Mathematical Sciences: Topics in Number Theory
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There are three foci of this research.  The first one                      concerns Artin's conjecture for composite numbers.  That is, what               can one say about the elements of maximal order modulo a                        composite number.  The second problem concerns finding efficient                discrete logarithm algorithms and efficient algorithms for                      factoring large numbers.  The principal investigator and his                    colleagues have built a special purpose computer for implementing               his quadratic sieve algorithm for factoring large integers.  He                 will study the practical aspects of implementing on this and                    other computers linear and cubic sieve algorithms which are                     promising practical methods and he will also attempt to find new                methods, especially for the discrete logarithm problem.  The                    third problem concerns elliptic curves over finite fields and                   their applications to primality testing.  It is hoped that a                    polylog algorithm for constructing an elliptic curve with a                     prescribed order modulo a given prime can be found.  This is                    known from a result of the principal investigator to give a                     polylog primality test.                                                              This research is in the area of computational number theory                with a heavy concentration on algorithms for factoring integers                 and testing whether they are primes.
{'FirstName': 'Carl', 'LastName': 'Pomerance', 'PI_MID_INIT': 'B', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Carl B Pomerance', 'EmailAddress': 'carl.b.pomerance@Dartmouth.EDU', 'NSF_ID': '000159960', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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[{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}, {'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}, {'Code': '2860', 'Text': 'THEORY OF COMPUTING'}, {'Code': '2865', 'Text': 'NUMERIC, SYMBOLIC & GEO COMPUT'}]
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