Trong tương lai chúng tôi có thể sẽ phát triển ứng dụng bằng cách mở rộng phạm vi sang một trường bất kỳ với đầy đủ các chức năng cần thiết, nghiên cứu các giải thuật tối ưu thay thế các giải thuật hiện tại và đặc biệt là tìm cách khai thác có hiệu quả kho cơ sở dữ liệu đã xây dựng được bằng cách sử dụng kết quả vào các ứng dụng thực tiễn, đặc biệt là trong các lĩnh vực mã hóa-mật mã và an toàn thông tin.
TÀI LIỆU THAM KHẢO
Tiếng Việt
[1] Bùi Doãn Khanh, Nguyễn Đình Thúc, Trần Đan Thư (2005), Cơ sở lý thuyết số
trong an toàn – bảo mật thông tin, Nhà xuất bản giáo dục, 2005.
Tiếng Anh
[2] A.J. Menezes, P. van Oorschot and S. Vanstore (1996), Handbook of Applied
Cyptography, CRC Press 1996.
[3] Alfred J. Menezes, I.F. Blake, X. Gao, R.C. Mullin, S.A. Vanstone and T. Yaghoobian (1993), Applications of Finite Fields, Kluwer Academic Publishers, Boston Dordrecht-Lancaster, 1993.
[4] E. Selmer (1956), On the Irreducibility of Certain Trinomials, Math. Scandinavica, 4, 1956, 287-302.
[5] E.R. Rodemich and H. Rumsey Jr. (1968), Primitive polynomials of high
degree, Math. Comp., 22 (1968) pp. 863-865.
[6] Erich Kaltofen (1992), Polynomial Factorization 1987-1991, Proc. Latin’92, I. Simon (Ed.), Springer Lect. Notes Comput. Sci., vol 583, pp. 294-313 (1992). [7] Gary L. Miller (1975), Riemann’s Hypothesis and Tests for Primality, Research
Report CS-75-27, University of Waterloo, Waterloo, Ontario, Canada, October 1975.
[8] I.F. Gao and R. J. Lambert (1994), Constructive problems for irreducible
polynomials over finite fields, in Information Theory and Applications (A.
[9] I.F. Blake, S. Gao and R.J. Lambert (1996), Construction and distribution
problems for irreducible trinomials over finite fields, Applications of Finite
Fields, ed., D. Gollmann, Oxford, Clarendon Press, 1996, 19-32.
[10] J. von zur Gathen (1986), Irreducible polynomials over finite fields, Computer Sciences Technical Report No. 188/86, University of Toronto.
[11] J. von zur Gathen and J. Gerhard (1999), Modern Computer Algebra, Cambridge University Press, 1999.
[12] J. von zur Gathen and V. Shoup (1992), Computing Frobenius maps and
factoring polynomials, Computational Complexity, 2 (1992), pp. 58-63.
[13] J. von zur Gathen (1999), Irreducible trinomials over finite fields, Proc. Amer. Math. Soc. 127 (6) (1999), 1615-1623.
[14] J. Watson (1962), Primitive polynomials (mod 2), Math. Comp. 16 (1962), 368- 369.
[15] Joel V. Brawley, Shuhong Gao and Donald Mills (1991), Computing Composed
Products of Polynomials, Mathematics Subject Classification, 1991.
[16] K.O. Geddes, S.R. Czapor and G. Labahn (1992), Algorithms for Computer
Algebra, Kluwer Academic Publishers, 1992.
[17] L. Carlitz (1970), Factorization of a special polynomial over a finite field, Pac. J. Math., 32 (1970) pp. 603-614.
[18] L.M. Adleman and H.W. Lenstra, Jr. (1986), Finding irreducible polynomials
over finite fields, in Proceedings of the 18th Annual ACM Symposium on Theory of Computing (STOC), Berkeley, 1986, pp. 350-355.
[19] M. Huang (1985), Riemann hypothesis and finding roots over finite fields, Proceedings of the 17th Annual ACM Symposium on Theory of Computing (1985), 121-130.
[20] M.K. Kyuregyan (2004), Iterated constructions of irreducible polynomials over
finite fields with linearly independent roots, Finite Fields Appl. 10 (2004) 323-
431.
[21] M.K. Kyuregyan, M.G. Evoyan (2009), Two methods for constructing
irreducible polynomials over finite fields based on polynomial composition,
proceedings of CSIT 2009, Yerevan, Armenia.
[22] Melsik K. Kyuregyan, Gohar M. Kyureghyan (2009), Irreducible Compositions
of Polynomials over Finite Fields, Otto-von-Guericke University, Armenia.
[23] Nidal Ali (2009), On the Irreducibility for Composition of Polynomials, International Mathematical Forum, 4, 2009, no. 40, 2001-2008.
[24] P. Camion (1983), Improving an algorithm for factoring polynomials over a
finite field and constructing large irreducible polynomials, IEEE Transactions
on Informtion Theory, vol. 29, no. 3, pp. 378-385.
[25] R. Lidl and H. Niederreiter (1987), Finite Fields, Cambridge University Press, 1987.
[26] R. Lidl, H. Niederreiter (1986), Introduction to finite fields and their
applications, Cambridge University Press, 1986.
[27] R. P. Brent, S. Larvala and P. Zimmermann (2003), A fast algorithm for testing
reducibility of trinomials mod 2 and some new primitive trinomials of degree 3021377, Math. Comp. 72 (2003), 1443-1452.
[28] Richard P. Brent and Paul Zimmermann (2010), The great trinomial hunt, Notices of the American Mathematical Society, 4 January 2010.
[29] R.G. Swan (1962), Factorization of polynomials over finite fields, Pac. J. Math.,
12 (1962) 1099-1106.
[30] Ramzi A. Haraty (2004), A Comparative Study of RSA Based Digital Signature
Algorithms, Proceedings of the Sixth International Conference on Enterprise
Information Systems (ICEIS 2004), vol. 3, pp. 79-84, 2004.
[31] Shuhong Gao and Daniel Panario (1997), Tests and Constructions of Irreducible
Polynomials over Finite Fields, To appear in Foundations of Computional
Mathematics, F. Cucker and M. Shub (Eds.), Springer 1997, 346-361.
[32] Thomas W. Judson (2009), Abstract Algebra Theory and Applications, Stephen F. Austin State University, February 14, 2009.
[33] Tom Hansen and Gary L. Mullen (1992), Primitive polynomials over Finite Fields,
[34] Victor Shoup (2008), A Computational Introduction to Number Theory and Algebra, New York 2008.
[35] Victor Shoup (1996), A New Polynomial Factorization Algorithm and Its
Implementation, To appear in Jornal of Symbolic Computation, 1996.
[36] Victor Shoup (1994), Fast Construction of Irreducible Polynomials Over Finite
Fields, J. Symbolic Comput. 17 (1994), no. 5, 371-391.
[37] Victor Shoup (1990), New Algorithms for Finding Irreducible Polynomials over