Wyniki wyszukiwania - BazTech

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ID-based, Proxy, Threshold Signature Scheme

Pomykała Jacek, Kułakowski Henryk, Sapiecha Piotr, Grela Błażej

International Journal of Electronics and Telecommunications

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2021

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Vol. 67, No. 2

201--205

EN

We propose the proxy threshold signature scheme with the application of elegant construction of verifiable delegating key in the ID-based infrastructure, and also with the bilinear pairings. The protocol satisfies the classical security requirements used in the proxy delegation of signing rights. The description of the system architecture and the possible application of the protocol in edge computing designs is enclosed.

2

Deterministic Integer Factorization with Oracles for Euler's Totient Function

Hittmeir Markus, Pomykała Jacek

Fundamenta Informaticae

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2020

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Vol. 172, nr 1

39--51

EN

In this paper, we construct deterministic factorization algorithms for natural numbers N under the assumption that the prime power decomposition of Euler’s totient function φ (N ) is known. Their runtime complexities depend on the number ω (N ) of distinct prime divisors of N , and we present efficient methods for relatively small values of ω (N ) as well as for its large values. One of our main goals is to establish an asymptotic expression with explicit remainder term O (x /A ) for the number of positive integers N ≤ x composed of s distinct prime factors that can be factored nontrivially in deterministic time t = t (x ), provided that the prime power decomposition of φ (N ) is known. We obtain it for A = A (x ) = x 1–ɛ , where ɛ = ɛ (s ) > 0 is sufficiently small and t = t (x ) is a polynomial in log x of degree d = d (ɛ ). An analogous bound is deduced under the assumption of the oracle providing the decomposition of orders of elements in ℤN *.

3

Jacobians of Hyperelliptic Curves over ℤn and Factorization of n

Dryło Robert, Pomykała Jacek

Fundamenta Informaticae

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2019

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Vol. 169, nr 4

275--283

EN

E. Bach showed that factorization of an integer n can be reduced in probabilistic polynomial time to the problem of computing exponents of elements in ℤn* (in particular the group order of ℤ*n). It is also known that factorization of square-free integer n can be reduced to the problem of computing the group order of an elliptic curve E/ℤn. In this paper we describe the analogous reduction for computing the orders of Jacobians over ℤn of hyperelliptic curves C over ℤn using the Mumford representation of divisor classes and Cantor’s algorithm for addition. These reductions are based on the group structure of the Jacobian. We also propose other reduction of factorization to the problem of determining the number of points |C(ℤn)|, which makes use of elementary properties of twists of hyperelliptic curves.