Abstract: A method for compliance with Know Your Customer (KYC) and other regulations includes a pseudonymous globally unique identifier stored on a blockchain that associates a pseudonymous first party address with a globally unique identifier representing the vetted identity of the owner of the address. The method also includes a trusted third party issuing a verifiable credential for a first pseudonymous party to a proposed transaction to a second pseudonymous party to the transaction.

Abstract: An empirical approach to providing differential privacy includes applying a common statistical query to a set of databases to produce sample values, both with and without any particular entity's data. The probability density is empirically estimated by sorting the sample values to generate an empirical cumulative distribution function. The cumulative distribution function is differenced across approximately the square root of the number of sample points to get an empirical density function. The statistical query is empirically (?,?)-private if the empirical densities with and without any particular individual differ by a factor of no more than exp(?), with the exception of a set for which the densities exceed that bound by a total of no more than ?.

Abstract: A method is provided for solving a computational problem that is reducible to a problem of counting solutions to an associated decision problem. The method includes estimating a number of the solutions to the decision problem using a quantum computer by determining if there is at least one simultaneous solution to both (i) the decision problem and (ii) an associated hashing problem. The method also includes increasing a precision of the estimated number of the solutions to the decision problem using the quantum computer by determining if there are multiple solutions to the decision problem that are simultaneously solutions to the associated hashing problem. The method further includes outputting or using the estimated number of the solutions to the decision problem as a solution to the computational problem.

Abstract: An empirical approach to providing differential privacy includes applying a common statistical query to a set of databases to produce sample values, both with and without any particular entity's data. The probability density is empirically estimated by sorting the sample values to generate an empirical cumulative distribution function. The cumulative distribution function is differenced across approximately the square root of the number of sample points to get an empirical density function. The statistical query is empirically (?,?)-private if the empirical densities with and without any particular individual differ by a factor of no more than exp(?), with the exception of a set for which the densities exceed that bound by a total of no more than ?.

Abstract: A method is provided for solving a computational problem that is reducible to a problem of counting solutions to an associated decision problem. The method includes estimating a number of the solutions to the decision problem using a quantum computer by determining if there is at least one simultaneous solution to both (i) the decision problem and (ii) an associated hashing problem. The method also includes increasing a precision of the estimated number of the solutions to the decision problem using the quantum computer by determining if there are multiple solutions to the decision problem that are simultaneously solutions to the associated hashing problem. The method further includes outputting or using the estimated number of the solutions to the decision problem as a solution to the computational problem.