Abstract
Recent research in cryptography has led to the construction of several pseudo-random bit generators, programs producing bits as hard to predict as solving a hard problem. In this paper,
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1.
We present a new pseudo-random bit generator based on elliptic curves.
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2.
To construct our generator, we also develop two techniques that are of independent interest:
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(a)
an algorithm that computes the order of an element in an arbitrary Abelian group; and
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(b)
a new oracle proof method for demonstrating the simultaneous security of multiple bits of a discrete logarithm in an arbitrary Abelian group.
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(a)
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3.
We present a new candidate hard problem for future use in cryptography: the elliptic logarithm problem.
This research was supported by NSF grant MCS-8006938.
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Kaliski, B.S. (1987). A Pseudo-Random Bit Generator Based on Elliptic Logarithms. In: Odlyzko, A.M. (eds) Advances in Cryptology — CRYPTO’ 86. CRYPTO 1986. Lecture Notes in Computer Science, vol 263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47721-7_7
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