Public Key Cryptography – PKC 2012: 15th International - download pdf or read online

By Craig Gentry, Shai Halevi, Nigel P. Smart (auth.), Marc Fischlin, Johannes Buchmann, Mark Manulis (eds.)

ISBN-10: 364230057X

ISBN-13: 9783642300578

This booklet constitutes the refereed lawsuits of the fifteenth overseas convention on perform and conception in Public Key Cryptography, PKC 2012, held in Darmstadt, Germany, in may perhaps 2012. The forty-one papers awarded have been rigorously reviewed and chosen from 188 submissions. The e-book additionally comprises one invited speak. The papers are prepared within the following topical sections: homomorphic encryption and LWE, signature schemes, code-based and multivariate crypto, public key encryption: designated homes, identity-based encryption, public-key encryption: buildings, safe two-party and multi-party computations, key alternate and safe periods, public-key encryption: relationships, DL, DDH, and extra quantity concept, and past traditional signature schemes.

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Read or Download Public Key Cryptography – PKC 2012: 15th International Conference on Practice and Theory in Public Key Cryptography, Darmstadt, Germany, May 21-23, 2012. Proceedings PDF

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Extra info for Public Key Cryptography – PKC 2012: 15th International Conference on Practice and Theory in Public Key Cryptography, Darmstadt, Germany, May 21-23, 2012. Proceedings

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Similarly, if something were uniform, either statistically or computationally, modulo R∨ , then m times it will be uniform modulo mR∨ and thus uniform modulo R, since mR∨ is an additive subgroup of R. This transformation is not completely tight (except in the case that Φm (X) = X m/2 + 1) because we end up with something that is uniform modulo a subgroup of R, whereas we only use the randomness modulo R. This loss of tightness, however, is very small, resulting in the noise being at most m/φ(m) “larger than necessary” (see the discussion after Theorem 2).

Furthermore, if deg gi = di ≤ b for all gi and the underlying monomial ordering is compatible with deg, we have the following alternative sampling algorithm, which gives the same distribution: Let ti ←$ P≤b−di uniformly for i ∈ {1, . . , m} and sample f ∈ I as f = m i=1 ti · gi . Proof. Clearly, both ways of sampling give us polynomials from I≤b . We observe that both f → f mod G and (t1 , . . tm ) → f = m i=1 ti · gi are Fq -linear maps. Since surjective linear maps preserve uniform distributions, both resulting distributions are uniform on their respective supports.

7 By the properties of a monomial order, LT(t · h) = t · H. Since t·H ∈ Q, this is not reduced modulo G, so we have LT((t·h) mod G) = t·H. Since A(t · h) = 0, we have t · h ∈ I≤b ⊕ Q≤k . This implies (t · h) mod G ∈ Q≤k , in particular (t · h) mod G has degree at most k. It follows that H has degree at most k − deg t = k − α − 1. This finally proves the theorem. Remark 3. Algorithm 5 was optimized for simplicity of analysis. We can get a better running time by using the highly structured nature of the equations on 7 Note that if k < d, any t of degree α + 1 will do without the restriction on n.

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Public Key Cryptography – PKC 2012: 15th International Conference on Practice and Theory in Public Key Cryptography, Darmstadt, Germany, May 21-23, 2012. Proceedings by Craig Gentry, Shai Halevi, Nigel P. Smart (auth.), Marc Fischlin, Johannes Buchmann, Mark Manulis (eds.)


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