Multi-party computation with omnipresent adversary

Secure multi-party computation (MPC) protocols enable a set of n mutually distrusting participants P 1, ..., P n , each with their own private input x i , to compute a function Y = F(x 1, ..., x n ), such that at the end of the protocol, all participants learn the correct value of Y, while secrecy of the private inputs is maintained. Classical results in the unconditionally secure MPC indicate that in the presence of an active adversary, every function can be computed if and only if the number of corrupted participants, t a , is smaller than n/3. Relaxing the requirement of perfect secrecy and utilizing broadcast channels, one can improve this bound to t a  < n/2. All existing MPC protocols assume that uncorrupted participants are truly honest, i.e., they are not even curious in learning other participant secret inputs. Based on this assumption, some MPC protocols are designed in such a way that after elimination of all misbehaving participants, the remaining ones learn all information in the system. This is not consistent with maintaining privacy of the participant inputs. Furthermore, an improvement of the classical results given by Fitzi, Hirt, and Maurer indicates that in addition to t a actively corrupted participants, the adversary may simultaneously corrupt some participants passively. This is in contrast to the assumption that participants who are not corrupted by an active adversary are truly honest. This paper examines the privacy of MPC protocols, and introduces the notion of an omnipresent adversary, which cannot be eliminated from the protocol. The omnipresent adversary can be either a passive, an active or a mixed one. We assume that up to a minority of participants who are not corrupted by an active adversary can be corrupted passively, with the restriction that at any time, the number of corrupted participants does not exceed a predetermined threshold. We will also show that the existence of a t-resilient protocol for a group of n participants, implies the existence of a t’-private protocol for a group of n′ participants. That is, the elimination of misbehaving participants from a t-resilient protocol leads to the decomposition of the protocol. Our adversary model stipulates that a MPC protocol never operates with a set of truly honest participants (which is a more realistic scenario). Therefore, privacy of all participants who properly follow the protocol will be maintained. We present a novel disqualification protocol to avoid a loss of privacy of participants who properly follow the protocol.

An efficient scheme of common secure indices for conjunctive keyword-based retrieval on encrypted data

We consider the following problem: members in a dynamic group retrieve their encrypted data from an untrusted server based on keywords and without any loss of data confidentiality and member’s privacy. In this paper, we investigate common secure indices for conjunctive keyword-based retrieval over encrypted data, and construct an efficient scheme from Wang et al. dynamic accumulator, Nyberg combinatorial accumulator and Kiayias et al. public-key encryption system. The proposed scheme is trapdoorless and keyword-field free. The security is proved under the random oracle, decisional composite residuosity and extended strong RSA assumptions.

Double-authentication-preventing signatures

Digital signatures are often used by trusted authorities to make unique bindings between a subject and a digital object; for example, certificate authorities certify a public key belongs to a domain name, and time-stamping authorities certify that a certain piece of information existed at a certain time. Traditional digital signature schemes however impose no uniqueness conditions, so a trusted authority could make multiple certifications for the same subject but different objects, be it intentionally, by accident, or following a (legal or illegal) coercion. We propose the notion of a double-authentication-preventing signature, in which a value to be signed is split into two parts: a subject and a message. If a signer ever signs two different messages for the same subject, enough information is revealed to allow anyone to compute valid signatures on behalf of the signer. This double-signature forgeability property discourages signers from misbehaving---a form of self-enforcement---and would give binding authorities like CAs some cryptographic arguments to resist legal coercion. We give a generic construction using a new type of trapdoor functions with extractability properties, which we show can be instantiated using the group of sign-agnostic quadratic residues modulo a Blum integer.

Spreadsheet Conditional Formatting Illuminates Investigations into Modular Arithmetic

Modular arithmetic has often been regarded as something of a mathematical curiosity, at least by those unfamiliar with its importance to both abstract algebra and number theory, and with its numerous applications. However, with the ubiquity of fast digital computers, and the need for reliable digital security systems such as RSA, this important branch of mathematics is now considered essential knowledge for many professionals. Indeed, computer arithmetic itself is, ipso facto, modular. This chapter describes how the modern graphical spreadsheet may be used to clearly illustrate the basics of modular arithmetic, and to solve certain classes of problems. Students may then gain structural insight and the foundations laid for applications to such areas as hashing, random number generation, and public-key cryptography.

Converse results to the Wiener attack on RSA

A well-known attack on RSA with low secret-exponent d was given by Wiener about 15 years ago. Wiener showed that using continued fractions, one can efficiently recover the secret-exponent d from the public key (N,e) as long as d < N 1/4. Interestingly, Wiener stated that his attack may sometimes also work when d is slightly larger than N 1/4. This raises the question of how much larger d can be: could the attack work with non-negligible probability for d=N 1/4 + ρ for some constant ρ > 0? We answer this question in the negative by proving a converse to Wiener’s result. Our result shows that, for any fixed ε > 0 and all sufficiently large modulus lengths, Wiener’s attack succeeds with negligible probability over a random choice of d < N δ (in an interval of size Ω(N δ )) as soon as δ > 1/4 + ε. Thus Wiener’s success bound d 1/4. The known attacks in this class (by Verheul and Van Tilborg and Dujella) run in exponential time, so it is natural to ask whether there exists an attack in this class with subexponential run-time. Our second converse result answers this question also in the negative.

