In this work, we construct a second price (Vickrey) auction protocol (SPA), which does not require any auctioneers and ensures total privacy in the presence of rational parties participating in the auction. In particular, the confidentiality of the highest bid and the identity of the second highest bidder are protected. We model the bidders participating in the second price auction as rational, computationally bounded and privacy-sensitive parties. These are self-interested agents who care about winning the auction more than learning about the private bids of other parties. A rational party does not deviate from the protocol arbitrarily but does so only for its own individual 'advantage' -- without any consideration for others. Such an advantage is modelled using suitable utility functions.

Sealed bid auctions are used to allocate a resource among a set of interested parties. Traditionally, auctions need the presence of a trusted auctioneer to whom the bidders provide their private bid values. Existence of such a trusted party is not an assumption easily realized in practice. Generic secure computation protocols can be used to remove a trusted party. However, generic techniques result in inefficient protocols, and typically do not provide fairness -- that is, a corrupt party can learn the output and abort the protocol thereby preventing other parties from learning the output.

At ITCS 2010, Dziembowski, Pietrzak, and Wichs introduced Non-malleable Codes (NMCs) which protect against tampering of a codeword of a given message into the codeword of a related message. A well-studied model of tampering is the 2-split-state model where the codeword consists of two independently tamperable states. As with standard error-correcting codes, it is of great importance to build codes with high rates.

We study the problem of “privacy amplification”: key agreement between two parties who both know a weak secret w , such as a password. (Such a setting is ubiquitous on the internet, where passwords are the most commonly used security device.) We assume that the key agreement protocol is taking place in the presence of an active computationally unbounded adversary Eve. The adversary may have partial knowledge about w , so we assume only that w has some entropy from Eve’s point of view. Thus, the goal of the protocol is to convert this nonuniform secret w into a uniformly distributed string R that is fully secret from Eve. R may then be used as a key for running symmetric cryptographic protocols (such as encryption, authentication, etc.). Because we make no computational assumptions, the entropy in R can come only from w . Thus, such a protocol must minimize the entropy loss during its execution, so that R is as long as possible. The best previous results have entropy loss of Θ( κ 2 ), where κ is the security parameter, thus requiring the password to be very long even for small values of κ . In this work, we present the first protocol for information-theoretic key agreement that has entropy loss linear in the security parameter. The result is optimal up to constant factors. We achieve our improvement through a somewhat surprising application of error-correcting codes for the edit distance. The protocol can be extended to provide also “information reconciliation,” that is, to work even when the two parties have slightly different versions of w (e.g., when biometrics are involved).

Consider two parties holding samples from correlated distributions$W$and$W^{\prime}$, respectively, where these samples are within distance$t$of each other in some metric space. The parties wish to agree on a close-to-uniformly distributed secret key$R$by sending a single message over an insecure channel controlled by an all-powerful adversary who may read and modify anything sent over the channel. We consider both the keyless case, where the parties share no additional secret information, and the keyed case, where the parties share a long-term secret${\ssr SK}_{\ssr Ext}$that they can use to generate a sequence of session keys$\{R_{j}\}$using multiple pairs$\{(W_{j}, W^{\prime}_{j})\}$. The former has applications to, e.g., biometric authentication, while the latter arises in, e.g., the bounded-storage model with errors. We show solutions that improve upon previous work in several respects.The best prior solution for the keyless case with no errors (i.e.,$t=0$) requires the min-entropy of$W$to exceed$2n/3$, where$n$is the bit length of$W$. Our solution applies whenever the min-entropy of$W$exceeds the minimal threshold$n/2$, and yields a longer key.

We study the problem of "privacy amplification": key agreement between two parties who both know a weak secret w, such as a password. (Such a setting is ubiquitous on the internet, where passwords are the most commonly used security device.) We assume that the key agreement protocol is taking place in the presence of an active computationally unbounded adversary Eve. The adversary may have partial knowledge about w, so we assume only that w has some entropy from Eve's point of view. Thus, the goal of the protocol is to convert this non-uniform secret w into a uniformly distributed string R that is fully secret from Eve. R may then be used as a key for running symmetric cryptographic protocols (such as encryption, authentication, etc.).