Linear algebra operations on private distributed data are frequently required in several practical scenarios (e.g., statistical analysis and privacy preserving databases). We present universally composable two-party protocols to compute inner products, determinants, eigenvalues, and eigenvectors. These protocols are built for a two-party scenario where the inputs are provided by mutually distrustful parties. After execution, the protocols yield the results of the intended operation while preserving the privacy of their inputs. Universal composability is obtained in the trusted initializer model, ensuring information theoretical security under arbitrary protocol composition in complex environments. Furthermore, our protocols are computationally efficient since they only require field multiplication and addition operations.

We present a detailed comparison of the Pret a Voter (PaV) and PunchScan (PS) protocols for booth voting. We also describe a simpler variation that keeps the ballot layout of PaV-Voter but borrows the cryptography from PS, which is based on any commitment scheme. By using unconditionally hiding commitments we obtain a conceptually very simple voting protocol with unconditional privacy.

This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an identification error, the Kolmogorov distance, the Bhattacharyya coefficient, and the Shannon (1948) distinguishability (as defined through mutual information). These measures have a long history of use in statistical pattern recognition and classical cryptography. We obtain several inequalities that relate the quantum distinguishability measures to each other, one of which may be crucial for proving the security of quantum cryptographic key distribution. In another vein, these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states. This is a tool that may prove useful in the analysis of various quantum-cryptographic protocols.