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Computing square, cube and n-th roots in general, in finite fields, are important computational problems with significant applications to cryptography. One interesting approach to computational problems is by using polynomial representations. Agou, Del´eglise and Nicolas proved results concerning the lower bounds for the length of polynomials representing square roots modulo a prime p. We generalize the results by considering n-th roots over finite fields for arbitrary n > 2.
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참고문헌 (23)
참고문헌 신청
A. Tonelli / 1891 / Bemerkung ¨uber die Aufl¨osung quadratischer Congruenzen, Nachrichten von der K¨oniglichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universit¨at z
A. Winterhof / 2002 / Polynomial interpolation of the discrete logarithm / Des. Codes Cryptogr 25 (1) : 63 ~ 72
D. Coppersmith / 2000 / On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping / J. Cryptology 13 (3) : 339 ~ 360
D. H. Lehmer / 1969 / Studies in number theory, volume 6 of MAA Studies in Mathematics / Prentice-Hall : 117 ~ 151
D. Shanks / 1972 / Five number-theoretic algorithms, Proceedings of the Second Manitoba Conference on Numerical Mathematics / Congressus Numerantium 7 : 51 ~ 70
A. Winterhof / 2002 / Polynomial interpolation of the discrete logarithm / Des. Codes Cryptogr 25 (1) : 63 ~ 72
D. Coppersmith / 2000 / On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping / J. Cryptology 13 (3) : 339 ~ 360
D. H. Lehmer / 1969 / Studies in number theory, volume 6 of MAA Studies in Mathematics / Prentice-Hall : 117 ~ 151
D. Shanks / 1972 / Five number-theoretic algorithms, Proceedings of the Second Manitoba Conference on Numerical Mathematics / Congressus Numerantium 7 : 51 ~ 70
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