The problem in which one of three pairwise interacting parties is required to securely compute a function of the inputs held by the other two, when one party may arbitrarily deviate from the computation protocol (active behavioral model), is studied. An information-theoretic characterization of unconditionally secure computation protocols under the active behavioral model is provided. A protocol for Hamming distance computation is provided and shown to be unconditionally secure under both active and passive behavioral models using the information-theoretic characterization. The difference between the notions of security under the active and passive behavioral models is illustrated by examining a protocol for computing quadratic and Hamming distances that is secure under the passive model, but is insecure under the active model.
The problem in which one of three pairwise interacting parties is required to securely compute a function of the inputs held by the other two, when one party may arbitrarily deviate from the computation protocol (active behavioral model), is studied. An information-theoretic characterization of unconditionally secure computation protocols under the active behavioral model is provided. A protocol for Hamming distance computation is provided and shown to be unconditionally secure under both active and passive behavioral models using the information-theoretic characterization. The difference between the notions of security under the active and passive behavioral models is illustrated by examining a protocol for computing quadratic and Hamming distances that is secure under the passive model, but is insecure under the active model.
The problem in which one of three pairwise interacting parties is required to securely compute a function of the inputs held by the other two, when one party may arbitrarily deviate from the computation protocol (active behavioral model), is studied. An information-theoretic characterization of unconditionally secure computation protocols under the active behavioral model is provided. A protocol for Hamming distance computation is provided and shown to be unconditionally secure under both active and passive behavioral models using the information-theoretic characterization. The difference between the notions of security under the active and passive behavioral models is illustrated through the BGW protocol for computing quadratic and Hamming distances; this protocol is secure under the passive model, but is shown to be not secure under the active model.
. This paper improves on the classical results in unconditionally secure multi-party computation among a set of n players, by considering a model with three simultaneously occurring types of player corruption: the adversary can actively corrupt (i.e. take full control over) up to ta players and, additionally, can passively corrupt (i.e. read the entire information of) up to tp players and fail-corrupt (i.e. stop the computation of) up to tf other players. The classical results in multi-party computation are for the special cases of only passive (ta = tf = 0) or only active (tp = tf = 0) corruption. In the passive case, every function can be computed securely if and only if tp ! n=2. In the active case, every function can be computed securely if and only if ta ! n=3; when a broadcast channel is available, then this bound is ta ! n=2. These bounds are tight. Strictly improving these results, one of our results states that, in addition to tolerating ta ! n=3 actively corrupted players, pr...
Two types of generalizations in secure multi-party computation are described. First, we report on a new general adversary model: while previous protocols were designed to tolerate misbehavior of one of two types (active or passive adversaries) the new protocols tolerate mixed types of adversaries, i.e. an adversary that can corrupt players actively, passively, or can let them crash (i.e. stop execution). We derive the necessary and sufficient conditions under which such a general adversary can be tolerated. Second, we present a generic protocol framework that unifies previous approaches achieving unconditional (or information-theoretic) security and cryptographic security (i.e. security based on a cryptographic intractability assumption). This is achieved by introducing secret sharing schemes with an additional property called the multiplication property and a new type of homomorphic commitment scheme, and by generalizing the concept of commitments.
This paper improves on the classical results in uncondition- ally secure multi-party computation among a set of n players, by consid- ering a model with three simultaneously occurring types of player cor- ruption: the adversary can actively corrupt (i.e. take full control over) up to ta players and, additionally, can passively corrupt (i.e. read the entire information of) up to tp players and fail-corrupt (i.e. stop the compu- tation of) up to tf other players. The classical results in multi-party computation are for the special cases of only passive (ta = tf =0 ) or only active (tp = tf = 0) corruption. In the passive case, every function can be computed securely if and only if tp <n = 2. In the active case, every function can be computed securely if and only if ta <n =3; when a broadcast channel is available, then this bound is ta <n =2. These bounds are tight. Strictly improving these results, one of our results states that, in addi- tion to tolerating ta <n =3 actively corrupted players, privacy can be guaranteed against every minority, thus tolerating additional tp n=6 passively corrupted players. These protocols require no broadcast and have an exponentially small failure probability. We further show that the bound t<n =2 for passive corruption holds even if the adversary is additionally allowed to make the passively corrupted players fail. Moreover, we characterize completely the achievable thresholds ta, tp and tf for four scenarios. Zero failure probability is achievable if and only if 3ta +2 tp + tf <n ; this holds whether or not a broadcast chan- nel is available. Exponentially small failure probability with a broadcast channel is achievable if and only if 2ta +2 tp +tf <n ; without broadcast, the additional condition 3ta + tf <n is necessary and sucient. In this corrected version, an error pointed out by Damg ard (Dam99) is corrected.
