Abstract. We present a new constant round additively homomorphic commitment scheme with (amortized) computational and communication complexity linear in the size of the string committed to. Our scheme is based on the non-homomorphic commitment scheme of Cascudo et al. presented at PKC 2015. However, we manage to add the additive homomorphic property, while at the same time reducing the constants. In fact, when opening a large enough batch of commitments we achieve an amortized communication complexity converging to the length of the message committed to, i.e., we achieve close to rate 1 as the commitment protocol by Garay et al. from Eurocrypt 2014. A main technical improvement over the scheme mentioned above, and other schemes based on using error correcting codes for UC commitment, we develop a new technique which allows to based the extraction property on erasure decoding as opposed to error correction. This allows to use a code with significantly smaller minimal distance and allows to use codes without efficient decoding. Our scheme only relies on standard assumptions. Specifically we require a pseudorandom number generator, a linear error correcting code and an ideal oblivious transfer functionality. Based on this we prove our scheme secure in the Universal Composability (UC) framework against a static and malicious adversary corrupting any number of parties. On a practical note, our scheme improves significantly on the non-homomorphic scheme of Cascudo et al. Based on their observations in regards to efficiency of using linear error correcting codes for commitments we conjecture that our commitment scheme might in practice be more efficient than all existing constructions of UC commitment, even non-homomorphic constructions and even constructions in the random oracle model. In particular, the amortized price of computing one of our commitments is less than that of evaluating a hash function once.
Abstract. We present a new constant round additively homomorphic commitment scheme with (amortized) computational and communication complexity linear in the size of the string committed to. Our scheme is based on the non-homomorphic commitment scheme of Cascudo et al. presented at PKC 2015. However, we manage to add the additive homomorphic property, while at the same time reducing the constants. In fact, when opening a large enough batch of commitments we achieve an amortized communication complexity converging to the length of the message committed to, i.e., we achieve close to rate 1 as the commitment protocol by Garay et al. from Eurocrypt 2014. A main technical improvement over the scheme mentioned above, and other schemes based on using error correcting codes for UC commitment, we develop a new technique which allows to based the extraction property on erasure decoding as opposed to error correction. This allows to use a code with significantly smaller minimal distance and allows to use codes without efficient decoding. Our scheme only relies on standard assumptions. Specifically we require a pseudorandom number generator, a linear error correcting code and an ideal oblivious transfer functionality. Based on this we prove our scheme secure in the Universal Composability (UC) framework against a static and malicious adversary corrupting any number of parties. On a practical note, our scheme improves significantly on the non-homomorphic scheme of Cascudo et al. Based on their observations in regards to efficiency of using linear error correcting codes for commitments we conjecture that our commitment scheme might in practice be more efficient than all existing constructions of UC commitment, even non-homomorphic constructions and even constructions in the random oracle model. In particular, the amortized price of computing one of our commitments is less than that of evaluating a hash function once.
