TIT.2004.826651. |
[2] |
N. Courtois and W. Meier, Algebraic attacks on stream ciphers with linear feedback, in Advances in Cryptology-EUROCRYPT 2003, Springer, 2003,345-359.
doi: 10.1007/3-540-39200-9_21. |
[3] |
M. Goresky and A. Klapper, Feedback registers based on ramified extensions of the 2-adic numbers, in Advances in Cryptology-EUROCRYPT '94, Springer, 1995,215-222.
doi: 10.1007/BFb0053437. |
[4] |
M. Goresky and A. Klapper, Algebraic Shift Register Sequences, Cambridge Univ. Press, 2012. |
[5] |
A. Klapper and M. Goresky, Cryptanalysis based on 2-adic rational approximation, in Advances in Cryptology-CRYPTO '95, Springer, 1995,262-273.
doi: 10.1007/3-540-44750-4_21. |
[6] |
A. Klapper and M. Goresky,
Feedback shift registers. 2-adic span, and combiners with memory, Cryptology J., 10 (1997), 111-147.
doi: 10.1007/s001459900024. |
[7] |
A. Klapper and J. Xu,
Algebraic feedback shift registers, Theoret. Comp. Sci., 226 (1999), 61-92.
doi: 10.1016/S0304-3975(99)00066-3. |
[8] |
A. Klapper and J. Xu,
Register synthesis for algebraic feedback shift registers based on nonprimes, Des. Codes Cryptogr., 31 (2004), 227-250.
doi: 10.1023/B:DESI.0000015886.71135.e1. |
[9] |
D. Lee, J. Kim, J. Hong, J. Han and D. Moon, Algebraic attacks on summation generators, in Fast Software Encryption, Springer, 2004, 34-48.
doi: 10.1007/978-3-540-25937-4_3. |
[10] |
W. LeVeque, Topics in Number Theory, Courier Corporation, 2002. |
[11] |
W. Liu and A. Klapper, A lattice rational approximation algorithm for AFSRs over quadratic integer rings, in Sequences and Their Applications -SETA 2014, Springer, 2014,200-211.
doi: 10.1007/978-3-319-12325-7_17. |
[12] |
J. L. Massey,
Shift register synthesis and BCH decoding, IEEE Trans. Inform. Theory, 15 (1969), 122-127.
|
[13] |
P. Q. Nguyen and D. Stehlé, Low-dimensional lattice basis reduction revisited, ACM Trans. Algor. (TALG), 5 (2009), 46.
doi: 10.1145/1597036.1597050. |
show all references
References:
[1] |
F. Arnault, T. P. Berger and A. Necer,
Feedback with carry shift registers synthesis with the Euclidean algorithm, IEEE Trans. Inform. Theory, 50 (2004), 910-917.
doi: 10.1109/TIT.2004.826651. |
[2] |
N. Courtois and W. Meier, Algebraic attacks on stream ciphers with linear feedback, in Advances in Cryptology-EUROCRYPT 2003, Springer, 2003,345-359.
doi: 10.1007/3-540-39200-9_21. |
[3] |
M. Goresky and A. Klapper, Feedback registers based on ramified extensions of the 2-adic numbers, in Advances in Cryptology-EUROCRYPT '94, Springer, 1995,215-222.
doi: 10.1007/BFb0053437. |
[4] |
M. Goresky and A. Klapper, Algebraic Shift Register Sequences, Cambridge Univ. Press, 2012. |
[5] |
A. Klapper and M. Goresky, Cryptanalysis based on 2-adic rational approximation, in Advances in Cryptology-CRYPTO '95, Springer, 1995,262-273.
doi: 10.1007/3-540-44750-4_21. |
[6] |
A. Klapper and M. Goresky,
Feedback shift registers. 2-adic span, and combiners with memory, Cryptology J., 10 (1997), 111-147.
doi: 10.1007/s001459900024. |
[7] |
A. Klapper and J. Xu,
Algebraic feedback shift registers, Theoret. Comp. Sci., 226 (1999), 61-92.
doi: 10.1016/S0304-3975(99)00066-3. |
[8] |
A. Klapper and J. Xu,
Register synthesis for algebraic feedback shift registers based on nonprimes, Des. Codes Cryptogr., 31 (2004), 227-250.
doi: 10.1023/B:DESI.0000015886.71135.e1. |
[9] |
D. Lee, J. Kim, J. Hong, J. Han and D. Moon, Algebraic attacks on summation generators, in Fast Software Encryption, Springer, 2004, 34-48.
doi: 10.1007/978-3-540-25937-4_3. |
[10] |
W. LeVeque, Topics in Number Theory, Courier Corporation, 2002. |
[11] |
W. Liu and A. Klapper, A lattice rational approximation algorithm for AFSRs over quadratic integer rings, in Sequences and Their Applications -SETA 2014, Springer, 2014,200-211.
doi: 10.1007/978-3-319-12325-7_17. |
[12] |
J. L. Massey,
Shift register synthesis and BCH decoding, IEEE Trans. Inform. Theory, 15 (1969), 122-127.
|
[13] |
P. Q. Nguyen and D. Stehlé, Low-dimensional lattice basis reduction revisited, ACM Trans. Algor. (TALG), 5 (2009), 46.
doi: 10.1145/1597036.1597050. |


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