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A new class of majority-logic decodable codes derived from polarity designs
Discrete logarithm like problems and linear recurring sequences
1. | Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo s/n, 33007 Oviedo, Spain, Spain |
2. | Departament de Ciènces Matemàtiques i Informàtica, Universitat de les Illes Balears, Ctra. de Valldemossa km 7, 5, 07122 Palma de Mallorca, Spain, Spain |
References:
[1] |
A. Agnew, R. C. Mullin, I. M. Onyszchuk and S. A. Vanstone, An implementation for a fast public-key cryptosystem, J. Cryptology, 3 (1991), 63-79. |
[2] |
A. Brouwer, R. Pellikaan and E. Verheul, Doing more with fewer bits, in "Advances in Cryptology - ASIACRYPT'99,'' Springer-Verlag, (1999), 321-332. |
[3] |
W. Diffie and M. Hellman, New directions in cryptography, IEEE Trans. Inform. Theory, 22 (1976), 644-654. |
[4] |
C. M. Fiduccia, An efficient formula for linear recurring sequences, SIAM J. Comput., 14 (1985), 106-112. |
[5] |
J. von zur Gathen and J. Gerhard, "Modern Computer Algebra,'' Cambridge Univ. Press, Cambridge, 2003. |
[6] |
K. Giuliani and G. Gong, Analogues to the Gong-Harn and XTR cryptosystems, in "Combinatorics and Optimization Research Report,'' Univ. Waterloo, 2003. |
[7] |
K. Giuliani and G. Gong, Efficient key agreement and signature schemes using compact representations in $GF(p$10$)$, in "Proceedings of the 2004 IEEE International Symposium on Information Theory - ISIT'04,'' Chicago, (2004), 13. |
[8] |
K. Giuliani and G. Gong, New LFSR-based cryptosystems and the trace discrete logarithm problem (Trace-DLP), in "Sequences and Their Applications'04,'' Springer-Verlag, (2005), 298-312. |
[9] |
G. Gong and L. Harn, Public-key cryptosystems based on cubic finite field extensions, IEEE Trans. Inform. Theory, 45 (1999), 2601-2605. |
[10] |
K. Karabina, Factor-4 and 6 compression of cyclotomic subgroups of $\mathbb F$*24m and $\mathbb F$*36m, J. Math. Crypt., 4 (2010), 1-42. |
[11] |
A. Lenstra, Using cyclotomic polynomials to construct efficient discrete logarithm cryptosystems over finite fields, in "Proceedings of ACISP'97,'' Springer-Verlag, (1997), 127-138. |
[12] |
A. Lenstra and E. Verheul, The XTR public key system, in "Advances in Cryptology - CRYPTO'00,'' Springer-Verlag, (2000), 1-19. |
[13] |
R. Lidl and H. Niederreiter, "Finite Fields,'' Addison-Wesley, 1983. |
[14] |
H. Niederreiter, A public-key cryptosystem based on shift-register sequences, in "Advances in Cryptology - EUROCRYPT'85,'' Springer-Verlag, (1986), 35-39.
doi: 10.1007/3-540-39805-8_4. |
[15] |
H. Niederreiter, Some new cryptosystems based on feedback shift register sequences, Math. J. Okayama Univ., 30 (1988), 121-149. |
[16] |
C. P. Schnorr, Efficient signature generation by smart cards, J. Cryptology, 4 (1991), 161-174. |
[17] |
M. Shirase, D. Han, Y. Hibin, H. Kim and T. Takagi, A more compact representation of XTR cryptosystem, IEICE T. Fund. Electr., E91-A (2008), 2843-2850. |
[18] |
P. Smith, LUC public-key encryption, Dr. Dobb's J., (1994), 44-49. |
[19] |
P. Smith and C. Skinner, A public-key cryptosystem and a digital signature system based on the Lucas function analogue to discrete logarithms, in "Advances in Cryptology - ASIACRYPT'94,'' Springer-Verlag, (1994), 14-21. |
[20] |
C. H. Tan, X. Yi and C. K. Siew, Signature schemes based on third order shift registers, in "Information Security and Privacy,'' Springer-Verlag, (2001), 445-459. |
[21] |
C. H. Tan, X. Yi and C. K. Siew, On the n-th order shift register based discrete logarithm, IECE Trans. Fund., E86-A (2003), 1213-1216. |
[22] |
C. H. Tan, X. Yi and C. K. Siew, On Diffie-Hellman problems in 3rd order shift register, IECE Trans. Fund., E87-A (2004), 1206-1208. |
