The hardness assumption of approximate shortest vector problem (SVP) within the polynomial factor in polynomial time reduced to the security of many lattice-based cryptographic primitives, so solving this problem, breaks these primitives. In this paper, we investigate the suitability of combining the best techniques in general search/optimization, lattice theory and parallelization technologies for solving the SVP into a single algorithm. Our proposed algorithm repeats three steps in a loop: an evolutionary search (a parallelized Genetic Algorithm), brute-force of tiny full enumeration (in role of too much local searches with random start points over the lattice vectors) and a single main enumeration. The test results showed that our proposed algorithm is better than LLL reduction and may be worse than the BKZ variants (except some so small block sizes). The main drawback for these test results is the notsufficient tuning of various parameters for showing the potential strength of our contribution. Therefore, we count the entire main problems and weaknesses in our work for clearer and better results in further studies. Also it is proposed a pure model of Genetic Algorithm with more solid/stable design for SVP problem which can be inspired by future works.

In this paper we explore a mechanized verification of the NTRUEncrypt scheme, with the formal proof system Isabelle/HOL. More precisely, the functional correctness of this algorithm, in its reduced form, is formally verified with computer support. We show that this scheme is correct what is a necessary condition for the usefulness of any cryptographic encryption scheme. Besides, we present a convenient and application specific formalization of the NTRUEncrypt scheme in the Isabelle/HOL system that can be used in further study around the functional and security analysis of NTRUEncrypt family.

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We introduce a new technique for BKZ reduction, which incorporated four improvements of BKZ 2.0 (including: sound pruning, preprocessing of local blocks, shorter enumeration radius and early-abortion). This algorithm is designed based on five claims which be verified strongly in experimental results. The main idea is that, similar to progressive BKZ which using decrement of enumeration cost after each sequence incremental reduction to augment the block size, we use the decrement of enumeration cost after each round of our algorithm to augment the success probability of bounding function. Also we discussed parallelization considerations in our technique.

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