An efficient eAuction potocol

A secure protocol for electronic, sealed-bid, single item auctions is presented. The protocol caters to both first and second price (Vickrey) auctions and provides full price flexibility. Both computational and communication cost are linear with the number of bidders and utilize only standard cryptographic primitives. The protocol strictly divides knowledge of the bidder's identity and their actual bids between, respectively, a registration authority and an auctioneer, who are assumed not to collude but may be separately corrupt. This assures strong bidder-anonymity, though only weak bid privacy. The protocol is structured in two phases, each involving only off-line communication. Registration, requiring the use of the public key infrastructure, is simultaneous with hash-sealed bid-commitment and generates a receipt to the bidder containing a pseudonym. This phase is followed by encrypted bid-submission. Both phases involve the registration authority acting as a communication conduit but the actual message size is quite small. It is argued that this structure guarantees non-repudiation by both the winner and the auctioneer. Second price correctness is enforced either by observing the absence of registration of the claimed second-price bid or, where registered but lower than the actual second price, is subject to cooperation by the second price bidder - presumably motivated through self-interest. The use of the registration authority in other contexts is also considered with a view to developing an architecture for efficient secure multiparty transactions

Higher order universal one-way hash functions from the subset sum assumption

Universal One-Way Hash Functions (UOWHFs) may be used in place of collision-resistant functions in many public-key cryptographic applications. At Asiacrypt 2004, Hong, Preneel and Lee introduced the stronger security notion of higher order UOWHFs to allow construction of long-input UOWHFs using the Merkle-Damgård domain extender. However, they did not provide any provably secure constructions for higher order UOWHFs. We show that the subset sum hash function is a kth order Universal One-Way Hash Function (hashing n bits to m < n bits) under the Subset Sum assumption for k = O(log m). Therefore we strengthen a previous result of Impagliazzo and Naor, who showed that the subset sum hash function is a UOWHF under the Subset Sum assumption. We believe our result is of theoretical interest; as far as we are aware, it is the first example of a natural and computationally efficient UOWHF which is also a provably secure higher order UOWHF under the same well-known cryptographic assumption, whereas this assumption does not seem sufficient to prove its collision-resistance. A consequence of our result is that one can apply the Merkle-Damgård extender to the subset sum compression function with ‘extension factor’ k+1, while losing (at most) about k bits of UOWHF security relative to the UOWHF security of the compression function. The method also leads to a saving of up to m log(k+1) bits in key length relative to the Shoup XOR-Mask domain extender applied to the subset sum compression function.

Efficient one-time proxy signatures

One-time proxy signatures are one-time signatures for which a primary signer can delegate his or her signing capability to a proxy signer. In this work we propose two one-time proxy signature schemes with different security properties. Unlike other existing one-time proxy signatures that are constructed from public key cryptography, our proposed schemes are based one-way functions without trapdoors and so they inherit the communication and computation efficiency from the traditional one-time signatures. Although from a verifier point of view, signatures generated by the proxy are indistinguishable from those created by the primary signer, a trusted authority can be equipped with an algorithm that allows the authority to settle disputes between the signers. In our constructions, we use a combination of one-time signatures, oblivious transfer protocols and certain combinatorial objects. We characterise these new combinatorial objects and present constructions for them.

Efficient extension of standard Schnorr/RSA signatures into Universal Designated-Verifier Signatures

Universal Designated-Verifier Signature (UDVS) schemes are digital signature schemes with additional functionality which allows any holder of a signature to designate the signature to any desired designated-verifier such that the designated-verifier can verify that the message was signed by the signer, but is unable to convince anyone else of this fact. Since UDVS schemes reduce to standard signatures when no verifier designation is performed, it is natural to ask how to extend the classical Schnorr or RSA signature schemes into UDVS schemes, so that the existing key generation and signing implementation infrastructure for these schemes can be used without modification. We show how this can be efficiently achieved, and provide proofs of security for our schemes in the random oracle model.

Threshold MACs

The power of sharing computation in a cryptosystem is crucial in several real-life applications of cryptography. Cryptographic primitives and tasks to which threshold cryptosystems have been applied include variants of digital signature, identification, public-key encryption and block ciphers etc. It is desirable to extend the domain of cryptographic primitives which threshold cryptography can be applied to. This paper studies threshold message authentication codes (threshold MACs). Threshold cryptosystems usually use algebraically homomorphic properties of the underlying cryptographic primitives. A typical approach to construct a threshold cryptographic scheme is to combine a (linear) secret sharing scheme with an algebraically homomorphic cryptographic primitive. The lack of algebraic properties of MACs rules out such an approach to share MACs. In this paper, we propose a method of obtaining a threshold MAC using a combinatorial approach. Our method is generic in the sense that it is applicable to any secure conventional MAC by making use of certain combinatorial objects, such as cover-free families and their variants. We discuss the issues of anonymity in threshold cryptography, a subject that has not been addressed previously in the literature in the field, and we show that there are trade-offis between the anonymity and efficiency of threshold MACs.

