By Zvika Brakerski, Shafi Goldwasser (auth.), Tal Rabin (eds.)

This booklet constitutes the refereed court cases of the thirtieth Annual overseas Cryptology convention, CRYPTO 2010, held in Santa Barbara, CA, united states in August 2010, co-located with CHES 2010, the workshop on Cryptographic and Embedded structures. The 39 revised complete papers provided have been rigorously reviewed and chosen from 203 submissions. Addressing all present foundational, theoretical and learn features of cryptology, cryptography, and cryptanalysis in addition to complicated purposes, the papers are prepared in topical sections on leakage, lattice, homomorphic encryption, conception and functions, key alternate, OAEP/RSA, CCA, assaults, composition, computation delegation and obfuscation, multiparty computation, pseudorandomness, and quantum.

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E (1, YL YR ) can be computed (with probability δ) making k+1 forward queries to Ψr . Leakage-Resilient Pseudorandom Functions 35 def Proof (of Claim). As Z = E(1, YL YR ) is YR f1 (YR )⊕YL , to get Z it is sufficient def to learn C = f1 (YR ). To get E (1, YL YR ) we then make one more Ψr query Z. Let Bg be as in Definition 7, we will use it to reconstruct C as follows: For every query Xi asked by Bg , we make the query YR Xi to Ψr . The answer will contain the leakage Λ2 = g(C ⊕ Xi ), which is exactly what Bg expects as answer to his query Xi .

Then Ψr (whose key is K = {K1 , . . 38r/2−1 s = sprf − |F | · q · r = (2 + q · r) · prf + q 6 r6 q2 + 5! · 2n 2n Where L contains, for every g1 , . . , gr ∈ L, the function g defined as g (K, X) = {g1 (K1 , R1 ), . . , gr (Kr , Rr ), R0 , . . , Rr+1 } with (R0 , . . , Rr+1 ) ← μ(Ψr , X). We will prove this theorem using a combinatorial lemma from [12]. Consider an adversary A making q queries (forward or inverse) to Ψr = Ψ [f1 , . . , fr ]. Let R[i, j] denote the input to the jth round function on the ith query.

Springer, Heidelberg (2006) 9. : Publickey encryption schemes with auxiliary inputs. In: Micciancio, D. ) TCC 2010. LNCS, vol. 5978, pp. 361–381. Springer, Heidelberg (2010) 10. : Cryptography against continuous memory attacks. org/ 11. : On cryptography with auxiliary input. In: STOC, pp. 621–630 (2009) 12. : Feistel networks made public, and applications. In: Naor, M. ) EUROCRYPT 2007. LNCS, vol. 4515, pp. 534–554. Springer, Heidelberg (2007) 13. : On perfect and adaptive security in exposureresilient cryptography.

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