The computational power of networks of small resource-limited mobile agents is explored. Two new models of computation based on pairwise interactions of finite-state agents in populations of finite but unbounded size are defined. With a fairness condition on interactions, the concept of stable computation of a function or predicate is defined. Protocols are given that stably compute any predicate in the class definable by formulas of Presburger arithmetic, which includes Boolean combinations of threshold-k, majority, and equivalence modulo m. All stably computable predicates are shown to be in NL. Assuming uniform random sampling of interacting pairs yields the model of conjugating automata. Any counter machine with O(1) counters of capacity O(n) can be simulated with high probability by a conjugating automaton in a population of size n. All predicates computable with high probability in this model are shown to be in P; they can also be computed by a randomized logspace machine in exponential time. Several open problems and promising future directions are discussed.

We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1))(log log n + k/2 + log k + log 1 ), where is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as < 1/(k log n)). An additional advantage of our constructions is their simplicity.

We explore the computational power of networks of small resource-limited mobile agents. We define two new models of computation based on pairwise interactions of finite-state agents in populations of finite but unbounded size. With a fairness condition on interactions, we define the concept of stable computation of a function or predicate, and give protocols that stably compute functions in a class including Boolean combinations of threshold-k, parity, majority, and simple arithmetic. We prove that all stably computable predicates are in NL. With uniform random sampling of pairs to interact, we define the model of conjugating automata and show that any counter machine with O(1) counters of capacity O(n) can be simulated with high probability by a protocol in a population of size n. We prove that all predicates computable with high probability in this model are in P ∩ RL. Several open problems and promising future directions are discussed.Abstract Devices]: Modes of Computation-parallelism and concurrency,

All comments are subject to release under the Freedom of Information Act (FOIA).ii Reports on Computer Systems TechnologyThe Information Technology Laboratory (ITL) at the National Institute of Standards and Technology (NIST) promotes the U.S. economy and public welfare by providing technical leadership for the Nation's measurement and standards infrastructure. ITL develops tests, test methods, reference data, proof of concept implementations, and technical analyses to advance the development and productive use of information technology. ITL's responsibilities include the development of management, administrative, technical, and physical standards and guidelines for the cost-effective security and privacy of other than national security-related information in federal information systems. AbstractIn recent years, there has been a substantial amount of research on quantum computersmachines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography (also called quantum-resistant cryptography) is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. This Internal Report shares the National Institute of Standards and Technology (NIST)'s current understanding about the status of quantum computing and post-quantum cryptography, and outlines NIST's initial plan to move forward in this space. The report also recognizes the challenge of moving to new cryptographic infrastructures and therefore emphasizes the need for agencies to focus on crypto agility.

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