By Rosario Gennaro, Matthew Robshaw

The volume-set, LNCS 9215 and LNCS 9216, constitutes the refereed court cases of the thirty fifth Annual foreign Cryptology convention, CRYPTO 2015, held in Santa Barbara, CA, united states, in August 2015. The seventy four revised complete papers provided have been conscientiously reviewed and chosen from 266 submissions. The papers are geared up within the following topical sections: lattice-based cryptography; cryptanalytic insights; modes and buildings; multilinear maps and IO; pseudorandomness; block cipher cryptanalysis; integrity; assumptions; hash capabilities and move cipher cryptanalysis; implementations; multiparty computation; zero-knowledge; idea; signatures; non-signaling and information-theoretic crypto; attribute-based encryption; new primitives; and entirely homomorphic/functional encryption.

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Additional info for Advances in Cryptology -- CRYPTO 2015: 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part I

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267–288. Springer, Heidelberg (1998) 18. : Approximate nearest neighbors: towards removing the curse of dimensionality. In: STOC, pp. 604–613 (1998) 19. : Parallel gauss sieve algorithm: solving the svp challenge over a 128-dimensional ideal lattice. In: Krawczyk, H. ) PKC 2014. LNCS, vol. 8383, pp. 411–428. Springer, Heidelberg (2014) 20. : Improved algorithms for integer programming and related lattice problems. In: STOC, pp. 193–206 (1983) 21. : Hardness of approximating the shortest vector problem in lattices.

In this case we have a huge improvement (see Table 2) in performance compared with other algorithms. Tables 1 and 2 show comparisons of different algorithms for solving various LWE and binary-LWE instances, respectively. , Duc et al. [17] for LWE or Albrecht et al. [3] for binary-LWE) and the estimates (under certain models [11,25,26,29]) for distinguishing LWE (or binary-LWE) samples from uniform using lattice reduction algorithms, when LWE is reduced to SIS. The results consolidate the understanding that BKW is asymptotically efficient.

Achieving an 80-bit or higher security level), thwarting of BKW-type attacks must be taken into consideration. The remainder of the paper is organized as follows. In Sect. 2 we describe the basic theory around the LWE problem. We give a short description of the BKW algorithm in Sect. 3, and then present the novel modification in the next section. We detail the algorithm in Sect. 5, analyze its complexity in Sect. 6, and then propose a variant for binary-LWE in Sect. 7. This is followed by the sections of implementation and results.

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