In secure multi-party computation n parties jointly evaluate an n-variate function f in the presence of an adversary which can corrupt up till t parties. Almost all the works that have appeared in the literature so far assume the presence of authenticated channels between the parties. This assumption is far from realistic. Two directions of research have been borne from relaxing this (strong) assumption: (a) The adversary is virtually omnipotent and can control all the communication channels in the network, (b) Only a partially connected topology of authenticated channels is guaranteed and adversary controls a subset of the communication channels in the network. This work introduces a new setting for (unconditional) secure multiparty computation problem which is an interesting intermediate model with respect to the above well studied models from the literature (by sharing a salient feature from both the above models). We consider the problem of (unconditional) secure multi-party computation when 'some' of the communication channels connecting the parties can be corrupted passively as well as actively. For this setting, some honest parties may be connected to several other honest parties via corrupted channels and may not be able to authentically communicate with them. Such parties may not be assured the canonical guarantees of correctness or privacy. We present refined definitions of security for this new intermediate model of unconditional multiparty computation. We show how to adapt protocols for (Unconditional) secure multiparty computation to realize the definitions and also argue the tightness of the results achieved by us.
In the problem of Secure Multi-party Computation, the objective is to design a protocol that allows a group of parties to securely compute functions of their collective private data, while ensuring that no party reveals any more information about its private data other than what must be inherently revealed by the computation results (privacy) and that no parties can disrupt or influence the computation results beyond the effects of changing their input data (correctness and consistency). Information theoretic approaches toward this problem, that provide provable (unconditional) security guarantees even against adversarial parties that have unbounded computational power, have established that general computation is possible in a variety of scenarios. However, these general solutions are not always efficient or finely tuned to the requirements of specific problems and applications.
The focus of this thesis is on the development of information theoretic approaches for multi-party computation applications with the common theme of secure and efficient computation and inference over a distributed data network. Specific applications include: 1) private information retrieval, where the objective is to privately retrieve data without revealing what was selected; 2) secure statistical analysis, the problem of extracting statistics without revealing anything else about the underlying data; 3) secure sampling, which is the secure generation of new data with a given distribution; and 4) secure authentication, where the identity of a party needs to authenticated via inference on his/her credentials and stored registration data.
The contributions of this thesis toward addressing these applications include the following: The development of an Oblivious Transfer (OT) protocol, applicable to private information retrieval, that trades off a small amount of privacy while being several times more efficient than other OT protocols. The efficiency of general se- cure two-party computation via OT realized from noisy channels is also analyzed. A technique for approximate secure multi-party computation applicable to secure statistical analysis of large scale distributed databases is developed. By exploiting a dimensionality reduction and the structure of a broad class of functions based on the computed statistics, the feasibility of simultaneously achieving both arbitrarily high accuracy and arbitrarily high communication efficiency is demonstrated. The region of distributions that can be securely sampled in the two-party scenario is characterized. It is further established that for those distributions, it can be accomplished with a protocol that only sends one message. Inner and outer bounds on the region of distributions that can be securely sampled in the general multi-party scenario are also developed. A new three-party protocol, applicable to the problem of secure biometric authentication, that securely computes the Hamming distance even when one of the parties arbitrarily deviates from the protocol is proposed and analyzed. A two-factor secure biometric authentication system that is robust against the compromise of registered biometric data, allowing for revocability and resistance against cross-enrollment attacks is also proposed.