## CryptoDB

### Papers from Journal of Cryptology 2012

**Year**

**Venue**

**Title**

2012

JOFC

Efficient Set Operations in the Presence of Malicious Adversaries
Abstract

We revisit the problem of constructing efficient secure two-party protocols for the problems of set intersection and set union, focusing on the model of malicious parties. Our main results are constant-round protocols that exhibit linear communication and a (practically) linear number of exponentiations with simulation-based security. At the heart of these constructions is a technique based on a combination of a perfectly hiding commitment and an oblivious pseudorandom function evaluation protocol. Our protocols readily transform into protocols that are UC secure, and we discuss how to perform these transformations.

2012

JOFC

Ideal Multipartite Secret Sharing Schemes
Abstract

Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. In this work, the characterization of ideal multipartite access structures is studied with all generality. Our results are based on the well-known connections between ideal secret sharing schemes and matroids and on the introduction of a new combinatorial tool in secret sharing, integer polymatroids .Our results can be summarized as follows. First, we present a characterization of multipartite matroid ports in terms of integer polymatroids. As a consequence of this characterization, a necessary condition for a multipartite access structure to be ideal is obtained. Second, we use representations of integer polymatroids by collections of vector subspaces to characterize the representable multipartite matroids. In this way we obtain a sufficient condition for a multipartite access structure to be ideal, and also a unified framework to study the open problems about the efficiency of the constructions of ideal multipartite secret sharing schemes. Finally, we apply our general results to obtain a complete characterization of ideal tripartite access structures, which was until now an open problem.

2012

JOFC

Perfectly Balanced Boolean Functions and Golić Conjecture
Abstract

In the current paper we consider the following properties of filters: perfect balancedness of a filter function (i.e. preserving pure randomness of the input sequence) and linearity of a filter function in the first or the last essential variable. Previous results on this subject are discussed, including misleading statements in Gouget and Sibert (LNCS, vol. 4876, 2007) about the connection between perfect balancedness and resistance to Anderson conditional correlation attack; the incorrectness of two known results, the sufficient condition of perfect balancedness in Golić (LNCS, vol. 1039, 1996) and the necessary condition of perfect balancedness in Dichtl (LNCS, vol. 1267, 1997), is demonstrated by providing counterexamples.We present a novel method of constructing large classes of perfectly balanced functions that are nonlinear in the first and the last essential variable and obtain a new lower bound of the number of such functions.Golić conjecture (LNCS, vol. 1039, 1996) states that the necessary and sufficient condition for a function to be perfectly balanced for any choice of a tapping sequence is linearity of a function in the first or the last essential variable. In the second part of the current paper we prove the Golić conjecture.

2012

JOFC

Programmable Hash Functions and Their Applications
Abstract

We introduce a new combinatorial primitive called programmable hash functions (PHFs). PHFs can be used to program the output of a hash function such that it contains solved or unsolved discrete logarithm instances with a certain probability. This is a technique originally used for security proofs in the random oracle model. We give a variety of standard model realizations of PHFs (with different parameters).The programmability makes PHFs a suitable tool to obtain black-box proofs of cryptographic protocols when considering adaptive attacks. We propose generic digital signature schemes from the strong RSA problem and from some hardness assumption on bilinear maps that can be instantiated with any PHF. Our schemes offer various improvements over known constructions. In particular, for a reasonable choice of parameters, we obtain short standard model digital signatures over bilinear maps.

2012

JOFC

Graph Coloring Applied to Secure Computation in Non-Abelian Groups
Abstract

We study the natural problem of secure n-party computation (in the computationally unbounded attack model) of circuits over an arbitrary finite non-Abelian group (G,⋅), which we call G-circuits. Besides its intrinsic interest, this problem is also motivating by a completeness result of Barrington, stating that such protocols can be applied for general secure computation of arbitrary functions. For flexibility, we are interested in protocols which only require black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our investigations focus on the passive adversarial model, where up to t of the n participating parties are corrupted.Our results are as follows. We initiate a novel approach for the construction of black-box protocols for G-circuits based on k-of-k threshold secret-sharing schemes, which are efficiently implementable over any black-box (non-Abelian) group G. We reduce the problem of constructing such protocols to a combinatorial coloring problem in planar graphs. We then give three constructions for such colorings. Our first approach leads to a protocol with optimal resilience t<n/2, but it requires exponential communication complexity $O({\binom{2 t+1}{t}}^{2} \cdot N_{g})$ group elements and round complexity $O(\binom{2 t + 1}{t} \cdot N_{g})$, for a G-circuit of size Ng. Nonetheless, using this coloring recursively, we obtain another protocol to t-privately compute G-circuits with communication complexity $\mathcal{P}\mathit{oly}(n)\cdot N_{g}$ for any t∈O(n1−ϵ) where ϵ is any positive constant. For our third protocol, there is a probability δ (which can be made arbitrarily small) for the coloring to be flawed in term of security, in contrast to the first two techniques, where the colorings are always secure (we call this protocol probabilistic, and those earlier protocols deterministic). This third protocol achieves optimal resilience t<n/2. It has communication complexity O(n5.056(n+log δ−1)2⋅Ng) and the number of rounds is O(n2.528⋅(n+log δ−1)⋅Ng).

