The discrete logarithm problem in Bergman's non-representable ring
نویسندگان
چکیده
منابع مشابه
The discrete logarithm problem in Bergman's non-representable ring
Bergman’s ring Ep , parameterized by a prime number p, is a ring with p elements that cannot be embedded in a ring of matrices over any commutative ring. This ring was discovered in 1974. In 2011, Climent, Navarro and Tortosa described an efficient implementation of Ep using simple modular arithmetic, and suggested that this ring may be a useful source for intractable cryptographic problems. We...
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Bergman’s Ring Ep, parameterized by a prime number p, is a ring with p 5 elements that cannot be embedded in a ring of matrices over any commutative ring. This ring was discovered in 1974. In 2011, Climent, Navarro and Tortosa described an efficient implementation of Ep using simple modular arithmetic, and suggested that this ring may be a useful source for intractable cryptographic problems. W...
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Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
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This can be a significantly harder problem. For example, say we are using a randomized (Las Vegas) algorithm. If β lies in 〈α〉 then we are guaranteed to eventually find logα β, but if not, we will never find it and it may be impossible to tell whether we are just very unlucky or β 6∈ 〈α〉. On the other hand, with a deterministic algorithm such as the baby-steps giant-steps method, we can unequiv...
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ژورنال
عنوان ژورنال: Journal of Mathematical Cryptology
سال: 2012
ISSN: 1862-2976,1862-2984
DOI: 10.1515/jmc-2012-0014