Abstract
In this paper, we present a design strategy of elliptic curves whose extension degrees needed for reduction attacks have a controllable lower boundary, based on the complex multiplication fields method of Atkin and Morain over prime fields.
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References
Miller, V. S.: Use of elliptic curves in cryptography. Advances in Cryptology-CRYPTO’85, Lecture Notes in Computer Science, 218 (1986) 417–426
Koblitz, N.: Elliptic Curve Cryptosystems. Math. Comp. 48 (1987) 203–209
Menezes, A. J.: Elliptic Curve Public Key Cryptosystems Kluwer Academic Publishers (1993)
Knuth, D. E.: The art of computer programming, Sorting and searching. vol. 3, Addison Wesley (1973)
Menezes, A. J., Vanstone, S., Okamoto T.: Reducing elliptic curve logarithms to logarithms in a finite field. Proc. of STOC’91 (1991) 80–89
Pohlig, S. C., Hellman, M. E.: An improved algorithm for computing logarithm over GF(p) and its cryptographic significance. IEEE Trans. Information Theory, IT-24,1 (1978) 106–110
Adleman, L. M.: A subexponential algorithm for the discrete logarithm problem with applications to cryptography. Proc. of IEEE 20th Symp. on Foundations of Comp. Sci. (1979) 55–60
Koblitz, N.: Elliptic curve implementation of zero-knowledge blobs. Journal of Cryptology, vol. 4, No. 3 (1991) 207–213
Atkin, A. O. L., Morain F.: Elliptic curves and primality proving. Research Report 1256, INRIA, June (1990)
Morain, F., Building cyclic elliptic curves modulo large primes. Advances in Cryptology-EUROCRYPT’91, Lecture Notes in Computer Science, 547 (1991) 328–336
Chao, J., Tanada, K., Tsujii S.: On secure elliptic curves against the “reduction attack” and their design strategy. Proc. of SCIS’94 (1994) 10A, IEICE Tech. Report, ISEC93-100, 29–37
Schoof, R.: Elliptic curves over finite fields and the computation of square roots mod p. Math. Comp. 44 (1985) 483–494
Berlekamp, E. R.: Algebraic coding theory. MacGraw-Hill (1968)
Robin, M. O.: Probabilistic algorithm in finite fields. SIAM J. on Comput., Vol.9, No.2 (1980) 273–280
Miyaji, A.: On ordinary elliptic curve cryptosystems. Advances in Cryptology-ASIACRYPT’91, Lecture Notes on Computer Science 739 (1991) 460–469
Miyaji, A.: Fast elliptic curve cryptosystems, Technical Report of IEICE (1993) COMP93–25
Chao, J., Ikemoto, H., Tanada, K., Tsujii, S.: On Discrete Logarithm Problems over elliptic curves with p-divisible groups. Proc. of Joint Workshop on Information Security and Cryptography, JW-ISC93 (1993) 99–104
Koblitz, N.: Constructing elliptic curve cryptosystems in characteristic 2. Advances in Cryptology-CRYPTO’90, Lecture Notes in Computer Science, 537 (1990) 156–167
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© 1994 Springer-Verlag Berlin Heidelberg
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Chao, J., Tanada, K., Tsujii, S. (1994). Design of Elliptic Curves with Controllable Lower Boundary of Extension Degree for Reduction Attacks. In: Desmedt, Y.G. (eds) Advances in Cryptology — CRYPTO ’94. CRYPTO 1994. Lecture Notes in Computer Science, vol 839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48658-5_6
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DOI: https://doi.org/10.1007/3-540-48658-5_6
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