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On robust combiners for oblivious transfer and other primitives
 In Proc. Eurocrypt ’05
, 2005
"... At the mouth of two witnesses... shall the matter be establishedDeuteronomy Chapter 19. ..."
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At the mouth of two witnesses... shall the matter be establishedDeuteronomy Chapter 19.
On robust combiners for private information retrieval and other primitives
 CRYPTO
, 2006
"... Abstract. Let A and B denote cryptographic primitives. A (k, m)robust AtoB combiner is a construction, which takes m implementations of primitive A as input, and yields an implementation of primitive B, which is guaranteed to be secure as long as at least k input implementations are secure. The ma ..."
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Abstract. Let A and B denote cryptographic primitives. A (k, m)robust AtoB combiner is a construction, which takes m implementations of primitive A as input, and yields an implementation of primitive B, which is guaranteed to be secure as long as at least k input implementations are secure. The main motivation for such constructions is the tolerance against wrong assumptions on which the security of implementations is based. For example, a (1,2)robust AtoB combiner yields a secure implementation of B even if an assumption underlying one of the input implementations of A turns out to be wrong. In this work we study robust combiners for private information retrieval (PIR), oblivious transfer (OT), and bit commitment (BC). We propose a (1,2)robust PIRtoPIR combiner, and describe various optimizations based on properties of existing PIR protocols. The existence of simple PIRtoPIR combiners is somewhat surprising, since OT, a very closely related primitive, seems difficult to combine (Harnik et al., Eurocrypt’05). Furthermore, we present (1,2)robust PIRtoOT and PIRtoBC combiners. To the best of our knowledge these are the first constructions of AtoB combiners with A � = B. Such combiners, in addition to being interesting in their own right, offer insights into relationships between cryptographic primitives. In particular, our PIRtoOT combiner together with the impossibility result for OTcombiners of Harnik et al. rule out certain types of reductions of PIR to OT. Finally, we suggest a more finegrained approach to construction of robust combiners, which may lead to more efficient and practical combiners in many scenarios.
Nontrivial blackbox combiners for collisionresistant hashfunctions don’t exist
 In Proc. Eurocrypt ’07
, 2007
"... 1 Introduction A function H: f0; 1g ..."
Robust MultiProperty Combiners for Hash Functions Revisited
"... Abstract. A robust multiproperty combiner for a set of security properties merges two hash functions such that the resulting function satisfies each of the properties which at least one of the two starting functions has. Fischlin and Lehmann (TCC 2008) recently constructed a combiner which simultan ..."
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Abstract. A robust multiproperty combiner for a set of security properties merges two hash functions such that the resulting function satisfies each of the properties which at least one of the two starting functions has. Fischlin and Lehmann (TCC 2008) recently constructed a combiner which simultaneously preserves collisionresistance, target collisionresistance, message authentication, pseudorandomness and indifferentiability from a random oracle (IRO). Their combiner produces outputs of 5n bits, where n denotes the output length of the underlying hash functions. In this paper we propose improved combiners with shorter outputs. By sacrificing the indifferentiability from random oracles we obtain a combiner which preserves all of the other aforementioned properties but with output length 2n only. This matches a lower bound for blackbox combiners for collisionresistance as the only property, showing that the other properties can be achieved without penalizing the length of the hash values. We then propose a combiner which also preserves the IRO property, slightly increasing the output length to 2n + ω(log n). Finally, we show that a twist on our combiners also makes them robust for onewayness (but at the price of a fixed input length). 1
Robuster Combiners for Oblivious Transfer
"... Abstract. A(k; n)robust combiner for a primitive F takes as input n candidate implementations of F and constructs an implementation of F, which is secure assuming that at least k of the input candidates are secure. Such constructions provide robustness against insecure implementations and wrong ass ..."
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Abstract. A(k; n)robust combiner for a primitive F takes as input n candidate implementations of F and constructs an implementation of F, which is secure assuming that at least k of the input candidates are secure. Such constructions provide robustness against insecure implementations and wrong assumptions underlying the candidate schemes. In a recent work Harnik et al. (Eurocrypt 2005) have proposed a (2; 3)robust combiner for oblivious transfer (OT), and have shown that (1; 2)robust OTcombiners of a certain type are impossible. In this paper we propose new, generalized notions of combiners for twoparty primitives, which capture the fact that in many twoparty protocols the security of one of the parties is unconditional, or is based on an assumption independent of the assumption underlying the security of the other party. This finegrained approach results in OTcombiners strictly stronger than the constructions known before. In particular, we propose an OTcombiner which guarantees secure OT even when only one candidate is secure for both parties, and every remaining candidate is flawed for one of the parties. Furthermore, we present an efficient uniform OTcombiner, i.e., a single combiner which is secure simultaneously for a wide range of candidates ’ failures. Finally, our definition allows for a very simple impossibility result, which shows that the proposed OTcombiners achieve optimal robustness.
Hybridsecure MPC: trading informationtheoretic robustness for computational privacy
 PODC '10 Proceeding of the 29th ACM SIGACTSIGOPS symposium on Principles of distributed computing
, 2010
"... Most protocols for distributed, faulttolerant computation, or multiparty computation (MPC), provide security guarantees in an allornothing fashion. In contrast, a hybridsecure protocol provides different security guarantees depending on the set of corrupted parties and the computational power of ..."
