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89
NonMalleable Cryptography
 SIAM Journal on Computing
, 2000
"... The notion of nonmalleable 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. ..."
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Cited by 447 (22 self)
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The notion of nonmalleable 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 zeroknowledge proofs of possession of knowledge. Nonmalleable 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.
A modular approach to the design and analysis of authentication and key exchange protocols
, 1998
"... 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 e ..."
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Cited by 223 (20 self)
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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 keyexchange protocols. In particular, we provide a security analysis of some wellknown key exchange protocols (e.g. authenticated DiffieHellman key exchange), and of some of the techniques underlying the design of several authentication protocols that are currently being
The Decision DiffieHellman Problem
, 1998
"... The Decision DiffieHellman 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 are ..."
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Cited by 198 (6 self)
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The Decision DiffieHellman 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 DiffieHellman 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 DiffieHellman function defined as: dh g (g a ; g b ) = g ab . We say that the group G satisfies the Computational DiffieHellman assumption (cdh) if no efficient algorithm can compute the function dh g (x; y) in G. Precise definitions are given in the next sectio...
On the (im)possibility of obfuscating programs
 Lecture Notes in Computer Science
, 2001
"... 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 an ..."
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Cited by 189 (10 self)
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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 complexitytheoretic applications, ranging from software protection to homomorphic encryption to complexitytheoretic 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.
Numbertheoretic constructions of efficient pseudorandom functions
 In 38th Annual Symposium on Foundations of Computer Science
, 1997
"... ..."
Perfectly OneWay Probabilistic Hash Functions
"... 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 onewayness", in the following sense: Having access to the function value on some input is equivalent ..."
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Cited by 73 (9 self)
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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 onewayness", 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 renamed perfectly oneway functions) were given based on certain strong variants of the DiffieHellman assumption. In this work we present several constructions of perfectly oneway functions; some constructions are based on clawfree 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.
Correcting errors without leaking partial information
 In 37th Annual ACM Symposium on Theory of Computing (STOC
, 2005
"... 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 sig ..."
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Cited by 56 (10 self)
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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 errorcorrection information with significant probability. This leads to several new results: (a) the design of noisetolerant “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 reuse 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.
On the Security of ElGamal Based Encryption
 PKC'98, LNCS 1431
, 1998
"... 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 DiffieHellman assum ..."
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Cited by 47 (2 self)
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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 DiffieHellman 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 DiffieHellman 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. Nonmalleability is equivalent to the decision DiffieHellman assumption, the existence of a random oracle (in practice a secure hash function) or a trusted beacon (as needed for the FiatShamir argument), and one assumption about the unforgeability of Schnorr signatures. Our proof employs the tool of message awareness. 1
Advances in Cryptographic Voting Systems
, 2006
"... Democracy depends on the proper administration of popular elections. Voters should receive assurance that their intent was correctly captured and that all eligible votes were correctly tallied. The election system as a whole should ensure that voter coercion is unlikely, even when voters are willing ..."
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Cited by 41 (1 self)
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Democracy depends on the proper administration of popular elections. Voters should receive assurance that their intent was correctly captured and that all eligible votes were correctly tallied. The election system as a whole should ensure that voter coercion is unlikely, even when voters are willing to be influenced. These conflicting requirements present a significant challenge: how can voters receive enough assurance to trust the election result, but not so much that they can prove to a potential coercer how they voted? This dissertation explores cryptographic techniques for implementing verifiable, secretballot elections. We present the power of cryptographic voting, in particular its ability to successfully achieve both verifiability and ballot secrecy, a combination that cannot be achieved by other means. We review a large portion of the literature on cryptographic voting. We propose three novel technical ideas: 1. a simple and inexpensive paperbase cryptographic voting system with some interesting advantages over existing techniques, 2. a theoretical model of incoercibility for human voters with their inherent limited computational ability, and a new ballot casting system that fits the new definition, and