Finite field computing device, finite field computing method, program, and recording medium

摘要

E (R (i, 0), ..., R (i, K- operations over finite original R finite field GF of the K (p ^m) (i, k) ∈GF for (p ^m) The calculated efficiently (R (i, 0), (i, a K-1)) ..., R operation Π _{i = 0}^N-1 e in assuming that 1)). Polynomial poly indicating respectively obtained in the course of (R (i, 0), (i, K-1) ..., R) operations for each e i, d the following extension field finite field GF (p ^m) is multiplied by ((i, K-1) (i, 0), ..., R R) and each other, and accumulating the multiplication result of the multiplication. (R (i, 0), (i, K-1) ..., R) the polynomial poly is a mapping from the original finite field GF entered the (p ^m), the terms of at least some coefficients are zero. Run the combinations of i different similar processing is performed (R (i, 0), (i, K-1) ..., R) operations Π _{i = 0}^N-1 e with the result.