By Sanjam Garg, Craig Gentry, Shai Halevi (auth.), Thomas Johansson, Phong Q. Nguyen (eds.)
This ebook constitutes the court cases of the thirty second Annual overseas convention at the idea and purposes of Cryptographic suggestions, EUROCRYPT 2013, held in Athens, Greece, in might 2013. The forty-one complete papers incorporated during this quantity have been rigorously reviewed and chosen from 201 submissions. They take care of cryptanalysis of hash capabilities, side-channel assaults, quantity thought, lattices, public key encryption, electronic signatures, homomorphic cryptography, quantum cryptography, garage, instruments, and safe computation.
Read Online or Download Advances in Cryptology – EUROCRYPT 2013: 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings PDF
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Additional resources for Advances in Cryptology – EUROCRYPT 2013: 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings
Let m(n), k(n) = poly(n). Assume that DLWE(n, m, q, χ) is pseudorandom. Then the distribution (A, AX + E) is also pseudorandom, where and X ∈ Zn×k are chosen uniformly at random and E is chosen A ∈ Zm×n q q according to Ψ¯αm×k . 26 3 N. D¨ ottling and J. M¨ uller-Quade Lossy Codes In this section, we introduce the main technical tool of this work, lossy codes, and show that the existence of lossy codes implies that the associated decoding problems for random codes are hard. Deﬁnition 1 (Families of Lossy Codes).
Proof. Assume ﬁrst that G was chosen from χm×k , where χ is a symmetrical strictly B-bounded distribution. Fix an e with Prg [ e −g ∞ ≤ r] ≥ n−c , where g is distributed according to χm . Let g1 , . . , gk be the columns of G, thus each gi is distributed according to χm . We ﬁrst show that e is 2-ambiguous for the matrix G and distance r with high probability over the choice of G. If there is at least one column gi of G such that e − gi ∞ ≤ r, then e − Gx(i) ∞ ≤ r (where x(i) is the i-th unit vector) and we have that e is 2-ambiguous.
For instance, their result can be instantiated with binary errors and O( n · (1 + Ω(1/ log(n))) samples or polynomial errors (n for some small ) and a linear number of samples (m = (1 + /3)n). The main similarity of [MP13] and our work is on a conceptual level. In both [MP13] and our work a lossiness-argument is essential to establish the main result. To prove their result, Micciancio and Peikert restate the LWE problem in terms of SIS (Short Integer Solution) functions. This formulation states that, (m−n)×m and y = Hx, where x is given a randomly drawn SIS-function H ∈ Zq n drawn from an input-distribution χ , it is hard to ﬁnd x.
Advances in Cryptology – EUROCRYPT 2013: 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings by Sanjam Garg, Craig Gentry, Shai Halevi (auth.), Thomas Johansson, Phong Q. Nguyen (eds.)