This paper proposes a new sieving algorithm that employs a bucket sort as a part of a factoring algorithm such as the number field sieve. The sieving step requires an enormous number of memory updates;however, these u...
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This paper proposes a new sieving algorithm that employs a bucket sort as a part of a factoring algorithm such as the number field sieve. The sieving step requires an enormous number of memory updates;however, these updates usually cause cache hit misses. The proposed algorithm significantly reduces the number of cache hit misses when the size of the sieving region is roughly less than the square of the cache size, and the memory updates are several times faster than the straightforward implementation according to the PC experiments.
In the present paper we describe and analyse a sieving algorithm for determining prime numbers. This external memory algorithm contains several parameters which are related to the sizes of the levels in the memory hie...
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In the present paper we describe and analyse a sieving algorithm for determining prime numbers. This external memory algorithm contains several parameters which are related to the sizes of the levels in the memory hierarchy. We examine how we should choose the values of these parameters in order to obtain an optimal running time. We compare the running times obtained by varying the parameters. We conclude that in this specific problem fine tuning pays off as we got a speed-up of almost 40%. (c) 2007 Elsevier Ltd. All rights reserved.
Cryptanalysis of lattice-based cryptography is an important field in cryptography since lattice problems are among the most robust assumptions and have been used to construct a variety of cryptographic primitives. The...
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Cryptanalysis of lattice-based cryptography is an important field in cryptography since lattice problems are among the most robust assumptions and have been used to construct a variety of cryptographic primitives. The security estimation model for concrete parameters is one of the most important topics in lattice-based cryptography. In this research, we focus on the Gauss Sieve algorithm proposed by Micciancio and Voulgaris, a heuristic lattice sieving algorithm for the central lattice problem, shortest vector problem (SVP). We propose a technique of lifting computations in prime-cyclotomic ideals into that in cyclic ideals. Lifting makes rotations easier to compute and reduces the complexity of inner products from O(n(3)) to O(n(2)). We implemented the Gauss Sieve on multi-GPU systems using two layers of parallelism in our framework, and achieved up to 55 times speed of previous results of dimension 96. We were able to solve SVP on ideal lattice in dimension up to 130, which is the highest dimension SVP instance solved by sieve algorithm so far. As a result, we are able to provide a better estimate of the complexity of solving central lattice problem.
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