Universal designated-verifier signatures

Motivated by privacy issues associated with dissemination of signed digital certificates, we define a new type of signature scheme called a ‘Universal Designated-Verifier Signature’ (UDVS). A UDVS scheme can function as a standard publicly-verifiable digital signature but has additional functionality which allows any holder of a signature (not necessarily the signer) to designate the signature to any desired designated-verifier (using the verifier’s public key). Given the designated-signature, the designated-verifier can verify that the message was signed by the signer, but is unable to convince anyone else of this fact. We propose an efficient deterministic UDVS scheme constructed using any bilinear group-pair. Our UDVS scheme functions as a standard Boneh-Lynn-Shacham (BLS) signature when no verifier-designation is performed, and is therefore compatible with the key-generation, signing and verifying algorithms of the BLS scheme. We prove that our UDVS scheme is secure in the sense of our unforgeability and privacy notions for UDVS schemes, under the Bilinear Diffie-Hellman (BDH) assumption for the underlying group-pair, in the random-oracle model. We also demonstrate a general constructive equivalence between a class of unforgeable and unconditionally-private UDVS schemes having unique signatures (which includes the deterministic UDVS schemes) and a class of ID-Based Encryption (IBE) schemes which contains the Boneh-Franklin IBE scheme but not the Cocks IBE scheme.

Analytical study of implementation issues of NTRU

Nth-Dimensional Truncated Polynomial Ring (NTRU) is a lattice-based public-key cryptosystem that offers encryption and digital signature solutions. It was designed by Silverman, Hoffstein and Pipher. The NTRU cryptosystem was patented by NTRU Cryptosystems Inc. (which was later acquired by Security Innovations) and available as IEEE 1363.1 and X9.98 standards. NTRU is resistant to attacks based on Quantum computing, to which the standard RSA and ECC public-key cryptosystems are vulnerable to. In addition, NTRU has higher performance advantages over these cryptosystems. Considering this importance of NTRU, it is highly recommended to adopt NTRU as part of a cipher suite along with widely used cryptosystems for internet security protocols and applications. In this paper, we present our analytical study on the implementation of NTRU encryption scheme which serves as a guideline for security practitioners who are novice to lattice-based cryptography or even cryptography. In particular, we show some non-trivial issues that should be considered towards a secure and efficient NTRU implementation.

Security issues for future intelligent transport systems

Cooperative Intelligent Transportation Systems (C-ITS) allow in-vehicle systems, and ultimately the driver, to enhance their awareness of their surroundings by enabling communication between vehicles and road infrastructure. C-ITS are widely considered as the next major step in driving assistance systems, aiming at increasing safety, comfort and mobility for drivers. However, any communicating systems are subjected to security threats. A key component for providing secure communications at a large scale is a Public Key Infrastructure (PKI). Due to the safety-critical nature of Vehicle-to-Vehicle (V2V) communications, a C-ITS PKI has functional, performance and scalability requirements that differ from traditional non-automotive environments. This paper identifies and defines the key functional and security requirements for C-ITS PKI systems and analyses proposed C-ITS PKI standards against these requirements. In particular, the proposed US and European C-ITS PKI systems are identified as being too complex and not scalable. The paper also highlights various privacy, security and scalability concerns that should be considered for a secure C-ITS PKI solution in the Australian transport landscape.

On the leakage resilience of secure channel establishment

Secure communication channels are typically constructed from an authenticated key exchange (AKE) protocol, which authenticates the communicating parties and establishes shared secret keys, and a secure data transmission layer, which uses the secret keys to encrypt data. We address the partial leakage of communicating parties' long-term secret keys due to various side-channel attacks, and the partial leakage of plaintext due to data compression. Both issues can negatively affect the security of channel establishment and data transmission. In this work, we advance the modelling of security for AKE protocols by considering more granular partial leakage of parties' long-term secrets. We present generic and concrete constructions of two-pass leakage-resilient key exchange protocols that are secure in the proposed security models. We also examine two techniques--heuristic separation of secrets and fixed-dictionary compression--for enabling compression while protecting high-value secrets.

Double-authentication-preventing signatures

Digital signatures are often used by trusted authorities to make unique bindings between a subject and a digital object; for example, certificate authorities certify a public key belongs to a domain name, and time-stamping authorities certify that a certain piece of information existed at a certain time. Traditional digital signature schemes however impose no uniqueness conditions, so a trusted authority could make multiple certifications for the same subject but different objects, be it intentionally, by accident, or following a (legal or illegal) coercion. We propose the notion of a double-authentication-preventing signature, in which a value to be signed is split into two parts: a subject and a message. If a signer ever signs two different messages for the same subject, enough information is revealed to allow anyone to compute valid signatures on behalf of the signer. This double-signature forgeability property discourages signers from misbehaving—a form of self-enforcement—and would give binding authorities like CAs some cryptographic arguments to resist legal coercion. We give a generic construction using a new type of trapdoor functions with extractability properties, which we show can be instantiated using the group of sign-agnostic quadratic residues modulo a Blum integer; we show an additional application of these new extractable trapdoor functions to standard digital signatures.