A table of primitive binary polynomials

Živković, Miodrag

doi:10.1090/S0025-5718-1994-1201073-4

A table of primitive binary polynomials
HTML articles powered by AMS MathViewer

by Miodrag Živković PDF

Math. Comp. 62 (1994), 385-386 Request permission

Abstract:

For those $n < 5000$ for which the factorization of ${2^n} - 1$ is known, the first primitive trinomial (if such exists) and a randomly generated primitive 5- and 7-nomial of degree n in ${\text {GF}}(2)$ are given.

References

John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman, and S. S. Wagstaff Jr., Factorizations of $b^n \pm 1$, 2nd ed., Contemporary Mathematics, vol. 22, American Mathematical Society, Providence, RI, 1988. $b=2,3,5,6,7,10,11,12$ up to high powers. MR 996414, DOI 10.1090/conm/022
Yoshiharu Kurita and Makoto Matsumoto, Primitive $t$-nomials $(t=3,5)$ over $\textrm {GF}(2)$ whose degree is a Mersenne exponent $\le 44497$, Math. Comp. 56 (1991), no. 194, 817–821. MR 1068813, DOI 10.1090/S0025-5718-1991-1068813-6

Editor’s corner

7

Arjen K. Lenstra and Mark S. Manasse, Factoring with two large primes (extended abstract), Advances in cryptology—EUROCRYPT ’90 (Aarhus, 1990) Lecture Notes in Comput. Sci., vol. 473, Springer, Berlin, 1991, pp. 72–82. MR 1102472, DOI 10.1007/3-540-46877-3_{7}
Willi Meier and Othmar Staffelbach, Fast correlation attacks on certain stream ciphers, J. Cryptology 1 (1989), no. 3, 159–176. MR 1007217, DOI 10.1007/BF02252874
Eugene R. Rodemich and Howard Rumsey Jr., Primitive trinomials of high degree, Math. Comp. 22 (1968), 863–865. MR 238813, DOI 10.1090/S0025-5718-1968-0238813-1
Wayne Stahnke, Primitive binary polynomials, Math. Comp. 27 (1973), 977–980. MR 327722, DOI 10.1090/S0025-5718-1973-0327722-7
Robert C. Tausworthe, Random numbers generated by linear recurrence modulo two, Math. Comp. 19 (1965), 201–209. MR 184406, DOI 10.1090/S0025-5718-1965-0184406-1
E. J. Watson, Primitive polynomials $(\textrm {mod}\ 2)$, Math. Comp. 16 (1962), 368–369. MR 148256, DOI 10.1090/S0025-5718-1962-0148256-1
Neal Zierler and John Brillhart, On primitive trinomials $(\textrm {mod}\ 2)$, Information and Control 13 (1968), 541–554. MR 237468, DOI 10.1016/S0019-9958(68)90973-X
Neal Zierler and John Brillhart, On primitive trinomials $(\textrm {mod}\ 2)$. II, Information and Control 14 (1969), 566–569. MR 244204, DOI 10.1016/S0019-9958(69)90356-8
Neal Zierler, Primitive trinomials whose degree is a Mersenne exponent, Information and Control 15 (1969), 67–69. MR 244205, DOI 10.1016/S0019-9958(69)90631-7