Abstract. In this note, we report on the first large-scale and practical application of multiparty computation, which took place in January 2008. We also report on the novel cryptographic protocols that were used.

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We discuss the widely increasing range of applications of a cryptographic technique called Multi-Party Computation. For many decades this was perceived to be of purely theoretical interest, but now it has started to find application in a number of use cases. We highlight in this paper a number of these, ranging from securing small high value items such as cryptographic keys, through to securing an entire database.

We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem.Beame has shown a lower bound of ª´Ò ¾ µ for this product leaving a gap of a logarithmic factor up to the previously best known upper bound of Ç´Ò ¾ ÐÓ Òµ due to Frederickson. Since then, no progress has been made towards tightening this gap.The main contribution of this paper is a comparison based sorting algorithm which closes the gap by meeting the lower bound of Beame. The time-space product Ç´Ò ¾ µ upper bound holds for the full range of space bounds between ÐÓ Ò and Ò ÐÓ Ò. Hence in this range our algorithm is optimal for comparison based models as well as for the very powerful general models considered by Beame.

Abstract. We consider applications involving a number of servers in the cloud that go through a sequence of online periods where the servers communicate, separated by offline periods where the servers are idle. During the offline periods, we assume that the servers need to securely store sensitive information such as cryptographic keys. Applications like this include many cases where secure multiparty computation is outsourced to the cloud, and in particular a number of online auctions and benchmark computations with confidential inputs. We consider fully autonomous servers that switch between online and offline periods without communicating with anyone from outside the cloud, and semi-autonomous servers that need a limited kind of assistance from outside the cloud when doing the transition. We study the levels of security one can -and cannot -obtain in this model, propose light-weight protocols achieving maximal security, and report on their practical performance.

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We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem.Beame has shown a lower bound of Ω(n 2 ) for this product leaving a gap of a logarithmic factor up to the previously best known upper bound of O(n 2 log n) due to Frederickson. Since then, no progress has been made towards tightening this gap.The main contribution of this paper is a comparison based sorting algorithm which closes this gap by meeting the lower bound of Beame. The time-space product O(n 2 ) upper bound holds for the full range of space bounds between log n and n/ log n. Hence in this range our algorithm is optimal for comparison based models as well as for the very powerful general models considered by Beame.