We present a new compact verifiable secret sharing scheme, based on this we present the first construction of a homomorphic UC commitment scheme that requires only cheap symmetric cryptography, except for a small number of seed OTs. To commit to a k -bit string, the amortized communication cost is O ( k ) bits. Assuming a sufficiently efficient pseudorandom generator, the computational complexity is O ( k ) for the verifier and O ( k 1 + ε ) for the committer (where ε < 1 is a constant). In an alternative variant of the construction, all complexities are O ( k · polylog ( k )). Our commitment scheme extends to vectors over any finite field and is additively homomorphic. By sending one extra message, the prover can allow the verifier to also check multiplicative relations on committed strings, as well as verifying that committed vectors a , b satisfy a = φ ( b ) for a linear function φ . These properties allow us to non-interactively implement any one-sided functionality where only one party has input (this includes UC secure zero-knowledge proofs of knowledge). We also present a perfectly secure implementation of any multiparty functionality, based directly on our VSS. The communication required is proportional to a circuit implementing the functionality, up to a logarithmic factor. For a large natural class of circuits the overhead is even constant. We also improve earlier results by Ranellucci et al. on the amount of correlated randomness required for string commitments with individual opening of bits. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We present a general framework for constructing non-interactive universally composable (UC) commitment schemes that are secure against adaptive adversaries in the non-erasure setting under a single re-usable common reference string. Previously, such “fully-equipped ” UC commitment schemes are only known in [8, 9], with an unavoidable overhead of O(κ) in the sense of communication and computational complexities; meaning that to commit λ bits, the communication and computational costs require O(λκ), where κ denotes the security parameter. Efficient construction of a fully-equipped UC commitment scheme was a long-standing open problem. We introduce a cryptographic primitive, called all-but-many encryptions (ABMEs), and prove that it is a translation of fully-equipped UC commitment in the primitive level. We then construct ABMEs from cryptographic primitives that we call a probabilistic pseudo random function family and extractable sigma protocols – the former is a probabilistic version of a pseudo random function family and the latter is a special kind of sigma (i.e., canonical 3-round public-coin HVSZK) protocols with some extractability. We provide fully-equipped UC commitment schemes from ABMEs under DDH and DCR-based assumptions, respectively. In particular, the DCR-based scheme is the first fully-equipped UC commitment scheme with optimal expansion factor Ω(1); to commit κ bits, the communication and computational costs are Ω(κ). We further construct a fully-equipped UC commitment scheme from a general assumption (in which trap-door permutations exist), which is far more efficient than the previous construction [9], because, unlike [9], our construction does not require non-interactive zero-knowledge proof systems. 1
This paper presents a new non-interactive string-commitment scheme that achieves universally composable security. Security is proven under the decisional composite residuosity (DCR) assumption (or the decisional Diffie-Hellman (DDH) assumption) in the common reference string (CRS) model. The universal composability (UC) is a very strong security notion. If cryptographic protocols are proven secure in the UC framework, then they remain secure even if they are composed with arbitrary protocols and polynomially many copies of the protocols are run concurrently. Many UC commitment schemes in the CRS model have been proposed, but they are either interactive commitment or bit-commitment (not string-commitment) schemes. We note, however, that although our scheme is the first non-interactive UC string-commitment scheme, a CRS is not reusable. We use an extension of all-but-one trapdoor functions (ABO-TDFs) proposed by Peikert and Waters at STOC 2008 as an essential building block. Our main idea is to extend (original deterministic) ABO-TDFs to probabilistic ones by using the homomorphic properties of their function indices. The function indices of ABO-TDFs consist of ciphertexts of homomorphic encryption schemes (such as ElGamal, and Damgård-Jurik encryption). Therefore we can re-randomize the output of ABO-TDFs by re-randomization of ciphertexts. This is a new application of ABO-TDFs.
Non-committing encryption achieved only semantic security,in contrast,applications often require security against chosen ciphertext attacks.A main ingredient in the previous adaptive universally composable(UC)oblivious transfer protocols are non-committing encryptions.the previous proposals are not UC secure against adaptive adversaries in the so-called non-erase model.A new UC secure oblivious transfer protocols were proposed and schemes utilize two primitives of the verifiably smooth projective hashing and deniable encryption as constructed by.the double trapdoor decryption mechanism based on trapdoor commitment.Our construction is based on the decisional composite residuosity in common reference string (CRS) model.We constructed a two-message(1-round) string oblivious transfer protocol,which improves computational efficient that supports message spaces of size exponential and save O(n)-1 rounds communications efficient than bit-OT protocols.
Abstract. In 2011, Lindell proposed an efficient commitment scheme, with a non-interactive opening algorithm, in the Universal Composability (UC) framework. He recently acknowledged a bug in its security analysis for the adaptive case. We analyze the proof of the original paper and propose a simple patch of the scheme. More interestingly, we then modify it and present a more efficient commitment scheme secure in the UC framework, with the same level of security as Lindell’s protocol: adaptive corruptions, with erasures. The security is proven in the standard model (with a Common Reference String) under the classical Decisional Diffie-Hellman assumption. Our proposal is the most efficient UC-secure commitment proposed to date (in terms of computational workload and communication complexity).
