Collaborative business applications can use secure multiparty computation to preserve input privacy. These applications need protocols that provide all the basic operations with integers and rational numbers and allow secure composition and efficient application development. Secure computation with rational numbers is a long-standing open problem. We present in this paper several components of a protocol family for secure computation with fixed-point numbers based on secret sharing.
Collaborative business applications can use secure multiparty computation to preserve input privacy. These applications need protocols that provide all the basic operations with integers and rational numbers and allow secure composition and efficient application development. Secure computation with rational numbers is a long-standing open problem. We present in this paper several components of a protocol family for secure computation with fixed-point numbers based on secret sharing.
As a fundamental part of cryptography, secure multiparty computation (SMC) is a building block of various cryptographic protocols, and it is also a hot topic in the international cryptographic community.In recent years, many SMC problems, such as secret information comparison, secret set problems and secure multiparty computational geometry, have been widely studied.As many practical problems need to be described by rational numbers, it is both theoretically and practically important to study the SMC problems in the rational number field.However, most of the existing researches focus on integers and the studied data are mainly one-dimensional data.There are few researches on secure multiparty computation of multi-dimensional data in the rational number field, but they can’t be generalized.Based on the fractional representation of rational numbers, the new encoding schemes about rational numbers and rational number vectors were proposed, which could encode multi-dimensional data in the rational number field and provided new solutions for other SMC problems in the rational number field.Based on the encoding scheme and one-way hash function, some protocols were designed for equality problems and set problems in the rational number field.These protocols used basic arithmetic operation and hash operation to guarantee efficiency than existing related protocols.And these protocols didn’t limit the range of research data and they were more widely applicable.It proves that these protocols are secure in the semi-honest model using simulation paradigm, and demonstrates the efficiency and the applicability of these protocols by theoretical analysis and experiment.A practical example was also given to illustrate that approaches are more versatile, and they could also be directly used to solve some secure multiparty computational geometry problems in the rational number field.
Secure multiparty computation (SMC) allows a set of parties to jointly compute a function on private inputs such that, they learn only the output of the function, and the correctness of the output is guaranteed even when a subset of the parties is controlled by an adversary. SMC allows data to be kept in an uncompromisable form and still be useful, and it also gives new meaning to data ownership, allowing data to be shared in a useful way while retaining its privacy. Thus, applications of SMC hold promise for addressing some of the security issues information-driven societies struggle with. In this thesis, we implement two SMC protocols. Our primary objective is to gain a solid understanding of the basic concepts related to SMC. We present a brief survey of the field, with focus on SMC based on secret sharing. In addition to the protocol im- plementations, we implement circuit randomization, a common technique for efficiency improvement. The implemented protocols are run on a simulator to securely evaluate some simple arithmetic functions, and the round complexities of the implemented protocols are compared. Finally, we attempt to extend the implementation to support more general computations.
