Given an arbitrary k-bit to k-bit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string x of length slightly less than k bits can be encrypted as f(rx), where rx is a simple probabilistic encoding of x depending on the hash function; and (ii) the scheme can be proven semantically secure assuming the hash function is \ideal. " Moreover, a slightly enhanced scheme is shown to have the property that the adversary can create ciphertexts only of strings for which she \knows " the corresponding plaintexts|such ascheme is not only semantically secure but also non-malleable and secure against chosen-ciphertext attack.

This paper provides a general treatment of privacy amplification by public discussion, a concept introduced by Bennett, Brassard and Robert [1] for a special scenario. The results have applications to unconditionally-secure secret-key agreement protocols, quantum cryptography and to a non-asymptotic and constructive treatment of the secrecy capacity of wire-tap and broadcast channels, even for a considerably strengthened definition of secrecy capacity. I. Introduction This paper is concerned with unconditionally-secure secretkey agreement by two communicating parties Alice and Bob who both know a random variable W, for instance a random n--bit string, about which an eavesdropper Eve has incomplete information characterized by the random variable V jointly distributed with W according to PV W . This distribution may partially be under Eve's control. Alice and Bob know nothing about PV W , except that it satisfies a certain constraint. We present protocols by which Alice and Bob can us...

The Decision Diffie-Hellman assumption (ddh) is a gold mine. It enables one to construct efficient cryptographic systems with strong security properties. In this paper we survey the recent applications of DDH as well as known results regarding its security. We describe some open problems in this area. 1 Introduction An important goal of cryptography is to pin down the exact complexity assumptions used by cryptographic protocols. Consider the Diffie-Hellman key exchange protocol [12]: Alice and Bob fix a finite cyclic group G and a generator g. They respectively pick random a; b 2 [1; jGj] and exchange g a ; g b . The secret key is g ab . To totally break the protocol a passive eavesdropper, Eve, must compute the Diffie-Hellman function defined as: dh g (g a ; g b ) = g ab . We say that the group G satisfies the Computational Diffie-Hellman assumption (cdh) if no efficient algorithm can compute the function dh g (x; y) in G. Precise definitions are given in the next sectio...

We show that modified versions of the linear congruential generator and the shift register generator are provably good for amplifying the correctness of a probabilistic algorithm. More precisely, if r random bits are needed for a BPP algorithm to be correct with probability at least 2=3, then O(r + k 2 ) bits are needed to improve this probability to 1 \Gamma 2 \Gammak . We also present a different pseudo-random generator that is optimal, up to a constant factor, in this regard: it uses only O(r + k) bits to improve the probability to 1 \Gamma 2 \Gammak . This generator is based on random walks on expanders. Our results do not depend on any unproven assumptions. Next we show that our modified versions of the shift register and linear congruential generators can be used to sample from distributions using, in the limit, the information-theoretic lower bound on random bits. 1. Introduction Randomness plays a vital role in almost all areas of computer science, both in theory and in...

A two party protocol in which party A uses one of several secret witnesses to an NP assertion is witness indistinguishable if party B cannot tell which witness A is actually using. The protocol is witness hiding

A new public key encryption scheme, along with several variants, is proposed and analyzed. The scheme and its variants are quite practical, and are proved secure against adaptive chosen ciphertext attack under standard intractability assumptions. These appear to be the first public-key encryption schemes in the literature that are simultaneously practical and provably secure.

Informally, an obfuscator O is an (efficient, probabilistic) “compiler ” that takes as input a program (or circuit) P and produces a new program O(P) that has the same functionality as P yet is “unintelligible ” in some sense. Obfuscators, if they exist, would have a wide variety of cryptographic and complexity-theoretic applications, ranging from software protection to homomorphic encryption to complexity-theoretic analogues of Rice’s theorem. Most of these applications are based on an interpretation of the “unintelligibility ” condition in obfuscation as meaning that O(P) is a “virtual black box, ” in the sense that anything one can efficiently compute given O(P), one could also efficiently compute given oracle access to P. In this work, we initiate a theoretical investigation of obfuscation. Our main result is that, even under very weak formalizations of the above intuition, obfuscation is impossible. We prove this by constructing a family of efficient programs P that are unobfuscatable in the sense that (a) given any efficient program P ′ that computes the same function as a program P ∈ P, the “source code ” P can be efficiently reconstructed, yet (b) given oracle access to a (randomly selected) program P ∈ P, no efficient algorithm can reconstruct P (or even distinguish a certain bit in the code from random) except with negligible probability. We extend our impossibility result in a number of ways, including even obfuscators that (a) are not necessarily computable in polynomial time, (b) only approximately preserve the functionality, and (c) only need to work for very restricted models of computation (TC 0). We also rule out several potential applications of obfuscators, by constructing “unobfuscatable” signature schemes, encryption schemes, and pseudorandom function families.

The Cipher Block Chaining -- Message Authentication Code (CBC MAC) specifies that a message x = x 1 \Delta \Delta \Delta xm be authenticated among parties who share a secret key a by tagging x with a prefix of f (m) a (x) def = f a (f a (\Delta \Delta \Delta f a (f a (x 1 )\Phix 2 )\Phi \Delta \Delta \Delta \Phix m\Gamma1 )\Phix m ) ; where f is some underlying block cipher (eg. f = DES). This method is a pervasively used international and U.S. standard. We provide its first formal justification, showing the following general lemma: that cipher block chaining a pseudorandom function gives a pseudorandom function. Underlying our results is a technical lemma of independent interest, bounding the success probability of a computationally unbounded adversary in distinguishing between a random ml-bit to l-bit function and the CBC MAC of a random l-bit to l-bit function. Advanced Networking Laboratory, IBM T.J. Watson Research Center, PO Box 704, Yorktown Heights, NY 10598, USA. e-m...

Constant-round zero-knowledge proof systems for every language in NP are presented, assuming the existence of a collection of claw-free functions. In particular, it follows that such proof systems exist assuming the intractability of either the Discrete Logarithm Problem or the Factoring Problem for Blum Integers.

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