Elliptic curve transformation device, utilization device and utilization system

摘要

A parameter receiving unit receives parameters alpha and beta of an elliptic curve E and an element G=(x0,y0) on the elliptic curve E. A transformation coefficient acquiring unit calculates a transformation coefficient t which is an element on a finite field GF(p) so that t &circ& 4 x alpha (mod p) will not exceed 32 bits. A transformed elliptic curve calculating unit calculates parameters alpha ' and beta ' of an elliptic curve Et that is defined over the finite field GF(p) and expressed as Et: y' &circ& 2=x' &circ& 3+ alpha ' x x'+ beta ', and calculates an element Gt=(xt0,yt0) that is present on the elliptic curve Et and corresponds to the element G, as follows: $$ $ $ $ A\; parameter\; sending\; unit\; sends\; the\; parameters\; alpha\; \text{'}\; and\; beta\; \text{'}\; and\; the\; element\; Gt\; to\; an\; external\; device.$$$$$