It seems to be a generally acknowledged fact that you should never trust a computer and that you should trust the person operating the computer even less. This in particular becomes a problem when the party that you do not trust is one which is separated from you and is one on which you depend, e.g. because that party is the holder of some data or some capability that you need in order to operate correctly. How do you perform a given task involving interaction with other parties while allowing these parties a minimal influence on you and, if privacy is an issue, allowing them to learn as little about you as possible. This is the general problem of secure multiparty computation. The usual way of formalizing the problem is to say that a number of parties who do not trust each other wish to compute some function of their local inputs, while keeping their inputs as secret as possible and guaranteeing the correctness of the output. Both goals should be obtained even if some parties stop participating or some malevolent coalition of the parties start deviating arbitrarily from the agreed protocol. The task is further complicated by the fact that besides their mutual distrust, nor do the parties trust the channels by which they communicate. A general solution to the secure multiparty computation problem is a compiler which given any feasible function describes an efficient protocol which allows the parties to compute the function securely on their local inputs over an open network. Over the past twenty years the secure multiparty computation problem has been the subject of a large body of research, both research into the models of multiparty computation and research aimed at realizing general secure multiparty computation. The main approach to realizing secure multiparty computation has been based on verifiable secret sharing as computation, where each party holds a secret share of each input and during the execution computes secret shares of all intermediate values. This approach allows the parties to keep all inputs and intermediate values secret and to pool the shares of the output values to learn exactly these values. More recently an approach based on joint homomorphic encryption was introduced, allowing for an efficient realization of general multiparty computation secure against an eavesdropper. A joint encryption scheme is an encryption scheme where all parties can encrypt, but where it takes the participation of all parties to open an encryption. The computation then starts by all parties broadcasting encryptions of their inputs and progresses through computing encryptions of the intermediary values using the homomorphic properties of the encryption scheme. The encryptions of the outputs can then be jointly decrypted. In this dissertation we extend this approach by using threshold homomorphic encryption to provide full-fledged security against an active attacker which might control some of the parties and which might take over parties during the course of the protocol execution. As opposed to a joint encryption scheme a threshold encryption scheme only requires that a given number of the parties are operating correctly for decryption to be possible. In this dissertation we show that threshold homomorphic encryption allows to solve the secure general multiparty computation problem more efficiently than previous approaches to the problem. Starting from an open point-to-point network there is a long way to general secure multiparty computation. The dissertation contains contributions at several points along the way. In particular we investigate how to realize secure channels. We also show how threshold signature schemes can be used to efficiently realize a broadcast channel and how threshold cryptography can be used to provide the parties of the network with a source of shared randomness. All three tools are well-known to be extremely powerful resources in a network, and our principle contribution is to provide efficient realizations. The dissertation also contains contributions to the definitional part of the field of multiparty computation. Most significantly we augment the recent model of universally composable security with a formal notion of what it means for a protocol to only realize a given problem under a given restricted input-output behavior of the environment. This e.g. allows us to give the first specification of a universally composable zero-knowledge proof of membership which does not at the same time require the proof system to be a proof of knowledge.
Secure multiparty computation (SMC) is a research focusing in the international cryptographic community. The protocols used to address the millionaires' problem are the basic building blocks of most SMC protocols and their efficiency dominates that of many other SMC protocols. To the best of our knowledge, almost all protocols used to address the millionaires' problem are based on integers, which means that their applications are limited. In this study, we propose precise and efficient protocols for rational numbers based on additively homomorphic encryptions. One of our protocols is inspired by computational geometry and it reduces the millionaires problem to computing the area of a triangle formed by three private points. This approach can determine whether the relationship between two private inputs is greater than, equal to or less than, and it has a much lower computational complexity compared with existing methods. We proved that these protocols are secure using simulation paradigm. Our approaches can be used in many SMC protocols that involve rational numbers and integers, and they can also be used directly to solve some secure multiparty computational geometry problem in rational number field.
The rapid development of cloud computing has probably benefited each of us. However, the privacy risks brought by untrusty cloud servers arise the attention of more and more people and legislatures. In the last two decades, plenty of works seek the way of outsourcing various specific tasks while ensuring the security of private data. Although the addition and multiplication are enough for implementing any functions, the direct utilization of existing schemes like homomorphic encryption will lead to significant efficiency and accuracy loss, which is not suitable for outsourcing computation tasks. The tasks to be outsourced are endless, however, the involved calculations are similar. In this paper, inspired by additive secret sharing and multiplicative secret sharing technologies, we construct a series of novel protocols which support the common secure calculations on numbers (e.g., basic elementary functions) or matrices (e.g., solve eigenvectors) in arbitrary n number of servers (n≥2), and the n-party protocols ensure the security of the original data even if n−1 servers collude. All protocols we designed only need constant interaction rounds, and we demonstrate them under universally composability security. We believe that these protocols can provide a new basic tool for actual outsourced tasks.