No abstract

No abstract

Abstract. We proposed a two-round protocol for solving the Millionaires' Problem in the setting of semi-honest parties. Our protocol uses either multiplicative or additive homomorphic encryptions. Previously proposed protocols used additive or XOR homomorphic encryption schemes only. The computation and communication costs of our protocol are in the same asymptotic order as those of the other efficient protocols. Nevertheless, since multiplicative homomorphic encryption scheme is more efficient than an additive one practically, our construction saves computation time and communication bandwidth in practicality.

An (n, d) permutation array (PA) is a subset of Sn with the property that the distance (under some metric) between any two permutations in the array is at least d. They became popular recently for communication over power lines. Motivated by an application to flash memories, in this paper the metric used is the Chebyshev metric. A number of different constructions are given as well as bounds on the size of such PA.

Abstract-Visual cryptography (VC) is a method of encrypting a secret image into shares such that stacking a sufficient number of shares reveals the secret image. Shares are usually presented in transparencies. Each participant holds a transparency. Most of the previous research work on VC focuses on improving two parameters: pixel expansion and contrast. In this paper, we studied the cheating problem in VC and extended VC. We considered the attacks of malicious adversaries who may deviate from the scheme in any way. We presented three cheating methods and applied them on attacking existent VC or extended VC schemes. We improved one cheat-preventing scheme. We proposed a generic method that converts a VCS to another VCS that has the property of cheating prevention. The overhead of the conversion is near optimal in both contrast degression and pixel expansion.

Abstract. In this paper we propose efficient two-round k-out-of-n oblivious transfer schemes, in which R sends O(k) messages to S, and S sends O(n) messages back to R. The computation cost of R and S is reasonable. The choices of R are unconditionally secure. For the basic scheme, the secrecy of unchosen messages is guaranteed if the Decisional Diffie-Hellman problem is hard. When k = 1, our basic scheme is as efficient as the most efficient 1-out-of-n oblivious transfer scheme. Our schemes have the nice property of universal parameters, that is each pair of R and S need neither hold any secret key nor perform any prior setup (initialization). The system parameters can be used by all senders and receivers without any trapdoor specification. Our k-out-of-n oblivious transfer schemes are the most efficient ones in terms of the communication cost, in both rounds and the number of messages. Moreover, one of our schemes can be extended in a straightforward way to an adaptive k-out-of-n oblivious transfer scheme, which allows the receiver R to choose the messages one by one adaptively. In our adaptivequery scheme, S sends O(n) messages to R in one round in the commitment phase. For each query of R, only O(1) messages are exchanged and O(1) operations are performed. In fact, the number k of queries need not be pre-fixed or known beforehand. This makes our scheme highly flexible.

Abstract. In this paper we propose an efficient (string) OT 1 n scheme for any n ≥ 2. We build our OT 1 n scheme from fundamental cryptographic techniques directly. It achieves optimal efficiency in terms of the number of rounds and the total number of exchanged messages for the case that the receiver's choice is unconditionally secure. The computation time of our OT 1 n scheme is very efficient, too. The receiver need compute 2 modular exponentiations only no matter how large n is, and the sender need compute 2n modular exponentiations. The distinct feature of our scheme is that the system-wide parameters are independent of n and universally usable, that is, all possible receivers and senders use the same parameters and need no trapdoors specific to each of them. For our OT 1 n scheme, the privacy of the receiver's choice is unconditionally secure and the secrecy of the un-chosen secrets is based on hardness of the decisional Diffie-Hellman problem. We extend our OT 1 n scheme to distributed oblivious transfer schemes. Our distributed OT 1 n scheme takes full advantage of the research results of secret sharing and is conceptually simple. It achieves better security than Naor and Pinkas's scheme does in many aspects. For example, our scheme is secure against collusion of the receiver R and t-1 servers and it need not restrict R to contact at most t servers, which is difficult to enforce. For applications, we present a method of transforming any singledatabase PIR protocol into a symmetric PIR protocol with only one extra unit of communication cost.

The group key management is for a group manager to maintain a consistent group key for a dynamic group of members through a broadcast channel. In this paper we propose a group key management scheme based on a meta proxy re-encryption (PRE) scheme. In particular, we propose an RSA-based PRE scheme with special properties. It is the first RSA-based PRE scheme for group key management and has the desired properties of uni-directionality and multi-hop.In our group key management scheme, each group member holds just one secret auxiliary key and log N public auxiliary keys. The size of rekey messages for each group key update remains O(log N ). Additionally, our scheme has some distinct features. Firstly, the size of the key update history is a constant O(N ) no matter how many times of group key updates occur. Secondly, the computation time of computing the newest group key from the key update history is always O(log N ) no matter how many group key updates are missed. This feature provides a practical solution for group key update when members go offline from time to time. Finally, the proposed scheme is immune to the collusion attack of other members.