| 摘要 |
PURPOSE: A method for forming recurrence formula is provided to apply to a public key encryption system capable of forming trapdoor one-way function easily solved under certain conditions in use of higher order linear recurrence defined on finite field. CONSTITUTION: A method for forming recurrence formula comprises a basic setting process(100) and a recurrence formula setting process(200). A selected natural number t ranges more than 64 and not more than 64. Decimal fraction p that equals 2¬t-c and natural number corresponding to the decimal fraction are sought. Decimal fraction p in 160 bits is sought that divides p¬6-p¬3+1 and does not divide p¬3-2. Element g of finite field GF(p¬18) is voluntarily selected. In case that h equals p¬18-1, g¬h/q equals 1 or not is determined. When the result is not 1, element g of finite field GF(p¬18) is voluntarily selected again, and when the result is 1, recurrence formula Vn(P)=tr(g¬n) where P equals tr(g) is sought and the value is outputted.
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