On One-way Functions and Kolmogorov Complexity

We prove that the equivalence of two fundamental problems in the theory of computing. For every polynomial $t(n)\geq (1+\varepsilon)n, \varepsilon>0$, the following are equivalent: - One-way functions exists (which in turn is equivalent to the existence of secure private-key encryption schemes, digital signatures, pseudorandom generators, pseudorandom functions, commitment schemes, and more); - $t$-time bounded Kolmogorov Complexity, $K^t$, is mildly hard-on-average (i.e., there exists a polynomial $p(n)>0$ such that no PPT algorithm can compute $K^t$, for more than a $1-\frac{1}{p(n)}$ fraction of $n$-bit strings). In doing so, we present the first natural, and well-studied, computational problem characterizing the feasibility of the central private-key primitives and protocols in Cryptography

Extractors: Low Entropy Requirements Colliding With Non-Malleability

The known constructions of negligible error (non-malleable) two-source extractors can be broadly classified in three categories: (1) Constructions where one source has min-entropy rate about $1/2$, the other source can have small min-entropy rate, but the extractor doesn't guarantee non-malleability. (2) Constructions where one source is uniform, and the other can have small min-entropy rate, and the extractor guarantees non-malleability when the uniform source is tampered. (3) Constructions where both sources have entropy rate very close to $1$ and the extractor guarantees non-malleability against the tampering of both sources. We introduce a new notion of collision resistant extractors and in using it we obtain a strong two source non-malleable extractor where we require the first source to have $0.8$ entropy rate and the other source can have min-entropy polylogarithmic in the length of the source. We show how the above extractor can be applied to obtain a non-malleable extractor with output rate $\frac 1 2$, which is optimal. We also show how, by using our extractor and extending the known protocol, one can obtain a privacy amplification secure against memory tampering where the size of the secret output is almost optimal

CCA-Secure Deterministic Identity-Based Encryption Scheme

Deterministic public-key encryption, encrypting a plaintext into a unique ciphertext without involving any randomness, was introduced by Bellare, Boldyreva, and O'Neill (CRYPTO 2007) as a realistic alternative to some inherent drawbacks in randomized public-key encryption. Bellare, Kiltz, Peikert and Waters (EUROCRYPT 2012) bring deterministic public-key encryption to the identity-based setting, and propose deterministic identity-based encryption scheme (DIBE). Although the construc- tions of chosen plaintext attack (CPA) secure DIBE scheme have been studied intensively, the construction of chosen ciphertext attack (CCA) secure DIBE scheme is still challenging problems. In this paper, we introduce the notion of identity-based all-but-one trapdoor functions (IB-ABO-TDF), which is an extension version of all-but-one lossy trapdoor function in the public-key setting. We give a instantiation of IB-ABO-TDF under decisional linear assumption. Based on an identity-based lossy trapdoor function and our IB-ABO-TDF, we present a generic construction of CCA-secure DIBE scheme