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A public key system with signature and master key functions. (English) Zbl 0933.94022
In the paper a new public key system has been introduced. This public key system is based on the theory of tame automorphism groups of an affine vector space. The public key is defined by a field \(GF(2^m)\) and a polynomial mapping \((f_1,\dots,f_{n+r}): GF(2^m)^n\to GF(2^m)^{n+r}\), with \(f_1,\dots,f_{n+r}\) defined by tame automorphisms \(\varphi_1,\varphi_2,\varphi_3,\varphi_4\) assumed as the private key. The securty of the system rests in part on the difficulty of computing the maps \(\varphi_1^{-1},\varphi_2^{-1},\varphi_3^{-1},\varphi_4^{-1}\) from the partial information provided by \((f_1,\dots,f_{n+r})\) and that it is impractical to write down the polynomial expresion each of \(\varphi_1^{-1},\varphi_2^{-1},\varphi_3^{-1},\varphi_4^{-1}\). The paper contains the comprehensive discussion of cryptoanalysis for this system.

94A60 Cryptography
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[1] Aabhyankar S.S., Journal ftir die reine und angewandte Mathematik 276 pp 148– (1975)
[2] Bajaj C., On the Application of Multi-Equational Resultants (1988)
[3] Bass H., Bull. Amer. Math. Soc 7 (2) pp 287– (1983) · Zbl 0539.13012
[4] Berlekamp E.R., Bell System Tech. J 46 (2) pp 1853– (1967)
[5] Brandstrom H., Cryptologia 7 (2) pp 347– (1983) · Zbl 0537.94014
[6] Brent R., Journal of the ACM 25 (4) pp 581– (1978) · Zbl 0388.68052
[7] DOI: 10.1007/978-3-662-02945-9
[8] Canny John F., Complexity of Robot Motion Planning (1988) · Zbl 0668.14016
[9] Dickerson Mathew, J. Symbolic Computation 13 pp 209– (1992) · Zbl 0805.13006
[10] Lidl R., Finite fields (1983)
[11] Moh T., Advances in Cryp-tology (Proceedings of EURO CRYPT 84 pp 10– (1983)
[12] Moh T., Algebraic Geometry and Commutative Algebra in honor of M. Nagata pp 267– (1988)
[13] Nagata M., On the automorphism group of K[X, Y] 5 (1972) · Zbl 0306.14001
[14] Niederreiter H., Contemporary Mathematics (Finite Fields) 168 (1993)
[15] DOI: 10.1145/359340.359342 · Zbl 0368.94005
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