Using the fact that the factorization of XN - 1 over GF(2) is especially explicit, we completely establish the distributions and the expected values of the linear complexity and the terror linear complexity of the N-periodic sequences respectively, where N is an odd prime and 2 is a ...
Faster deterministic integer factorization The best known unconditional deterministic complexity bound for computing the prime factorization of an integer Edgar,Costa,David,... - 《Math Comp》 被引量: 20发表: 2014年 Matrix Factorizations for Parallel Integer Transformation block factorizationinteger mapping...
. . , yt be points in Zn, let Q be an integer, and let Q = q1e1 ··· qmem be its prime factorization. Then there exists a multilinear polynomial hQ : Zn → Z such that (i) hQ (yi) ≡ 0 (mod Q) for all i ∈ [t], and (ii) hQ (z) = 1 for at least 2n − ...
On the power of quantum cryptography. In Proc. 35th Annual Symposium on Foundations of Computer Science 116–123 (IEEE Computer Society, 1994). Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41, 303–332 (1999). ...
where\(\phi ^{\prime }\)is any subgradient of\(\phi \)atx. The case with\(\mu _{\phi }(w)= 0\)reduces to convexity. We will also make use of the following characterization of strong convexity. For all\(x,y \in {{\mathrm{dom}}}\phi \)and\(\lambda \in [0,1]\), ...
is equivalent to saying that there is a polynomial time proof system for L. The proof system we have in mind is one where on input x, a prover creates a string a, and the verifier then computes on x and a in time polynomial in the length of the binary representation of x to check...
In recent years, rapid developments of quantum computer are witnessed in both the hardware and the algorithm domains, making it necessary to have an updated review of some major techniques and applications in quantum algorithm design. In this survey as well as tutorial article, the authors first ...
Computational complexity theory is the study of the minimal resources needed to solve computational problems. In particular, it aims to distin- guish between those problems that possess ecient algorithms (the easy problems) and those that are inherently intractable (the hard problems). Thus computatio...
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Using the fact that the factorization of xN -1over GF(2) is especially explicit, we completely establish the distributions and the expected values of the linear complexity and the k-error linear complexity of the N-periodic sequences respectively, where N is an odd prime and 2 is a ...