By Rosario Gennaro, Matthew Robshaw

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

**Read Online or Download Advances in Cryptology -- CRYPTO 2015: 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part I PDF**

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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**

**Sample text**

N n < m(n + 1) · , b−1 b−1 (7) Coded-BKW: Solving LWE Using Lattice Codes 35 Algorithm 1. 2 Standard BKW Reductions The previously described coded-BKW in Sect. 4 introduces noise that grows with each iteration, so it makes sense to start with a number of pure BKW reductions. , the noise increased by merging and the noise introduced by coding. This step zeros out the bottom t1 · b bits. We now explain the details. , z ˆ denoted by L0 . Similar as the other process only on the non-systematic part of A, BKW procedures [7], in each step we sort the vector by the last b unprocessed b entries and thus divide the total samples into at most q 2−1 classes.

By ncod we denote the total number of positions canceled by the codedt2 Ni . , ncod = i=1 last coded-BKW step by M . Following Sect. 3, the decoding cost is upper bounded by t2 i(q b − 1) )Ni , 4(M + C2 = 2 i=1 b where (M + i(q 2−1) ) is the number of samples processed in the (t2 − i + 1)-th step. 4 Nj )(M + j=1 (i − 1)(q b − 1) ). 2 (9) Partial Guessing The previous step outputs samples with smaller dimension but higher noise variance. In order to deal with the remaining unknowns in the secret ˆ s vector, we use a combination of testing all values by guessing and performing a hypothesis test using an FFT.

8805, pp. 48–59. Springer, Switzerland (2014) 31. : Parallel (probable) lock-free HashSieve: a practical sieving algorithm for the SVP. In: ICPP (2015) 32. : A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations. In: STOC (2010) 33. : Faster exponential time algorithms for the shortest vector problem. In: SODA, pp. 1468–1480 (2010) 34. : Fast lattice point enumeration with minimal overhead. In: SODA, pp. 276–294 (2015) 35. : Sieve algorithms for the shortest vector problem are practical.