Advances in Cryptology – EUROCRYPT 2011: 30th Annual - download pdf or read online

By Ronald Cramer (auth.), Kenneth G. Paterson (eds.)

ISBN-10: 3642204643

ISBN-13: 9783642204647

ISBN-10: 3642204651

ISBN-13: 9783642204654

This booklet constitutes the refereed complaints of the thirtieth Annual overseas convention at the concept and purposes of Cryptographic concepts, EUROCRYPT 2011, held in Tallinn, Estonia, in may possibly 2011.
The 31 papers, offered including 2 invited talks, have been rigorously reviewed and chosen from 167 submissions. The papers are equipped in topical sections on lattice-base cryptography, implementation and facet channels, homomorphic cryptography, signature schemes, information-theoretic cryptography, symmetric key cryptography, assaults and algorithms, safe computation, composability, key based message safety, and public key encryption.

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Extra info for Advances in Cryptology – EUROCRYPT 2011: 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tallinn, Estonia, May 15-19, 2011. Proceedings

Example text

In the first phase B O invokes A who expects access to Pτ,n (s ∈ Z22 ) . We now specify how B O samples the answer (R, z) to a query v ∈ {y ∈ Z22 : wt(y) = } made by A. Let u∗ := v ∧ v∗ u := v ∧ v∗ 1. B O queries its oracle n times on the input u. If the oracle’s output is ⊥ (which happens iff wt(u) < d), B O outputs 0 and stops. Otherwise let ˆ 1 ∈ Z2 ×n , z1 ∈ Zn denote the n outputs of the oracle. R 2 2 $ ˆ T · (x∗ ∧ u∗ ). ˆ0 ← Z22 ×n and set z0 = R 2. Sample R 0 ×n ˆ ˆ is uniquely 3. Return (R = R↓v ∈ Z2 , z = z0 ⊕ z1 ∈ Zn2 ), where R ˆ ˆ ˆ ˆ determined by requiring R↓v∗ = R0 and R↓v∗ = R1 .

With high probability, the polynomial f is invertible modulo q and modulo p, and if that is the case, the public-key is h = pg/f mod q (otherwise, the key generation process is restarted). To encrypt a message M ∈ RNTRU /p, one samples a random element s ∈ RNTRU of small Euclidean norm and computes the ciphertext C = hs + M mod q. The following procedure allows the owner of the secret key to decrypt: • Compute f C mod q. If C was properly generated, this gives pgs + f M mod q. Since p, g, s, f, M have small coefficients, it can be expected that after reduction modulo q the obtained representative is pgs + f M (in RNTRU ).

The authentication tag φ is computed in the same manner as the prover’s answer in the authentication protocol. That is, we sample a random matrix R ∈ Z2×n and compute a noisy $ inner product z := RT · s↓v ⊕ e, where e ← Bernτ . We note that using (R, z) as an authentication tag would not be secure, and we need to blind these values. 22 E. Kiltz et al. This is done by applying an (almost) pairwise independent permutation (PIP) π – which is part of the secret key – to (R, z, b) ∈ Z2×n+n+ν . Construction.

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Advances in Cryptology – EUROCRYPT 2011: 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tallinn, Estonia, May 15-19, 2011. Proceedings by Ronald Cramer (auth.), Kenneth G. Paterson (eds.)


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