Secure two-party comparing is a special case and a basic module of secure computations,and is applied in mobile code and e-commerce security etc.But known solutions have some disadvantages:expensive costs of computing and communicating,limited ranges of compared numbers.Based on a modified ElGamal algorithm,this paper presented and proved multiplicative,mixed-multiplicative,additive and subtractive homomorphic cryptosystem.Constructed an encrypted function unknown by two-party using the homomorphic cryptosystem.Based on the homomorphic cryptosystem and evaluation of encrypted functions,designed secure two-party comparing protocol under semi-honest model.Proof,example and comparing with other protocols show the proposed protocol has the merits of security,fairness,lower costs of communication and computational complexity,and comparing integers.
Secure two-party comparing is a special case and a basic module of secure computations,and is applied in mobile code and e-commerce security etc.But known solutions have some disadvantages:expensive costs of computing and communicating,limited ranges of compared numbers.Based on a modified ElGamal algorithm,this paper presented and proved multiplicative,mixed-multiplicative,additive and subtractive homomorphic cryptosystem.Constructed an encrypted function unknown by two-party using the homomorphic cryptosystem.Based on the homomorphic cryptosystem and evaluation of encrypted functions,designed secure two-party comparing protocol under semi-honest model.Proof,example and comparing with other protocols show the proposed protocol has the merits of security,fairness,lower costs of communication and computational complexity,and comparing integers.
The essential of Yao’s millionaire problem is securely comparing two numbers,which is a basic building block of secure computations and has many important applications in e-commerce,such as bidding,auction and so on.But known solutions have some disadvantagesf,or example expensive costs of computing and communicatingl,imited ranges of compared numbers.This paper proposes a modified ElGamal algorithm,based on which multiplicative and subtractive homomorphic cryp-tosystem is presented and proved.Based on the homomorphic cryptosystem,Fair and Efficient Protocol for Secure Two-party Comparing(FEPSTC) under semi-honest model is constructed.The main properties of the FEPSTC are securityf,airnessl,ower costs of communication and computational complexity,and comparing real numbers.They are proved and illustrated by an ex-ample and by comparing with other protocols.
Secure multi-party multiplication is a special secure multi-party computation problem, which can be used by multi-party to share the multiplication result. Present protocols frequently using the secure two-party multiplication protocol which has high communication cost and large amount of data. Based on the homomorphic encryption technology, a serial secure multi-party multiplication protocol in the complex communication environment and a parallel secure multi-party multiplication protocol in the ideal communication environment are presented for this problem in the semi-honest model.At last, correctness and security of those protocols are analyzed. Compared with the present protocols, the analysis shows that the proposed protocols have better advantages in the communication cost and the execution efficiency.
At present, research on secure multi-party computation is of great interest in modern cryptography. It should be acknowledged that if any function can be computed securely, then it results in a very powerful tool. In fact, all natural protocols are, or can be rephrased to be, special cases of the multi-party computation problems. Design and analysis of the special multi-party computation protocols is meaningful and has attracted much interest in this field. Based on the combination of a public-key cryptosystem of the homomorphic encryption and on the theoretic construction relying on the F-hiding assumption, a protocol for comparing information of equality is proposed. The protocol needs only a single round of interaction and ensures fairness, efficiency and security. The protocol is fair, which means that one party knows the sound result of the comparison if and only if the other one knows the result. The protocol is efficient with the help of an oblivious third party for calculating. However, the third party cannot learn any information about the participant抯 private inputs and even about the comparison result, and cannot collude with any participant. The protocol is secure for the two participants, that is, any information about their secret input will not leak except the final computation result. A precise proof of security of the protocol is presented. Applications of this protocol may include private bidding and auctions, secret ballot elections, commercial business, identification in a number of scenarios and so on. It is believed that the protocol may be of practical significance for electronic transaction.
Secure multi-party computation (SMC) allows multiple parties to jointly and securely compute a function while preserving the privacy of the involved parties. In this regard, homomorphic cryptosystems allow users to perform addition or multiplication operations on encrypted values without having to decrypt the input values. In this paper, we propose both a cryptographic and a non-cryptographic privacy-preserving protocols that allow one party to collaboratively compute a private polynomial function with at least two other parties using semantically secure cryptosystems. In this respect, the function to be evaluated is kept private to the party in question. In addition, we assume that there is no fully trusted party and that all parties are semi-honest. Moreover, we assume that there is no collusion between the different parties. We present the two protocols in question and report on the underlying performance through the presentation of our implementation results. The proposed protocols are relevant in many applications such as evidence sharing in multi-party forensic investigations, situation awareness through the secure sharing in distributed monitoring of plan execution, etc.
Private integer comparison has been an essential computation function for many applications, including online auction, credential identification, data mining, and joint bidding. In the setting of two-party computation, two parties with private inputs (x and y) want to jointly compare them without revealing the value of those inputs to others (also known as the Millionaires’ problem) while the output should ensure correctness and preserve data privacy. The private inputs only can be revealed if they are equal, i.e., x = y. Many related works have been proposed to solve the integer comparison problem in various settings, focusing on different properties such as round and computation complexity. Most solutions decompose integers into bitwise representation and then securely evaluate the function in a Boolean circuit on encrypted bits. However, this type of solution is costly (especially for large integers) as each bit requires encryption and decryption. In this paper, we transform the private integer comparison into a block comparison problem. In particular, we employ a block vectorization mechanism to encode the private inputs into blocks. We show the security of our two-party protocol in the semi-honest model. Also, we implement the protocol to demonstrate its efficiency using block vectorization mechanism and homomorphic encryption. The experimental result proves that our proposed solution achieves high efficiency, particularly for large integer comparisons.
Abstract. We show how two existing paradigms for two-party secure function evaluation (SFE) in the semi-honest model can be combined securely and efficiently – those based on additively homomorphic encryption (HE) with those based on garbled circuits (GC) and vice versa. Additionally, we propose new GC constructions for addition, subtraction, multiplication, and comparison functions. Our circuits are approximately two times smaller (in terms of garbled tables) than previous constructions. This implies corresponding computation and communication improvements in SFE of functions using the above building blocks (including the protocols for combining HE and GC). Based on these results, we present efficient constant-round protocols for secure integer comparison, and the related problems of minimum selection and minimum distance, which are crucial building blocks of many cryptographic schemes such as privacy preserving biometric authentication (e.g., face recognition, fingerprint matching, etc).