By Rosario Gennaro, Matthew Robshaw
The volume-set, LNCS 9215 and LNCS 9216, constitutes the refereed complaints 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 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 buildings; multilinear maps and IO; pseudorandomness; block cipher cryptanalysis; integrity; assumptions; hash features and circulate 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.
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Extra info for Advances in Cryptology -- CRYPTO 2015: 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part I
Using probing, the memory requirement is further reduced by a signiﬁcant amount, at the cost of a small increase in the time complexity (Fig. 3d). 2 High-Dimensional Extrapolations As explained at the start of this section, the experiments in Sect. 1 are aimed at verifying the heuristic analysis and at establishing trends which hold regardless of the amount of optimization of the code, the quality of preprocessing of the 20 T. Laarhoven input basis, the amount of parallelization etc. However, the linear estimates in Fig.
Guo et al. (2) where ∗ means any value. Then a new vector a1 = ai1 − ai2 is formed. An “observed symbol” is also formed, corresponding to this new column by forming (2) (2) (2) (2) (2) (2) (2) z1 = zi1 − zi2 . If y1 = s, a1 , then z1 = y1 + e1 , where now e1 = ei1 −ei2 . Recall that noise like ei1 follows the Gaussian distribution with variance (2) σ 2 , so e1 = ei1 −ei2 is considered to be Gaussian distributed with variance 2σ 2 . There is also a second obvious way of getting collisions, namely, combining any two vectors where the sum of the collision sets is zero.
2πe 12 1 We set G(ΛN,k ) to be 12 and surely this is a pessimistic estimation. Since the lattice is built from a linear code by Construction A, the volume of V is q N −k . Thus, we can approximate σ by σ ≈ q 1−k/N · G(ΛN,k ) = q 1−k/N √ . , [N, k] is [3, 1] or [2, 1], q is 631, 2053 or 16411) and veriﬁed that the above estimation works (see Table 3, where 1/G is bounding 1/G(ΛN,k )). We choose [N, 1] codes since for the covering or MMSE property, lower rate means worse performance. It is folklore that the value G will decrease when the dimension and length becomes larger, and all the cases listed in Table 3 fully obey the rule.
Advances in Cryptology -- CRYPTO 2015: 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part I by Rosario Gennaro, Matthew Robshaw