By Elad Barkan, Eli Biham, Adi Shamir (auth.), Cynthia Dwork (eds.)

This ebook constitutes the refereed court cases of the twenty sixth Annual overseas Cryptology convention, CRYPTO 2006, held in Santa Barbara, California, united states in August 2006.

The 34 revised complete papers awarded including 2 invited lectures have been rigorously reviewed and chosen from 250 submissions. The papers tackle all present foundational, theoretical and learn facets of cryptology, cryptography, and cryptanalysis in addition to complex applications.

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Extra info for Advances in Cryptology - CRYPTO 2006: 26th Annual International Cryptology Conference, Santa Barbara, California, USA, August 20-24, 2006. Proceedings

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Lemma 4. ,hk ) ← (Un ,Hk ) [f k (x, h1 , . . ,hk ) ← (f (Un ),Hk ) [(z, h1 , . . , hk ) ∈ T ] ≥ δ 2 /(k + 1). We stress that the probability in the latter inequality is over z drawn from f (Un ) and an independently chosen h1 , . . , hk ∈ H. Assuming Lemma 4, we may conclude the proof of Lemma 2. By Claim 3 we have that Pr[(xk , h1 , . . , hk ) ∈ SA ] ≥ ε2 . By Lemma 4, taking T = SA and δ = ε/2, we get that Pr[(z, h1 , . . , hk ) ∈ SA ] ≥ ε2 /4(k + 1). Thus, M A has a ε2 /4(k + 1) chance of hitting the set SA on which it will succeed with probability at least ε/2.

Pubic randomness in cryptography. In CRYPTO ’92, LNCS, volume 740, pages 421–432. Springer, 1992. T. Holenstein. Pseudorandom generators from one-way functions: A simple construction for any hardness. In TCC ’06, LNCS. Springer, 2006. R. Impagliazzo and M. Luby. One-way functions are essential for complexity based cryptography. In 30th FOCS, pages 230–235, 1989. R. Impagliazzo, N. Nisan, and A. Wigderson. Pseudorandomness for network algorithms. In 26th STOC, pages 356–364, 1994. 40 [IZ89] [Lev87] [LR88] [Nao91] [Nis92] [NZ96] [Phi93] [Yao82] I.

Hk 1 ) ∈ T . This happens with probability at least δ 2 . Then, once inside T , we know that the probability of collision is at least 1/ |T |. Altogether: CP (f k (Un , Hk )) ≥ δ 2 1 |T | (2) |T | δ Combining (1) and (2) we get |H|k |Im(f ≥ k+1 . )| But the probability of getting a value in T when choosing a random element in |T | Im(f ) × Hk is exactly |H|k |Im(f . Thus, Pr[(z, h1 , . . , hk ) ∈ T ] ≥ δ 2 /(k + 1) as )| 2 requested. 34 I. Haitner, D. Harnik, and O. Reingold Remark: The proof of Lemma 4 is where the regularity of the one-way function is required.

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Advances in Cryptology - CRYPTO 2006: 26th Annual by Elad Barkan, Eli Biham, Adi Shamir (auth.), Cynthia Dwork
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