Primality Proving (GIMPS), Computational Number Theory, Cryptology, Biometry, Complex and numerical analysis.
Preda Mihailescu has proved a theorem that is likely to lead to a solution of Catalan\'s conjecture, a venerable problem involving relationships among whole numbers.
P.Mihailescu. \"Fast Generation of Provable Primes using Search in Arithmetic Progressions\", Proceedings CRYPTO 94, Lecture Notes in Computer Science vol 939, Springer 1994, pp. 282-293.
P.Mihailescu, D.Muster. \"Efficient Generation of Elliptic Curves for Cryptographic use. A Variable Field Approach\", preprint, 1996.
P.Mihailescu. \"Low Exponent and Related Messages Elliptic Curve RSA Attacks\", preprint 1996.
P.Mihailescu. \"Cyclotomy Primality Proving - Recent Developments\", Proceedings of the III Applied Number Theory Seminar, ANTS III, Portland, Oregon 1998. Lecture Notes in Computer Science vol xxx.
P.Mihailescu. \"Recent Developments in Primality Proving\" to appear in `High Performance Symbolic Computing\'.
P.Mihailescu, C.Nash. \"Some Facts for Lucas - Lehmer Primality Testers\", preprint, 1999.
P.Mihailescu, F.Morain. \"Dual Elliptic Primes and Cyclotomy Primality Proving\", presented at the 6-th Conference of the Canadian Society for Number Theory, Winnipeg, 1999.
Preda Mihailescu, Primary cyclotomic units and a proof of Catalan\'s conjecture, manuscript (April 2002).