| 摘要 |
PROBLEM TO BE SOLVED: To provide a hyperelliptic curve parameter fast generating device for generating parameters of a genus 2 hyperelliptic curve suitable for hyperelliptic curve encipherment. SOLUTION: This device generates a genus 2 hyperelliptic curve at random; obtains a numerator coefficient of a zeta function to the hyperelliptic curve with a characteristic of a defined body adopted as a modulo; decides a coefficient value from a condition to satisfy the coefficient and the number of digits; calculates the number of digits of the hyperelliptic curve on an expanded body using Weil's prediction; and repeats discrimination of safety to the number of digits. A calculation amount can be reduced compared with direct calculation of the numerator of the zeta function, and a storage amount can be reduced due to recursive operation. Thus, it becomes possible to efficiently calculate the number of digits, and generate a hyperelliptic curve on a Galois field having a larger prime number as a characteristic.
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