By Xavier Boyen, Brent Waters (auth.), Tatsuaki Okamoto, Xiaoyun Wang (eds.)

ISBN-10: 3540716769

ISBN-13: 9783540716761

ISBN-10: 3540716777

ISBN-13: 9783540716778

This ebook constitutes the refereed court cases of the tenth foreign convention on perform and concept in Public-Key Cryptography, PKC 2007, held in Beijing, China in April 2007.

The 29 revised complete papers offered including invited lectures have been rigorously reviewed and chosen from 118 submissions. The papers are geared up in topical sections on signatures, cryptanalysis, protocols, multivariate cryptosystems, encryption, quantity theoretic concepts, and public-key infrastructure.

**Read Online or Download Public Key Cryptography – PKC 2007: 10th International Conference on Practice and Theory in Public-Key Cryptography Beijing, China, April 16-20, 2007. Proceedings PDF**

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**Additional info for Public Key Cryptography – PKC 2007: 10th International Conference on Practice and Theory in Public-Key Cryptography Beijing, China, April 16-20, 2007. Proceedings**

**Sample text**

If n is a special RSA modulus, with p, q, p , and q as in Definition 2 above, then |QRn | = p q and (p − 1)(q − 1) elements of QRn are generators of QRn . Property 2. If g is a generator of QRn , then g a mod n is a generator of QRn if and only if GCD(a, |QRn |) = 1. The security of our techniques relies on the following security assumptions which are widely accepted in the cryptography literature. (see, for example, [1,2,9,10,15]). Assumption 1 (Strong RSA Assumption). Let n be an RSA modulus.

In the random oracle model this is very easy. Namely, for a random function H simply deﬁne the hash function to be H(0, ·) and the randomness extractor to be H(1, ·), such that both functions essentially yield 1 2 A function is regular if any image has the same number of pre-images. In the literature randomness extractors are typically deﬁned to produce an output that is statistically close to the uniform distribution. Here we merely need the relaxation to computational indistinguishability where the output appears to be random for eﬃcient observers.

Let α, l, and lc be security parameters that are all greater than 1, and let X be a constant number. In the following protocol, Alice knows x, the discrete logarithm of T1 (so g x ≡ T1 (mod n)), where x ∈ [X − 2l , X + 2l ]. After the protocol is executed, Bob is convinced that Alice knows the discrete log x of T1 such that x ∈ [X − 2α(l+lc )+1 , X + 2α(l+lc )+1 ]. 1. Alice picks a random t ∈ ±{0, 1}α(l+lc) and computes T2 = g t (mod n). Alice sends (T1 , T2 ) to a verifier Bob. 2. Bob picks a random c ∈ {0, 1}lc and sends it to Alice.

### Public Key Cryptography – PKC 2007: 10th International Conference on Practice and Theory in Public-Key Cryptography Beijing, China, April 16-20, 2007. Proceedings by Xavier Boyen, Brent Waters (auth.), Tatsuaki Okamoto, Xiaoyun Wang (eds.)

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