| 摘要 |
PROBLEM TO BE SOLVED: To generate a key at a high speed. SOLUTION: In the key generation device of an elliptical curve cryptograph for deciding a modulus (p) and coefficients (a), (b) of an elliptical curve y2=x3+ ax+b (mod p), putting a=0, and by inputting b=±1, random numbers U, V satisfying U≡5 (mod 12) and V≡3 (mod 12), or U≡11 (mod 12) and V≡9 (mod 12) are createdcalculating (12) p=U2-UV+V2. If (p) is not a prime number, Uand V are created again, and moreover, it is judged (16) whetheror not (q) is a prime number, by calculating (14) S=p+1-b(U+V),and further calculating (15) q=S/(8+4b). If (q) is not aprime number, U and V are created again, and if p and q are bothprime numbers, the (p) is outputted.
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