A non-interactive public-key distribution system

Maurer, Ueli; Yacobi, Yacov

doi:10.1007/bf00129771

Cited by 43 publications

(29 citation statements)

References 21 publications

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“…This is extremely useful for applications which require the computation of many logarithms in the same field. To give an example, this was required by the identity based cryptosystem of Maurer and Yacobi [16]. …”

Section: Resultsmentioning

confidence: 99%

The Number Field Sieve in the Medium Prime Case

Joux

Lercier²,

Smart

et al. 2006

Lecture Notes in Computer Science

120

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Abstract. In this paper, we study several variations of the number field sieve to compute discrete logarithms in finite fields of the form Fpn, with p a medium to large prime. We show that when n is not too large, this yields a Lpn (1/3) algorithm with efficiency similar to that of the regular number field sieve over prime fields. This approach complements the recent results of Joux and Lercier on the function field sieve. Combining both results, we deduce that computing discrete logarithms have heuristic complexity Lpn (1/3) in all finite fields. To illustrate the efficiency of our algorithm, we computed discrete logarithms in a 120-digit finite field F p 3 .

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Section: Resultsmentioning

confidence: 99%

The Number Field Sieve in the Medium Prime Case

Joux

Lercier²,

Smart

et al. 2006

Lecture Notes in Computer Science

120

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“…One such example is the Boneh-Goh-Nissim homomorphic encryption [5], where in order to decrypt a ciphertext, a user has to first compute g m from the given ciphertext and then solve the discrete logarithm to recover the message m. Another example is the Maurer-Yacobi identity-based encryption [10]. Their construction uses a trapdoor discrete logarithm group, where the discrete logarithm problem is feasible to a user who has the trapdoor information, while hard for those who do not.…”

Section: Introductionmentioning

confidence: 99%

Generic Hardness of the Multiple Discrete Logarithm Problem

Yun

2015

Advances in Cryptology - EUROCRYPT 2015

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Abstract. We study generic hardness of the multiple discrete logarithm problem, where the solver has to solve n instances of the discrete logarithm problem simultaneously. There are known generic algorithms which perform O( √ np) group operations, where p is the group order, but no generic lower bound was known other than the trivial bound. In this paper we prove the tight generic lower bound, showing that the previously known algorithms are asymptotically optimal. We establish the lower bound by studying hardness of a related computational problem which we call the search-by-hyperplane-queries problem, which may be of independent interest.

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“…In 1991, Maurer and Yacobi presented a scheme referred to as MY [4], which is similar to our scheme, MK1. Maurer and Yacobi proposed improved versions of their scheme later [5,6]. All of these schemes can be regarded as a generalized version of Diffie-Hellman key sharing scheme using ID as a public key.…”

Section: Introductionmentioning

confidence: 99%

An ID-based key sharing scheme based on discrete logarithm problem over a product of three primes

Murakami

Kasahara

2010

JSIAM Letters

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In 1990, the present authors proposed the first ID-based non-interacrive key sharing scheme (ID-NIKS) based on the discrete logarithm problem (DLP) over a composite number n. With a rapid progress of computer system for the last two decades, ID-NIKS based on DLP over n would have more chance to be applied practically. However, there existed no secure ID-NIKS based on DLP over n against the square-root attack when n is a product of three prime numbers. In this paper, we propose an ID-NIKS based on DLP over a product of three prime numbers which can circumvent the square-root attack.Keywords ID-based cryptosystem, non-interactive key sharing, discrete logarithm problem, factoring problemResearch Activity Group Algorithmic Number Theory and Its Applications

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A non-interactive public-key distribution system

Cited by 43 publications

References 21 publications

The Number Field Sieve in the Medium Prime Case

The Number Field Sieve in the Medium Prime Case

Generic Hardness of the Multiple Discrete Logarithm Problem

An ID-based key sharing scheme based on discrete logarithm problem over a product of three primes

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