By Rosario Gennaro, Matthew Robshaw

ISBN-10: 3662479885

ISBN-13: 9783662479889

ISBN-10: 3662479893

ISBN-13: 9783662479896

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 prepared within the following topical sections: lattice-based cryptography; cryptanalytic insights; modes and buildings; multilinear maps and IO; pseudorandomness; block cipher cryptanalysis; integrity; assumptions; hash services and circulate cipher cryptanalysis; implementations; multiparty computation; zero-knowledge; conception; signatures; non-signaling and information-theoretic crypto; attribute-based encryption; new primitives; and entirely 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

Example text

These combinatorial algorithms have the advantage that their complexity can be analyzed in a standard way and we can get explicit values on the complexity for different instantiations of the LWE problem. Even though we use approximations in the analysis, the deviation between theoretical analysis and actual performance seems to be small [3,17]. This approach tends to give algorithms with the best performance for some important parameter choices. A possible drawback with BKW-based algorithms is that they usually require a huge amount of memory, often of the same order as the time complexity.

We can then write A = aT 1 a2 · · · an and z = sA + e, $ where zi = yi + ei = s, ai + ei and ei ← X is the noise. We see that the problem has been reformulated as a decoding problem. The matrix A serves as the generator matrix for a linear code over Zq and z is the received word. Finding the codeword y = sA such that the distance ||y − z|| is minimum will give the secret vector s. If the secret vector s is drawn from the uniform distribution, there is a simple transformation [4,23] that can be applied, namely, we may through Gaussian elimination transform A into systematic form.

We can read the syndrome from its last N − k entries directly if the vector aI belongs to the partition with the first k entries all zero. Then we operate inductively. If we know one syndrome, we can compute another one in the same partition within 2(N − k) Zq operations, or compute one in a different partition whose first k entries with distance 1 from that in the known partition within 3(N − k) Zq operations. Suppose we have mdec vectors to decode here (generally, the value mdec is larger than q k ), then the complexity of this part is bounded by (N − k)(2mdec + q k ) < 3mdec (N − k).

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