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Most protocols for distributed, faulttolerant computation, or multiparty computation (MPC), provide security guarantees in an allornothing fashion. In contrast, a hybridsecure protocol provides different security guarantees depending on the set of corrupted parties and the computational power of the adversary, without being aware of the actual adversarial setting. Thus, hybridsecure MPC protocols allow for graceful degradation of security. We present a hybridsecure MPC protocol that provides an optimal tradeoff between IT robustness and computational privacy: For any robustness parameter ρ < n, we 2 obtain one MPC protocol that is simultaneously IT secure with robustness for up to t ≤ ρ actively corrupted parties, IT secure with fairness (no robustness) for up to t < n, and 2 computationally secure with agreement on abort (privacy and correctness only) for up to t < n − ρ. Our construction is secure in the universal composability (UC) framework (based on a network of secure channels, a broadcast channel, and a common reference string). It achieves the bound on the tradeoff between robustness and privacy shown by Ishai et al. [CRYPTO’06] and Katz [STOC’07], the bound on fairness shown by Cleve [STOC’86], and the bound on IT security shown by Kilian [STOC’00], and is the first protocol that achieves all these bounds simultaneously.
Compression from collisions, or why CRHF combiners have a long output
 Advances in Cryptology – CRYPTO 2008. Lecture Notes in Computer Science
, 2004
"... Abstract. A blackbox combiner for collision resistant hash functions (CRHF) is a construction which given blackbox access to two hash functions is collision resistant if at least one of the components is collision resistant. In this paper we prove a lower bound on the output length of blackbox co ..."
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Abstract. A blackbox combiner for collision resistant hash functions (CRHF) is a construction which given blackbox access to two hash functions is collision resistant if at least one of the components is collision resistant. In this paper we prove a lower bound on the output length of blackbox combiners for CRHFs. The bound we prove is basically tight as it is achieved by a recent construction of Canetti et al [Crypto’07]. The best previously known lower bounds only ruled out a very restricted class of combiners having a very strong security reduction: the reduction was required to output collisions for both underlying candidate hashfunctions given a single collision for the combiner (Canetti et al [Crypto’07] building on Boneh and Boyen [Crypto’06] and Pietrzak [Eurocrypt’07]). Our proof uses a lemma similar to the elegant “reconstruction lemma ” of Gennaro and Trevisan [FOCS’00], which states that any function which is not oneway is compressible (and thus uniformly random function must be oneway). In a similar vein we show that a function which is not collision resistant is compressible. We also borrow ideas from recent work by Haitner et al. [FOCS’07], who show that one can prove the reconstruction lemma even relative to some very powerful oracles (in our case this will be an exponential time collisionfinding oracle). 1
Unconditional security from noisy quantum storage
, 2009
"... We consider the implementation of twoparty cryptographic primitives based on the sole assumption that no largescale reliable quantum storage is available to the cheating party. We construct novel protocols for oblivious transfer and bit commitment, and prove that realistic noise levels provide sec ..."
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We consider the implementation of twoparty cryptographic primitives based on the sole assumption that no largescale reliable quantum storage is available to the cheating party. We construct novel protocols for oblivious transfer and bit commitment, and prove that realistic noise levels provide security even against the most general attack. Such unconditional results were previously only known in the socalled boundedstorage model which is a special case of our setting. Our protocols can be implemented with presentday hardware used for quantum key distribution. In particular, no quantum storage is required for the honest parties.
Errortolerant combiners for oblivious primitives
"... Abstract. A robust combiner is a construction that combines several implementations of a primitive based on different assumptions, and yields an implementation guaranteed to be secure if at least some assumptions (i.e. sufficiently many but not necessarily all) are valid. In this paper we generalize ..."
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Abstract. A robust combiner is a construction that combines several implementations of a primitive based on different assumptions, and yields an implementation guaranteed to be secure if at least some assumptions (i.e. sufficiently many but not necessarily all) are valid. In this paper we generalize this concept by introducing errortolerant combiners, which in addition to protection against insecure implementations provide tolerance to functionality failures: an errortolerant combiner guarantees a secure and correct implementation of the output primitive even if some of the candidates are insecure or faulty. We present simple constructions of errortolerant robust combiners for oblivious linear function evaluation. The proposed combiners are also interesting in the regular (not errortolerant) case, as the construction is much more efficient than the combiners known for oblivious transfer. 1
Tight Bounds for Protocols with Hybrid Security
"... Abstract. We define hybrid multiparty computation (HMPC) and hybrid broadcast (HBC) in a model without broadcast channels but assuming a signature scheme and a respective publickey infrastructure (PKI) among the players. The goal is to achieve unconditional (PKI and signatureindependent) securit ..."
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Abstract. We define hybrid multiparty computation (HMPC) and hybrid broadcast (HBC) in a model without broadcast channels but assuming a signature scheme and a respective publickey infrastructure (PKI) among the players. The goal is to achieve unconditional (PKI and signatureindependent) security up to a certain threshold, and security beyond this threshold under stronger assumptions, namely, that forgery of signatures is impossible and/or that the given PKI is consistent. We give a tight characterization of when HMPC and HBC are possible. 1 1