Key exchage by Chebyshev polynomials module 2^w (original) (raw)
We show that Chebyshev polynomials of odd degree are permutable polynomials module 2^w. We use this fact to construct a new key exchange algorithm.
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Polynomial representations of the Diffie-Hellman mapping
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We obtain lower bounds on the degrees of polynomials representing the Diffie-Hellman mapping (gx, gy) → gxy, where g is a primitive root of a finite field q of q elements. These bounds are exponential in terms of log q. In particular, these results can be used to obtain lower bounds on the parallel arithmetic complexity of breaking the Diffie-Hellman cryptosystem. The method is based on bounds of numbers of solutions of some polynomial equations.
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