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KEY EXCHANGE PROTOCOL USING MATRIX ALGEBRAS AND ITS ANALYSIS
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 Title & Authors
KEY EXCHANGE PROTOCOL USING MATRIX ALGEBRAS AND ITS ANALYSIS
CHO SOOJIN; HA KIL-CHAN; KIM YOUNG-ONE; MOON DONGHO;
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 Abstract
A key exchange protocol using commutative subalge-bras of a full matrix algebra is considered. The security of the protocol depends on the difficulty of solving matrix equations XRY
 Keywords
key exchange protocol;matrix algebra;Diffie-Hellman key exchange;
 Language
English
 Cited by
 References
1.
J. Barria and P. R. Halmos, Vector bases for two commuting matrices, Linear Multilinear Algebra 27 (1990), 147-157 crossref(new window)

2.
J. A. Buchmann, R. Scheidler, and H. C. Williams, A key-exchange protocol using real quadratic fields, J. Cryptology 7 (1994), 171-199 crossref(new window)

3.
M. A. Cherepnev, Schemes of public distribution of keys based on a non- commutative group, Discrete Math. Appl. 13 (2003), no. 3, 265-269 crossref(new window)

4.
M. A. Cherepnev, V. M. Sidelnikov, and V. V. Yashchenko, Systems of open distribution of keys on the basis of noncommutative semigroups, Russian Acad. Sci. Dokl. Math. 48 (1994), no. 2, 384-386

5.
W. Diffie and M. E. Hellman, New directions in cryptography, IEEE Trans. Inform Theory 22 (1976), 644-654 crossref(new window)

6.
J.-C. Faugere, A new efficient algorithm for computing grobner bases ($F_4$), J. Pure Appl. Algebra 139 (1999), 61-88 crossref(new window)

7.
J.-C. Faugere, A new efficient algorithm for computing grobner bases without reduction to zero ($F_5$), In Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation

8.
F. Gantmacher, The Theory of Matrices Vol. 1, A.M.S. Chelsea publishing, 1977

9.
J. A. Green, The character of finite general linear groups, Trans. Amer. Math. Soc. 80 (1955), 402-447 crossref(new window)

10.
J. H. Hodges, A bilinear matrix equations over a finite field, Duke Math. J. 31 (1964), 661-666 crossref(new window)

11.
J. H. Hodges, Representation by bilinear forms in a finite field, Duke Math. J. 22 (1955), 497-510 crossref(new window)

12.
N. Jacobson, Schur's theormes on commutative matrices, Bull. Amer. Math. Soc. 50 (1944), 431-436 crossref(new window)

13.
T. Laffey and S. Lazarus, Two-generated commutative matrix subalgebras, Linear Algebra Appl. 147 (1991), 249-273 crossref(new window)

14.
S. M. Mollevi, C. Pardo, I. Gracia, and P. Morillo, Linear key predistribution schemes, Des. Codes Cryptogr. 25 (2002), 281-298 crossref(new window)

15.
M. Neubauer and D. Saltman, Two-generated commutative subalgebras of $M_n$(f), J. Algebra 164 (1994), 545-562 crossref(new window)

16.
M. Qu, J. Solinas, L. Law, A. Menezes, and S. Vanstone, An efficient protocol for authenticated key agreement, Des. Codes Cryptogr. 28 (2003), no. 2, 119-134 crossref(new window)

17.
N. Strauss, Algorithm and implementation for computation of Jordan form over A$[x_1,...,x_m]$, In Computers and mathematics, Springer, 1989, 21-26.

18.
P. C. van Oorschot, A. J. Menezes, and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997

19.
V. Varadharajan, R. W. K. Odoni, and P. W. Sanders, Public key distribution in matrix rings, Electronic Letters, 20 (1974), no. 9, 386-387

20.
HongzengWei and Xingfen Zheng, The number of solutions to the bilinear matrix equation over a finite field, J. Statist. Plann. Inference 94 (2001), 359-369 crossref(new window)

21.
Wan Zhe-xian and Li Gen-dao, The two theorems of Schur on commutative matrices, Chinese Math. 5 (1964), 156-164