[23] |
E. Verheul, Certificates of recoverability with scalable recovery agent security, in "Proceedings of PKC 2000,'' Springer-Verlag, (2000), 258-275. |
show all references
References:
[1] |
A. Agnew, R. C. Mullin, I. M. Onyszchuk and S. A. Vanstone, An implementation for a fast public-key cryptosystem, J. Cryptology, 3 (1991), 63-79. |
[2] |
A. Brouwer, R. Pellikaan and E. Verheul, Doing more with fewer bits, in "Advances in Cryptology - ASIACRYPT'99,'' Springer-Verlag, (1999), 321-332. |
[3] |
W. Diffie and M. Hellman, New directions in cryptography, IEEE Trans. Inform. Theory, 22 (1976), 644-654. |
[4] |
C. M. Fiduccia, An efficient formula for linear recurring sequences, SIAM J. Comput., 14 (1985), 106-112. |
[5] |
J. von zur Gathen and J. Gerhard, "Modern Computer Algebra,'' Cambridge Univ. Press, Cambridge, 2003. |
[6] |
K. Giuliani and G. Gong, Analogues to the Gong-Harn and XTR cryptosystems, in "Combinatorics and Optimization Research Report,'' Univ. Waterloo, 2003. |
[7] |
K. Giuliani and G. Gong, Efficient key agreement and signature schemes using compact representations in $GF(p$10$)$, in "Proceedings of the 2004 IEEE International Symposium on Information Theory - ISIT'04,'' Chicago, (2004), 13. |
[8] |
K. Giuliani and G. Gong, New LFSR-based cryptosystems and the trace discrete logarithm problem (Trace-DLP), in "Sequences and Their Applications'04,'' Springer-Verlag, (2005), 298-312. |
[9] |
G. Gong and L. Harn, Public-key cryptosystems based on cubic finite field extensions, IEEE Trans. Inform. Theory, 45 (1999), 2601-2605. |
[10] |
K. Karabina, Factor-4 and 6 compression of cyclotomic subgroups of $\mathbb F$*24m and $\mathbb F$*36m, J. Math. Crypt., 4 (2010), 1-42. |
[11] |
A. Lenstra, Using cyclotomic polynomials to construct efficient discrete logarithm cryptosystems over finite fields, in "Proceedings of ACISP'97,'' Springer-Verlag, (1997), 127-138. |
[12] |
A. Lenstra and E. Verheul, The XTR public key system, in "Advances in Cryptology - CRYPTO'00,'' Springer-Verlag, (2000), 1-19. |
[13] |
R. Lidl and H. Niederreiter, "Finite Fields,'' Addison-Wesley, 1983. |
[14] |
H. Niederreiter, A public-key cryptosystem based on shift-register sequences, in "Advances in Cryptology - EUROCRYPT'85,'' Springer-Verlag, (1986), 35-39.
doi: 10.1007/3-540-39805-8_4. |
[15] |
H. Niederreiter, Some new cryptosystems based on feedback shift register sequences, Math. J. Okayama Univ., 30 (1988), 121-149. |
[16] |
C. P. Schnorr, Efficient signature generation by smart cards, J. Cryptology, 4 (1991), 161-174. |
[17] |
M. Shirase, D. Han, Y. Hibin, H. Kim and T. Takagi, A more compact representation of XTR cryptosystem, IEICE T. Fund. Electr., E91-A (2008), 2843-2850. |
[18] |
P. Smith, LUC public-key encryption, Dr. Dobb's J., (1994), 44-49. |
[19] |
P. Smith and C. Skinner, A public-key cryptosystem and a digital signature system based on the Lucas function analogue to discrete logarithms, in "Advances in Cryptology - ASIACRYPT'94,'' Springer-Verlag, (1994), 14-21. |
[20] |
C. H. Tan, X. Yi and C. K. Siew, Signature schemes based on third order shift registers, in "Information Security and Privacy,'' Springer-Verlag, (2001), 445-459. |
[21] |
C. H. Tan, X. Yi and C. K. Siew, On the n-th order shift register based discrete logarithm, IECE Trans. Fund., E86-A (2003), 1213-1216. |
[22] |
C. H. Tan, X. Yi and C. K. Siew, On Diffie-Hellman problems in 3rd order shift register, IECE Trans. Fund., E87-A (2004), 1206-1208. |
[23] |
E. Verheul, Certificates of recoverability with scalable recovery agent security, in "Proceedings of PKC 2000,'' Springer-Verlag, (2000), 258-275. |
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