National Security Agency

About: National Security Agency is a government organization based out in Fort George Meade, Maryland, United States. It is known for research contribution in the topics: Signal & Encryption. The organization has 393 authors who have published 485 publications receiving 15916 citations. The organization is also known as: NSA & N.S.A..

A Swan-like Theorem

Abstract: Richard G. Swan proved in 1962 that trinomials x^{8k} + x^m + 1 with 8k > m have an even number of irreducible factors, and so cannot be irreducible. In fact, he found the parity of the number of irreducible factors for any square-free trinomial in F_2[x]. We prove a result that is similar in spirit. Namely, suppose n is odd and f(x) = x^n + Sum_{i in S} x^i + 1 in F_2[x], where S subset {i : i odd, i < n/3} Union {i : i = n (mod 4), i < n} We show that if n = +-1 (mod 8) then f(x) has an odd number of irreducible factors, and if n = +=3 (mod 8) then f(x) has an even number of irreducible factors. This has an application to the problem of finding polynomial bases {1,a,a^2,...a^{n-1}} of F_{2^n} such that Tr(a^i) = 0 for all 1 <= i < n.

Device for and method of identifying minimum candidate codewords for list decoder

Abstract: A device and method of determining candidates to decode by receiving a message, selecting m, identifying m voltages in message near zero volts, generating binary version of message, generating candidates that are variations of the binary message by varying the m positions, multiplying a modified binary message by the parity check matrix of the message, generating a matrix of the rows of the parity check matrix corresponding to the m positions, determining a rank v of the matrix, eliminating rows that are not linearly independent, determining if the sixth step result is in a span of the ninth step result, if so then there are 2 m-1 -2 m-v (m−1) candidates, where the candidates can multiply the seventh step result to get the sixth step result and candidates with odd weights more than one Hamming distance from the candidates, otherwise there are 2 m-1 candidates having odd weight.

Methods of pairwise combinations in streaming data

Abstract: A method is disclosed for pairwise combination of data elements of an input data stream. Steps are performed for each data element. A master controller reads the data from the stream and increments a counter. A register is instantiated, holding at least two words of memory and corresponding to the counter, by updating a register map and sending a message to a target processor via a logical pathway. The message instructs the target processor to create the register in local memory, including first and second memory locations, and an index corresponding to a value i. The target processor copies the data into the first memory location. For every other register corresponding to a value less than i, the other register copies the data into the second memory location and outputs a unique pair, constructed from the data elements stored at the first and second memory locations, to a database.

Method of identifying connected data in relational database

Abstract: A method of identifying connected data in relational database by receiving relational database, receiving data components from relational database, initializing a first table and a second table with data identifiers and connection information, initializing a third table with data identifiers, initializing a transition table; replacing each entry in the third table with a user-definable relationship of its corresponding identifier in the second table, its corresponding connected data component identifier in the second table, and the identifier to which an equivalent identifier transitioned in the transition table; updating the transition table, updating the second table, returning to the replacement step if the third table changed, and, otherwise, identifying the received data components as connected that correspond to entries in the third table that are equal.