Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for implementing a zero knowledge prover are disclosed. In one aspect, a method includes the actions of accessing an instruction set of a processor. The actions include generating a representation of a computing instruction using Boolean logic operations. The actions include assigning a polynomial constraint of a group of polynomial constraints to each Boolean logic operation. The actions include providing, to the processor, an executable program that includes various computing instructions and a request to execute the executable program. The actions include monitoring a value of a register of the processor. The actions include determining whether the value of the register complies with polynomial constraints of the group of polynomial constraints that correspond to instructions performed on the register.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for implementing a zero knowledge prover are disclosed. In one aspect, a method includes the actions of executing a software program. The method further includes storing an execution trace that includes, for each address in memory, a value at each clock cycle during execution of the software program. The method further includes generating a sorted execution trace by sorting the execution trace. The method further includes determining a constraint for given values in the memory at adjacent clock cycles. The method further includes determining whether the sorted execution trace complies with the constraint and whether the sorted execution trace is a permutation of the execution trace. The method further includes providing, for output, data indicating whether the software program executed correctly while preventing outputting data included in the execution trace or the sorted execution trace.

Abstract: A facility for performing employing multiple frequencies in a secure distributed hierarchical convergence network is described. The facility receives a signal in a first frequency, converts the received signal to an internal representation, applies a business rule to the converted signal, and, when the business rule indicates that the signal should be transmitted in a second frequency, causes the internal representation of the signal to be translated to a second frequency and transmitted in the second frequency.

Abstract: A facility for performing employing multiple frequencies in a secure distributed hierarchical convergence network is described. The facility receives a signal in a first frequency, converts the received signal to an internal representation, applies a business rule to the converted signal, and, when the business rule indicates that the signal should be transmitted in a second frequency, causes the internal representation of the signal to be translated to a second frequency and transmitted in the second frequency.

Abstract: A facility for publishing information in a distributed network without a central management infrastructure is described. In various embodiments, the facility receives an indication of a new node and a destination node, the new node omitted from a contact list associated with the destination node, the contact list having an approximately logarithmic distribution of neighboring nodes; introduces the new node to the destination node via a permanent circuit; and causes the destination node to add the new node to the contact list when adding the new node improves the logarithmic distribution of neighboring nodes.

Abstract: A facility for performing employing multiple frequencies in a secure distributed hierarchical convergence network is described. The facility receives a signal in a first frequency, converts the received signal to an internal representation, applies a business rule to the converted signal, and, when the business rule indicates that the signal should be transmitted in a second frequency, causes the internal representation of the signal to be translated to a second frequency and transmitted in the second frequency.

Abstract: A facility for performing employing multiple frequencies in a secure distributed hierarchical convergence network is described. The facility receives a signal in a first frequency, converts the received signal to an internal representation, applies a business rule to the converted signal, and, when the business rule indicates that the signal should be transmitted in a second frequency, causes the internal representation of the signal to be translated to a second frequency and transmitted in the second frequency.

Abstract: A facility for publishing information in a distributed network without a central management infrastructure is described. In various embodiments, the facility receives an indication of a new node and a destination node, the new node omitted from a contact list associated with the destination node, the contact list having an approximately logarithmic distribution of neighboring nodes; introduces the new node to the destination node via a permanent circuit; and causes the destination node to add the new node to the contact list when adding the new node improves the logarithmic distribution of neighboring nodes.

Abstract: A facility for publishing information in a distributed network without a central management infrastructure is described. In various embodiments, the facility receives an indication of a new node and a destination node, the new node omitted from a contact list associated with the destination node, the contact list having an approximately logarithmic distribution of neighboring nodes; introduces the new node to the destination node via a permanent circuit; and causes the destination node to add the new node to the contact list when adding the new node improves the logarithmic distribution of neighboring nodes.

Abstract: A facility for publishing information in a distributed network without a central management infrastructure is described. In various embodiments, the facility receives an indication of a new node and a destination node, the new node omitted from a contact list associated with the destination node, the contact list having an approximately logarithmic distribution of neighboring nodes; introduces the new node to the destination node via a permanent circuit; and causes the destination node to add the new node to the contact list when adding the new node improves the logarithmic distribution of neighboring nodes.

Abstract: A facility for publishing information in a distributed network without a central management infrastructure is described. In various embodiments, the facility receives an indication of a new node and a destination node, the new node omitted from a contact list associated with the destination node, the contact list having an approximately logarithmic distribution of neighboring nodes; introduces the new node to the destination node via a permanent circuit; and causes the destination node to add the new node to the contact list when adding the new node improves the logarithmic distribution of neighboring nodes.

Abstract: A facility for performing employing multiple frequencies in a secure distributed hierarchical convergence network is described. The facility receives a signal in a first frequency, converts the received signal to an internal representation, applies a business rule to the converted signal, and, when the business rule indicates that the signal should be transmitted in a second frequency, causes the internal representation of the signal to be translated to a second frequency and transmitted in the second frequency.

Abstract: A facility for performing employing multiple frequencies in a secure distributed hierarchical convergence network is described. The facility receives a signal in a first frequency, converts the received signal to an internal representation, applies a business rule to the converted signal, and, when the business rule indicates that the signal should be transmitted in a second frequency, causes the internal representation of the signal to be translated to a second frequency and transmitted in the second frequency.

Abstract: A facility for publishing information in a distributed network without a central management infrastructure is described. In various embodiments, the facility receives an indication of a new node and a destination node, the new node omitted from a contact list associated with the destination node, the contact list having an approximately logarithmic distribution of neighboring nodes; introduces the new node to the destination node via a permanent circuit; and causes the destination node to add the new node to the contact list when adding the new node improves the logarithmic distribution of neighboring nodes.

Abstract: A facility for performing employing multiple frequencies in a secure distributed hierarchical convergence network is described. The facility receives a signal in a first frequency, converts the received signal to an internal representation, applies a business rule to the converted signal, and, when the business rule indicates that the signal should be transmitted in a second frequency, causes the internal representation of the signal to be translated to a second frequency and transmitted in the second frequency.