Cryptography grew to be much more than "the study of secret writing". Modern cryptography is concerned with establishing properties such as privacy, integrity and authenticity in protocols for secure communication and computation. This comes at a price: Cryptographic tools usually introduce an overhead, both in terms of communication complexity (that is, number and size of messages transmitted) and computational efficiency (that is, time and memory required). As in many settings communication between the parties involved is the bottleneck, this thesis is concerned with improving communication complexity in cryptographic protocols. One direction towards this goal is scalable cryptography: In many cryptographic schemes currently deployed, the security degrades linearly with the number of instances (e.g. encrypted messages) in the system. As this number can be huge in contexts like cloud computing, the parameters of the scheme have to be chosen considerably larger - and in particular depending on the expected number of instances in the system - to maintain security guarantees. We advance the state-of-the-art regarding scalable cryptography by constructing schemes where the security guarantees are independent of the number of instances. This allows to choose smaller parameters, even when the expected number of instances is immense. - We construct the first scalable encryption scheme with security against active adversaries which has both compact public keys and ciphertexts. In particular, we significantly reduce the size of the public key to only about 3% of the key-size of the previously most efficient scalable encryption scheme. (Gay,Hofheinz, and Kohl, CRYPTO, 2017) - We present a scalable structure-preserving signature scheme which improves both in terms of public-key and signature size compared to the previously best construction to about 40% and 56% of the sizes, respectively. (Gay, Hofheinz, Kohl, and Pan, EUROCRYPT, 2018) Another important area of cryptography is secure multi-party computation, where the goal is to jointly evaluate some function while keeping each party’s input private. In traditional approaches towards secure multi-party computation either the communication complexity scales linearly in the size of the function, or the computational efficiency is poor. To overcome this issue, Boyle, Gilboa, and Ishai (CRYPTO, 2016) introduced the notion of homomorphic secret sharing. Here, inputs are shared between parties such that each party does not learn anything about the input, and such that the parties can locally evaluate functions on the shares. Homomorphic secret sharing implies secure computation where the communication complexity only depends on the size of the inputs, which is typically much smaller than the size of the function. A different approach towards efficient secure computation is to split the protocol into an input-independent preprocessing phase, where long correlated strings are generated, and a very efficient online phase. One example for a useful correlation are authenticated Beaver triples, which allow to perform efficient multiplications in the online phase such that privacy of the inputs is preserved and parties deviating the protocol can be detected. The currently most efficient protocols implementing the preprocessing phase require communication linear in the number of triples to be generated. This results typically in high communication costs, as the online phase requires at least one authenticated Beaver triple per multiplication. We advance the state-of-the art regarding efficient protocols for secure computation with low communication complexity as follows. - We construct the first homomorphic secret sharing scheme for computing arbitrary functions in NC 1 (that is, functions that are computably by circuits with logarithmic depth) which supports message spaces of arbitrary size, has only negligible correctness error, and does not require expensive multiplication on ciphertexts. (Boyle, Kohl, and Scholl, EUROCRYPT, 2019) - We introduce the notion of a pseudorandom correlation generator for general correlations. Pseudorandom correlation generators allow to locally extend short correlated seeds into long pseudorandom correlated strings. We show that pseudorandom correlation generators can replace the preprocessing phase in many protocols, leading to a preprocessing phase with sublinear communication complexity. We show connections to homomorphic secret sharing schemes and give the first instantiation of pseudorandom correlation generators for authenticated Beaver triples at reasonable computational efficiency. (Boyle, Couteau, Gilboa, Ishai, Kohl, and Scholl, CRYPTO, 2019)