On Multiple Deletion Codes

In 1965 Levenshtein introduced the deletion correcting codes and found an asymptotically optimal family of 1-deletion correcting codes. During the years there has been a little or no research on t-deletion correcting codes for larger values of t. In this paper, we consider the problem of finding the maximal cardinality L2(n;t) of a binary t-deletion correcting code of length n. We construct an infinite family of binary t-deletion correcting codes. By computer search, we construct t-deletion codes for t = 2;3;4;5 with lengths n ≤ 30. Some of these codes improve on earlier results by Hirschberg-Fereira and Swart-Fereira. Finally, we prove a recursive upper bound on L2(n;t) which is asymptotically worse than the best known bounds, but gives better estimates for small values of n

Signing on Elements in Bilinear Groups for Modular Protocol Design

A signature scheme is called structure-preserving if its verification keys, messages, and signatures are group elements and the verification predicate is a conjunction of pairing product equations. We answer to the open problem of constructing a constant-size structure-preserving signature scheme. The security is proven in the standard model based on a novel non-interactive assumption that can be justified and has an optimal bound in the generic bilinear group model. We also present efficient structure-preserving signature schemes with advanced properties including signing unbounded number of group elements, allowing simulation in the common reference string model, signing messages from mixed groups in the asymmetric bilinear group setting, and strong unforgeability. Among many applications, we show two examples; an adaptively secure round optimal blind signature scheme and a group signature scheme with efficient concurrent join. As a bi-product, several homomorphic trapdoor commitment schemes and one-time signature schemes are presented, too. In combination with the Groth-Sahai non-interactive proof system, these schemes contribute to give efficient instantiations to modular constructions of cryptographic protocols

HBNHB^N: An HB-like protocol secure against man-in-the-middle attacks

We construct a simple authentication protocol whose security is based solely on the problem of Learning Parity with Noise (LPN) which is secure against Man-in-the-Middle attacks. Our protocol is suitable for RFID devices, whose limited circuit size and power constraints rule out the use of more heavyweight operations such as modular exponentiation. The protocol is extremely simple: both parties compute a noisy bilinear function of their inputs. The proof, however, is quite technical, and we believe that some of our technical tools may be of independent interest

Composable & Modular Anonymous Credentials: Definitions and Practical Constructions

It takes time for theoretical advances to get used in practical schemes. Anonymous credential schemes are no exception. For instance, existing schemes suited for real-world use lack formal, composable definitions, partly because they do not support straight-line extraction and rely on random oracles for their security arguments. To address this gap, we propose unlinkable redactable signatures (URS), a new building block for privacy-enhancing protocols, which we use to construct the first efficient UC-secure anonymous credential system that supports multiple issuers, selective disclosure of attributes, and pseudonyms. Our scheme is one of the first such systems for which both the size of a credential and its presentation proof are independent of the number of attributes issued in a credential. Moreover, our new credential scheme does not rely on random oracles. As an important intermediary step, we address the problem of building a functionality for a complex credential system that can cover many different features. Namely, we design a core building block for a single issuer that supports credential issuance and presentation with respect to pseudonyms and then show how to construct a full-fledged credential system with multiple issuers in a modular way. We expect this flexible definitional approach to be of independent interest

Structure Preserving CCA Secure Encryption and Its Application to Oblivious Third Parties

In this paper we present the first public key encryption scheme that is structure preserving, i.e., our encryption scheme uses only algebraic operations. In particular it does not use hash-functions or interpret group elements as bit-strings. This makes our scheme a perfect building block for cryptographic protocols where parties for instance want to prove, to each other, properties about ciphertexts or jointly compute ciphertexts. Our scheme is also very efficient and is secure against \dkg adaptive\blk{} chosen ciphertext attacks. We also provide a few example protocols for our scheme. For instance, a joint computation of a ciphertext\dkg, generated from two secret plaintexts from each party respectively\blk, where in the end, only one of the parties learns the ciphertext. This latter protocol serves as a building block for our second contribution which is a set of protocols that implement the concept of oblivious trusted third parties. This concept has been proposed before, but no concrete realization was known

Efficient Cryptographic Primitives for Non-Interactive Zero-Knowledge Proofs and Applications

Non-interactive zero-knowledge (NIZK) proofs have enjoyed much interest in cryptography since they were introduced more than twenty years ago by Blum et al. [BFM88]. While quite useful when designing modular cryptographic schemes, until recently NIZK could be realized efficiently only using certain heuristics. However, such heuristic schemes have been widely criticized. In this work we focus on designing schemes which avoid them. In [GS08], Groth and Sahai presented the first efficient (and currently the only) NIZK proof system in the standard model. The construction is based on bilinear maps and is limited to languages of certain satisfiable system of equations. Given this expressibility limitation of the system of equations, we are interested incryptographic primitives that are “compatible” with it. Equipped with such primitives and the Groth-Sahai proof system, we show how to construct cryptographic schemes efficiently in a modular fashion. In this work, we describe properties required by any cryptographic scheme to mesh well with Groth-Sahai proofs. Towards this, we introduce the notion of “structure-preserving” cryptographic schemes. We present the first constant-size structure-preservin

Optimal Structure-Preserving Signatures in Asymmetric Bilinear Groups

Abstract. Structure-preserving signatures are signatures defined over bilinear groups that rely on generic group operations. In particular, the messages and signatures consist of group elements and the verification of signatures consists of evaluating pairing product equations. Due to their purist nature structure-preserving signatures blend well with other pairingbased protocols. We show that structure-preserving signatures must consist of at least 3 group elements when the signer uses generic group operations. Usually, the generic group model is used to rule out classes of attacks by an adversary trying to break a cryptographic assumption. In contrast, here we use the generic group model to prove a lower bound on the complexity of digital signature schemes. We also give constructions of structure-preserving signatures that consist of 3 group elements only. This improves significantly on previous structure-preserving signatures that used 7 group elements and matches our lower bound. Our structure-preserving signatures have additional nice properties such as strong existential unforgeability and can sign multiple group elements at once. Keywords: Structure-Preservation, Digital Signatures, Generic Group Model.