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# SCALAR MULTIPLIER AND SCALAR MULTIPLICATION PROGRAM

外国特許コード F110002875 S2009-0170-C0 2011年5月6日 世界知的所有権機関（ＷＩＰＯ） 2009JP070127 WO 2010/061951 平成21年11月30日(2009.11.30) 平成22年6月3日(2010.6.3) 特願2008-305121 (2008.11.28) JP SCALAR MULTIPLIER AND SCALAR MULTIPLICATION PROGRAM Provided are a scalar multiplier which makes it possible to execute scalar multiplication at high speed, and a scalar multiplication program. When calculating a scalar multiplication [s]P of a rational point P of an additive group E (Fp) comprising rational points on an elliptical curve wherein a characteristic p, an order r, and a trace t of a Frobenius endomorphism map at an embedded degree k = 12 using an integer variable .chi. are provided as p(.chi.)=36.chi.4-36.chi.3+24.chi.2-6.chi.+1, r(.chi.)=36.chi.4-36.chi.3+18.chi.2-6.chi.+1=p(.chi.)+1-t(.chi.), t(.chi.)=6.chi.2+1, assuming that the twist degree d is 6 and a positive integer e is 2 where k=d * e, [s]P=([A].phi.'2+[B])P is calculated using the Frobenius map .phi.'2 where [p2]P=.phi.'2(P). NATIONAL UNIVERSITY CORPORATION OKAYAMA UNIVERSITY NOGAMI, Yasuyuki SAKEMI, Yumi MORIKAWA, Yoshitaka G09C   1/00      あらかじめ決められた方式によって，符号または符号群を入れかえ，またはそれらと他を置き換えることによって，与えられた符号の順序，例．理解できる原文，を理解できない符号の順序に交換する装置または方法 AE(UTILITY MODEL),AG,AL(UTILITY MODEL),AM(PROVISIONAL PATENT)(UTILITY MODEL),AO(UTILITY MODEL),AT(UTILITY MODEL),AU,AZ(UTILITY MODEL),BA,BB,BG(UTILITY MODEL),BH(UTILITY MODEL),BR(UTILITY MODEL),BW(UTILITY MODEL),BY(UTILITY MODEL),BZ(UTILITY MODEL),CA,CH,CL(UTILITY MODEL),CN(UTILITY MODEL),CO(UTILITY MODEL),CR(UTILITY MODEL),CU(INVENTOR'S CERTIFICATE),CZ(UTILITY MODEL),DE(UTILITY MODEL),DK(UTILITY MODEL),DM,DO(UTILITY MODEL),DZ,EC(UTILITY MODEL),EE(UTILITY MODEL),EG(UTILITY MODEL),ES(UTILITY MODEL),FI(UTILITY MODEL),GB,GD,GE(UTILITY MODEL),GH(UTILITY CERTIFICATE),GM,GT(UTILITY MODEL),HN,HR(CONSENSUAL PATENT),HU(UTILITY MODEL),ID,IL,IN,IS,JP(UTILITY MODEL),KE(UTILITY MODEL),KG(UTILITY MODEL),KM,KN,KP(INVENTOR'S CERTIFICATE)(UTILITY MODEL),KR(UTILITY MODEL),KZ(PROVISIONAL PATENT)(UTILITY MODEL),LA,LC,LK,LR,LS(UTILITY MODEL),LT,LU,LY,MA,MD(UTILITY MODEL),ME,MG,MK,MN,MW,MX(UTILITY MODEL),MY(UTILITY-INNOVATION),MZ(UTILITY MODEL),NA,NG,NI(UTILITY MODEL),NO,NZ,OM(UTILITY MODEL),PE(UTILITY MODEL),PG,PH(UTILITY MODEL),PL(UTILITY MODEL),PT(UTILITY MODEL),RO,RS(PETTY PATENT),RU(UTILITY MODEL),SC,SD,SE,SG,SK(UTILITY MODEL),SL(UTILITY MODEL),SM,ST,SV(UTILITY MODEL),SY,TJ(UTILITY MODEL),TM(PROVISIONAL PATENT),TN,TR(UTILITY MODEL),TT(UTILITY CERTIFICATE),TZ,UA(UTILITY MODEL),UG(UTILITY CERTIFICATE),US,UZ(UTILITY MODEL),VC(UTILITY CERTIFICATE),VN(PATENT FOR UTILITY SOLUTION),ZA,ZM,ZW,EP(AT,BE,BG,CH,CY,CZ,DE,DK,EE,ES,FI,FR,GB,GR,HR,HU,IE,IS,IT,LT,LU,LV,MC,MK,MT,NL,NO,PL,PT,RO,SE,SI,SK,SM,TR),OA(BF(UTILITY MODEL),BJ(UTILITY MODEL),CF(UTILITY MODEL),CG(UTILITY MODEL),CI(UTILITY MODEL),CM(UTILITY MODEL),GA(UTILITY MODEL),GN(UTILITY MODEL),GQ(UTILITY MODEL),GW(UTILITY MODEL),ML(UTILITY MODEL),MR(UTILITY MODEL),NE(UTILITY MODEL),SN(UTILITY MODEL),TD(UTILITY MODEL),TG(UTILITY MODEL)),AP(BW(UTILITY MODEL),GH(UTILITY MODEL),GM(UTILITY MODEL),KE(UTILITY MODEL),LS(UTILITY MODEL),MW(UTILITY MODEL),MZ(UTILITY MODEL),NA(UTILITY MODEL),SD(UTILITY MODEL),SL(UTILITY MODEL),SZ(UTILITY MODEL),TZ(UTILITY MODEL),UG(UTILITY MODEL),ZM(UTILITY MODEL),ZW(UTILITY MODEL)),EA(AM,AZ,BY,KG,KZ,MD,RU,TJ,TM)