Mulan Liu

Rational secret sharing as extensive games

The threat that comes from previously used punishment strategies in rational secret sharing is weakened because the punishment somtimes also causes loss to the punisher himself. In this paper, we first model 2-out-of-2 rational secret sharing in an extensive game with imperfect information, and then provide a strategy for achieving secret recovery in this game. Moreover, we prove that the strategy is a sequential equilibrium which means after any history of the game no player can benefit from deviations so long as the other players stick to the strategy. In particular, when a deviation is detected, the punishment executed by the punisher is still his optimal option. Therefor, by considering rational secret sharing as an extensive game, we design punishment strategies that effectively punish the deviants and meanwhile guarantee punishers’ benefit. Hence, these punishments are more credible than previous ones. Except assuming the existence of simultaneous channels, our scheme can have dealer off-line and extend to the t-out-of-n setting, and also satisfies computational equilibria in some sense.

Multiplicative Linear Secret Sharing Schemes Based on Connectivity of Graphs

The multiplicative property is important for a linear secret sharing scheme (LSSS) to be used in constructing a multiparty computation (MPC) protocol. In general, an LSSS has to expand its share size to obtain the multiplicative property. In this paper, with respect to an MPC problem based on connectivity of graphs we devise an ideal multiplicative LSSS, that is, the LSSS is of the multiplicative property without expanding its share size. Moreover, it provides a new class of access structures that have ideal multiplicative LSSSs.

Strongly Multiplicative and 3-Multiplicative Linear Secret Sharing Schemes

Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multi-party computation protocols. However, it remains open whether or not there exist efficient constructions of strongly multiplicative LSSS from general LSSS . In this paper, we propose the new concept of 3-multiplicative LSSS , and establish its relationship with strongly multiplicative LSSS. More precisely, we show that any 3-multiplicative LSSS is a strongly multiplicative LSSS, but the converse is not true; and that any strongly multiplicative LSSS can be efficiently converted into a 3-multiplicative LSSS. Furthermore, we apply 3-multiplicative LSSS to the computation of unbounded fan-in multiplication, which reduces its round complexity to four (from five of the previous protocol based on multiplicative LSSS). We also give two constructions of 3-multiplicative LSSS from Reed-Muller codes and algebraic geometric codes. We believe that the construction and verification of 3-multiplicative LSSS are easier than those of strongly multiplicative LSSS. This presents a step forward in settling the open problem of efficient constructions of strongly multiplicative LSSS from general LSSS.

Classification of signature-only signature models

We introduce a set of criterions for classifying signature-only signature models. By the criterions, we classify signature models into 5 basic types and 69 general classes. Theoretically, 21141 kinds of signature models can be derived by appropriately combining different general classes. The result comprises almost existing signature models. It will be helpful for exploring new signature models. To the best of our knowledge, it is the first time for investigation of the problem of classification of signature-only signature models.

Rearrangements of access structures and their realizations in secret sharing schemes

Firstly, the definitions of the secret sharing schemes (SSS), i.e. perfect SSS, statistical SSS and computational SSS are given in an uniform way, then some new schemes for several familiar rearrangements of access structures with respect to the above three types of SSS are constructed from the old schemes. It proves that the new schemes and the old schemes are of the same security. A method of constructing the SSS which realizes the general access structure by rearranging some basic access structures is developed. The results of this paper can be used to key managements and access controls.