2012

JOFC

Bonsai Trees, or How to Delegate a Lattice Basis
Abstract

We introduce a new lattice-based cryptographic structure called a bonsai tree, and use it to resolve some important open problems in the area. Applications of bonsai trees include an efficient, stateless ‘hash-and-sign’ signature scheme in the standard model (i.e., no random oracles), and the first hierarchical identity-based encryption (HIBE) scheme (also in the standard model) that does not rely on bilinear pairings. Interestingly, the abstract properties of bonsai trees seem to have no known realization in conventional number-theoretic cryptography.

2012

JOFC

On-line Ciphers and the Hash-CBC Constructions
Abstract

We initiate a study of on-line ciphers. These are ciphers that can take input plaintexts of large and varying lengths and will output the i th block of the ciphertext after having processed only the first i blocks of the plaintext. Such ciphers permit length-preserving encryption of a data stream with only a single pass through the data. We provide security definitions for this primitive and study its basic properties. We then provide attacks on some possible candidates, including CBC with fixed IV. We then provide two constructions, HCBC1 and HCBC2, based on a given block cipher E and a family of computationally AXU functions. HCBC1 is proven secure against chosen-plaintext attacks assuming that E is a PRP secure against chosen-plaintext attacks, while HCBC2 is proven secure against chosen-ciphertext attacks assuming that E is a PRP secure against chosen-ciphertext attacks.

2012

JOFC

Secure Two-Party Computation via Cut-and-Choose Oblivious Transfer
Abstract

Protocols for secure two-party computation enable a pair of parties to compute a function of their inputs while preserving security properties such as privacy, correctness and independence of inputs. Recently, a number of protocols have been proposed for the efficient construction of two-party computation secure in the presence of malicious adversaries (where security is proven under the standard simulation-based ideal/real model paradigm for defining security). In this paper, we present a protocol for this task that follows the methodology of using cut-and-choose to boost Yao’s protocol to be secure in the presence of malicious adversaries. Relying on specific assumptions (DDH), we construct a protocol that is significantly more efficient and far simpler than the protocol of Lindell and Pinkas (Eurocrypt 2007) that follows the same methodology. We provide an exact, concrete analysis of the efficiency of our scheme and demonstrate that (at least for not very small circuits) our protocol is more efficient than any other known today.

2012

JOFC

Batch Verification of Short Signatures
Abstract

With computer networks spreading into a variety of new environments, the need to authenticate and secure communication grows. Many of these new environments have particular requirements on the applicable cryptographic primitives. For instance, a frequent requirement is that the communication overhead inflicted be small and that many messages be processable at the same time. In this paper, we consider the suitability of public key signatures in the latter scenario. That is, we consider (1) signatures that are short and (2) cases where many signatures from (possibly) different signers on (possibly) different messages can be verified quickly. Prior work focused almost exclusively on batching signatures from the same signer.We propose the first batch verifier for messages from many (certified) signers without random oracles and with a verification time where the dominant operation is independent of the number of signatures to verify. We further propose a new signature scheme with very short signatures, for which batch verification for many signers is also highly efficient. Combining our new signatures with the best known techniques for batching certificates from the same authority, we get a fast batch verifier for certificates and messages combined. Although our new signature scheme has some restrictions, it is very efficient and still practical for some communication applications.

2012

JOFC

Security Analysis of Randomize-Hash-then-Sign Digital Signatures
Abstract

At CRYPTO 2006, Halevi and Krawczyk proposed two randomized hash function modes and analyzed the security of digital signature algorithms based on these constructions. They showed that the security of signature schemes based on the two randomized hash function modes relies on properties similar to the second preimage resistance rather than on the collision resistance property of the hash functions. One of the randomized hash function modes was named the RMX hash function mode and was recommended for practical purposes. The National Institute of Standards and Technology (NIST), USA standardized a variant of the RMX hash function mode and published this standard in the Special Publication (SP) 800-106.In this article, we first discuss a generic online birthday existential forgery attack of Dang and Perlner on the RMX-hash-then-sign schemes. We show that a variant of this attack can be applied to forge the other randomize-hash-then-sign schemes. We point out practical limitations of the generic forgery attack on the RMX-hash-then-sign schemes. We then show that these limitations can be overcome for the RMX-hash-then-sign schemes if it is easy to find fixed points for the underlying compression functions, such as for the Davies-Meyer construction used in the popular hash functions such as MD5 designed by Rivest and the SHA family of hash functions designed by the National Security Agency (NSA), USA and published by NIST in the Federal Information Processing Standards (FIPS). We show an online birthday forgery attack on this class of signatures by using a variant of Dean’s method of finding fixed point expandable messages for hash functions based on the Davies-Meyer construction. This forgery attack is also applicable to signature schemes based on the variant of RMX standardized by NIST in SP 800-106. We discuss some important applications of our attacks and discuss their applicability on signature schemes based on hash functions with ‘built-in’ randomization. Finally, we compare our attacks on randomize-hash-then-sign schemes with the generic forgery attacks on the standard hash-based message authentication code (HMAC).