Abstract. We consider the problem of secure integer division: given two Paillier encryptions of -bit values n and d, determine an encryption of n d without leaking any information about n or d. We propose two new protocols solving this problem. The first requires O( ) arithmetic operation on encrypted values (secure addition and multiplication) in O(1) rounds. This is the most efficient constant-rounds solution to date. The second protocol requires only O (log 2 )(κ + loglog ) arithmetic operations in O(log 2 ) rounds, where κ is a correctness parameter. Theoretically, this is the most efficient solution to date as all previous solutions have required Ω( ) operations. Indeed, the fact that an o( ) solution is possible at all is highly surprising.

Abstract. We propose a framework for formal analysis of privacy in location based services such as anonymous electronic toll collection. We give a formal definition of privacy, and apply it to the VPriv scheme for vehicular services. We analyse the resulting model using the ProVerif tool, concluding that our privacy property holds only if certain conditions are met by the implementation. Our analysis includes some novel features such as the formal modelling of privacy for a protocol that relies on interactive zero-knowledge proofs of knowledge and list permutations.

Abstract. Safety critical applications for recently proposed vehicle to vehicle ad-hoc networks (VANETs) rely on a beacon signal, which poses a threat to privacy since it could allow a vehicle to be tracked. Mix-zones, where vehicles encrypt their transmissions and then change their identifiers, have been proposed as a solution to this problem. In this work, we describe a formal analysis of mix-zones. We model a mix-zone and propose a formal definition of privacy for such a zone. We give a set of necessary conditions for any mix-zone protocol to preserve privacy. We analyse, using the tool ProVerif, a particular proposal for key distribution in mix-zones, the CMIX protocol. We show that in many scenarios it does not preserve privacy, and we propose a fix.