Probabilistic encryption becomes more and more important since its ability to against chosen-ciphertext attack. Applications like online voting schemes and one-show credentials are based on probabilistic encryption. Research on good probabilistic encryptions are on going, while many good deterministic encryption schemes are already well implemented and available in many systems. To convert any deterministic encryption scheme into a probabilistic encryption scheme, a randomized media is needed to apply on the message and carry the message over as an randomized input. In this paper, nonlinear codes obtained by certain mapping from linear error-correcting codes are considered to serve as such carrying media. Binary nonlinear codes obtained by Gray mapping from 4-linear codes are discussed as example for a such scheme.

This paper examines similarities between the Decision Diffie-Hellman (DDH) assumption and the Quadratic Residuosity (QR) assumption. In addition, we show that many cryptographic protocols based on the QR assumption can be reconstructed using the DDH assumption.

This paper presents a reshufflable and laziness tolerant mental card game protocol. First, our protocol can reshuffle any subset of cards. For example, some opened cards and some face down cards can be shuffled together. Next, we consider two types of honest players, currently active and currently nonactive. A player is currently nonactive if he dropped out the game or he declared "pass" and has not declared "rejoin" yet. In the proposed protocol, if more than half of the players are currently active, they can play the game. In this case, the privacy of the currently nonactive players are kept secret.