The notion of non-malleable cryptography, an extension of semantically secure cryptography, is defined. Informally, in the context of encryption the additional requirement is that given the ciphertext it is impossible to generate a different ciphertext so that the respective plaintexts are related. The same concept makes sense in the contexts of string commitment and zero-knowledge proofs of possession of knowledge. Non-malleable schemes for each of these three problems are presented. The schemes do not assume a trusted center; a user need not know anything about the number or identity of other system users. Our cryptosystem is the first proven to be secure against a strong type of chosen ciphertext attack proposed by Rackoff and Simon, in which the attacker knows the ciphertext she wishes to break and can query the decryption oracle on any ciphertext other than the target.

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We present a general framework for constructing and analyzing authentication protocols in realistic models of communication networks. This framework provides a sound formalization for the authentication problem and suggests simple and attractive design principles for general authentication and key exchange protocols. The key element in our approach is a modular treatment of the authentication problem in cryptographic protocols; this applies to the definition of security, to the design of the protocols, and to their analysis. In particular, following this modular approach, we show how to systematically transform solutions that work in a model of idealized authenticated communications into solutions that are secure in the realistic setting of communication channels controlled by an active adversary. Using these principles we construct and prove the security of simple and practical authentication and key-exchange protocols. In particular, we provide a security analysis of some well-known key exchange protocols (e.g. authenticated Diffie-Hellman key exchange), and of some of the techniques underlying the design of several authentication protocols that are currently being

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...

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.

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Probabilistic hash functions that hide all partial information on their input were recently introduced. This new cryptographic primitive can be regarded as a function that offers "perfect one-wayness", in the following sense: Having access to the function value on some input is equivalent to having access only to an oracle that answers "yes " if the correct input is queried, and answers "no " otherwise. Constructions of this primitive (originally called oracle hashing and here re-named perfectly one-way functions) were given based on certain strong variants of the Diffie-Hellman assumption. In this work we present several constructions of perfectly one-way functions; some constructions are based on claw-free permutation, and others are based on any oneway permutation. One of our constructions is simple and efficient to the point of being attractive from a practical point of view.

Abstract. The ElGamal encryption scheme has been proposed several years ago and is one of the few probabilistic encryption schemes. However, its security has never been concretely proven based on clearly understood and accepted primitives. Here we show directly that the decision Diffie-Hellman assumption implies the security of the original ElGamal encryption scheme (with messages from a subgroup) without modification. In addition, we show that the opposite direction holds, i.e., the semantic security of the ElGamal encryption is actually equivalent to the decision Diffie-Hellman problem. We also present an exact analysis of the efficiency of the reduction. Next we present additions on ElGamal encryption which result in nonmalleability under adaptive chosen plaintext attacks. Non-malleability is equivalent to the decision Diffie-Hellman assumption, the existence of a random oracle (in practice a secure hash function) or a trusted beacon (as needed for the Fiat-Shamir argument), and one assumption about the unforgeability of Schnorr signatures. Our proof employs the tool of message awareness. 1

This paper explores what kinds of information two parties must communicate in order to correct errors which occur in a shared secret string W. Any bits they communicate must leak a significant amount of information about W — that is, from the adversary’s point of view, the entropy of W will drop significantly. Nevertheless, we construct schemes with which Alice and Bob can prevent an adversary from learning any useful information about W. Specifically, if the entropy of W is sufficiently high, then there is no function f(W) which the adversary can learn from the error-correction information with significant probability. This leads to several new results: (a) the design of noise-tolerant “perfectly oneway” hash functions in the sense of Canetti et al. [7], which in turn leads to obfuscation of proximity queries for high entropy secrets W; (b) private fuzzy extractors [11], which allow one to extract uniformly random bits from noisy and nonuniform data W, while also insuring that no sensitive information about W is leaked; and (c) noise tolerance and stateless key re-use in the Bounded Storage Model, resolving the main open problem of Ding [10]. The heart of our constructions is the design of strong randomness extractors with the property that the source W can be recovered from the extracted randomness and any string W ′ which is close to W.

An off-line biometric identification protocol based on error correcting codes was recently developed as an enabling technology for secure biometric based user authentication. The protocol was designed to bind a user's iris biometric template with authorization information via a magnetic strip in the off-line case while reducing the exposure of a user's biometric data. In this paper we give an in depth discussion of the role of error correcting codes in the cryptographically secure biometric authentication scheme. An Iris scan is a biometric technology which uses the human iris to authenticate users [BAW96, HMW90, Dau92, Wil96]. This technology produces a 2048 bit user biometric template such that any future scan of the same user's iris will generate a "similar" template. By similar, we mean having an Center for Cryptography, Computer, and Network Security, University of WisconsinMilwaukee, USA. E-mail: davida@cs.uwm.edu. y CertCo LLC, New York, NY, USA. E-mail: yfrankel@cs.co...