Cheating immune secret sharing

We consider secret sharing with binary shares. This model allows us to use the well developed theory of cryptographically strong boolean functions. We prove that for given secret sharing, the average cheating probability over all cheating and original vectors, i.e., ρ ¯= 1 n ⋅ 2 −n ∑ n c=1 ∑ α∈Vn ρ c,α , satisfies ρ ¯⩾ 1 2 , and the equality holds ⇔ ρc,α satisfies ρc,α = 1/2 for every cheating vector δc and every original vector α. In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions. This enables us to construct cheating-immune secret sharing.

Constructions of cheating immune secret sharing

The work addresses the problem of cheating prevention in secret sharing. Two cheating scenarios are considered. In the first one, the cheaters always submit invalid shares to the combiner. In the second one, the cheaters collectively decide which shares are to be modified so the combiner gets a mixture of valid and invalid shares from the cheaters. The secret scheme is said to be k-cheating immune if any group of k cheaters has no advantage over honest participants. The paper investigates cryptographic properties of the defining function of secret sharing so the scheme is k-cheating immune. Constructions of secret sharing immune against k cheaters are given.

Formal analysis of card-based payment systems in mobile devices

To provide card holder authentication while they are conducting an electronic transaction using mobile devices, VISA and MasterCard independently proposed two electronic payment protocols: Visa 3D Secure and MasterCard Secure Code. The protocols use pre-registered passwords to provide card holder authentication and Secure Socket Layer/ Transport Layer Security (SSL/TLS) for data confidentiality over wired networks and Wireless Transport Layer Security (WTLS) between a wireless device and a Wireless Application Protocol (WAP) gateway. The paper presents our analysis of security properties in the proposed protocols using formal method tools: Casper and FDR2. We also highlight issues concerning payment security in the proposed protocols.

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

Democratic systems

Digital signature is a breakthrough of modern cryptographic systems. A (t, n) threshold digital signature allows every set of cardinality t or more (out-of n) co-signers to authenticate a message. In almost all existing threshold digital signatures the threshold parameter t is fixed. There are applications, however, in which the threshold parameter needs to be changed from time to time. This paper considers such a scenario, in order to discuss relevant problems, and proposes a model that solves the related problems.

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.

An ideal and robust threshold RSA

We present a novel implementation of the threshold RSA. Our solution is conceptually simple, and leads to an easy design of the system. The signing key is shared in additive form, which is desirable for collaboratively performing cryptographic transformations, and its size, at all times, is logn, where n is the RSA modulus. That is, the system is ideal.

Use of reverse phase protein microarrays and reference standard development for molecular network analysis of metastatic ovarian carcinoma

Cancer can be defined as a deregulation or hyperactivity in the ongoing network of intracellular and extracellular signaling events. Reverse phase protein microarray technology may offer a new opportunity to measure and profile these signaling pathways, providing data on post-translational phosphorylation events not obtainable by gene microarray analysis. Treatment of ovarian epithelial carcinoma almost always takes place in a metastatic setting since unfortunately the disease is often not detected until later stages. Thus, in addition to elucidation of the molecular network within a tumor specimen, critical questions are to what extent do signaling changes occur upon metastasis and are there common pathway elements that arise in the metastatic microenvironment. For individualized combinatorial therapy, ideal therapeutic selection based on proteomic mapping of phosphorylation end points may require evaluation of the patient's metastatic tissue. Extending these findings to the bedside will require the development of optimized protocols and reference standards. We have developed a reference standard based on a mixture of phosphorylated peptides to begin to address this challenge.

Lattice-based threshold-changeability for standard CRT secret-sharing schemes

We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a non-standard scheme designed specifically for this purpose, or to have secure channels between shareholders. In contrast, we show how to increase the threshold parameter of the standard CRT secret-sharing scheme without secure channels between the shareholders. Our method can thus be applied to existing CRT schemes even if they were set up without consideration to future threshold increases. Our method is a positive cryptographic application for lattice reduction algorithms, and we also use techniques from lattice theory (geometry of numbers) to prove statements about the correctness and information-theoretic security of our constructions.

Lattice-based threshold-changeability for standard Shamir secret-sharing schemes

We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a non-standard scheme designed specifically for this purpose, or to have communication between shareholders. In contrast, we show how to increase the threshold parameter of the standard Shamir secret-sharing scheme without communication between the shareholders. Our technique can thus be applied to existing Shamir schemes even if they were set up without consideration to future threshold increases. Our method is a new positive cryptographic application for lattice reduction algorithms, inspired by recent work on lattice-based list decoding of Reed-Solomon codes with noise bounded in the Lee norm. We use fundamental results from the theory of lattices (Geometry of Numbers) to prove quantitative statements about the information-theoretic security of our construction. These lattice-based security proof techniques may be of independent interest.

On cheating immune secret sharing

The paper addresses the cheating prevention in secret sharing. We consider secret sharing with binary shares. The secret also is binary. This model allows us to use results and constructions from the well developed theory of cryptographically strong boolean functions. In particular, we prove that for given secret sharing, the average cheating probability over all cheating vectors and all original vectors, i.e., 1/n 2n ∑c=1...n ∑α∈V n ρc,α , denoted by ρ, satisfies ρ ≥ ½, and the equality holds if and only if ρc,α satisfies ρc,α= ½ for every cheating vector δc and every original vector α. In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions.This enables us to construct cheating-immune secret sharing.

On secure multi-party computation in black-box groups

We study the natural problem of secure n-party computation (in the passive, computationally unbounded attack model) of the n-product function f G (x 1,...,x n ) = x 1 ·x 2 ⋯ x n in an arbitrary finite group (G,·), where the input of party P i is x i  ∈ G for i = 1,...,n. For flexibility, we are interested in protocols for f G which require only 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 results are as follows. First, on the negative side, we show that if (G,·) is non-abelian and n ≥ 4, then no ⌈n/2⌉-private protocol for computing f G exists. Second, on the positive side, we initiate an approach for construction of black-box protocols for f G based on k-of-k threshold secret sharing schemes, which are efficiently implementable over any black-box group G. We reduce the problem of constructing such protocols to a combinatorial colouring problem in planar graphs. We then give two constructions for such graph colourings. Our first colouring construction gives a protocol with optimal collusion resistance t < n/2, but has exponential communication complexity O(n*2t+1^2/t) group elements (this construction easily extends to general adversary structures). Our second probabilistic colouring construction gives a protocol with (close to optimal) collusion resistance t < n/μ for a graph-related constant μ ≤ 2.948, and has efficient communication complexity O(n*t^2) group elements. Furthermore, we believe that our results can be improved by further study of the associated combinatorial problems.

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.

Effective routing with utilisation of cross-layer information for industrial wireless sensor networks

This thesis focuses on providing reliable data transmissions in large-scale industrial wireless sensor networks through improving network layer protocols. It addresses three major problems: scalability, dynamic industrial environments and coexistence of multiple types of data traffic in a network. Theoretical developments are conducted, followed by simulation studies for verification of theoretic results. The approach proposed in this thesis has been shown to be effective for large-scale network implementation and to provide improved data transmission reliability for both periodic and sporadic traffic.