12 ?r 16, s????????t?? ???r??s??? t?? ?r???????t? t??t t?? ?r??r ?? P 0 ?s s ,
P 1 ) X ? t?? X????r????t? ?? id · P 1 , ??? g j = (jP 1 ) X ,
?? ??r? t?? ??rr?s??????? ??tr? a[q] ?? ?? ?rr?? t? s?????? ? ?r??? t??t ??t ????s t? ?? ????r??? ??t r ?? t?? s?????st ?r??? ??t ???????? d? ???? q | id ± j ??? q = id ± j ??????s q = (id ± j)/s ??t? s ? r s???? id ± j ? d, t??s q ? (id ± j)/r. ????? ?????s?t? ?????s ?? id±j ??t? i ? i 1 ??? ????r ???? ?r???s ?? t? ?(i 1 d+d (i, j)????r ??s? ????rs ? s?????r ?r??? q ? ?s ? ?????s?t? ?????? t??? a, r? ?s??? (i, j)????rs ??t? ??r?? i, ?? ??ss????? ?????? t??t ?? ??? ???r??s? t?? ???? i 0 ,
?? ??r? a[id ? j] ??st???? ???s ???? ??? ?r???s ?? ]B 1 , B 2 ] ?r? ????r??? ??? ???? ??t? ?? (i, j)????r ??t? t?? ??r??st ??ss???? i ? i 1 ? ,
X 1 ) ??r i 0 ? i ? i 1 . ?? ?? s?? ?? ???? ????s ?????s t??t ????r?t? ??? r?q??r?? ?????s ?? id ??? j? ?? tr? t? ??? ? s??rt ????s ????? t??t ?r?????s ??? r?q??r?? ?????s t? s??? ?r??? ???r?t???s ????? ?r? ??st?? ?s???????? ??r ???? ?? ?? ???? ?? ????????r ?r???? ????s ?????s ??r ?????s ?? ?? ?r?t???t?? ?r??r?ss??? ?r? ??rt?????r?? s?????? s???? t?? ????r???? ?? s????ss??? t?r?s ?s ???st??t? ?? ??r??? ???? t? st?rt t?? ????? ??t? t?r?s t??t ????r?t? t?? ,
?? ??? t?? ?????s ?? id ??t? i 0 ? i ? i 1 , ?? ???? t? ??? d ,
?? X 1 = X 2 ? ??t X 1 /Z 1 = X 2 /Z 2 , ???r? Z 1 ??? Z 2 ?r? ????r???? ??t ?q???? s? t?? X????r????t?s ?? t??s? ????ts ?????t ?? ?s?? ??r??t?? t? ????? t?? ??sts f i ??? g j ? ???r? ?r? s???r?? ???s t? ???r???? t??s ??str??t???? ????r?? ??t??rs ???r, )?T ((f i ) X (g j ) Z ? (g j ) X (f i ) Z ) ,
???r ??? ?s?s 3 ??????r ???t??????t???s ??st??? ?? 1 ?sQ i ) X ? (R j ) X (mod p), ?s ??s?r??? ??? ?? ??? s?t f i = (Q i ) X ??? g j = (R j ) X . ?? s????st t?? ??t???s ??r t??s? ??? ?s t? s?t ??? Z????r????t?s t? 1 (mod N ) ??? (X :: Z) = (XZ ?1 :: 1) ,
?ts idP 1 ??s ? r???t????? ??r?? s??r? ?? t??s ???r?? s????st??? t??t ? ????? ??r d s??? t??t B 2 /(d?(d)) ?s ???s?r t? 1 ????t r????? t?? t? ???s? ???r?s s????st t??t ? s??t??r? s??t??r? ??r ??r? s???? ?????rs ??t? ??? B 1 ??? B 2 ?????s? ??P???? ?s ??t?????? ??r s??r????? ??r?? ?r??? ???t?rs ??s ??r?? ?s r??s?????? ??ss???? ??t? ???? ?? ?????rs ?? ?t ???st ? ????r?? ????ts s??? ?? ?s? ?? ?s???t?t?????? ??st ????r?t??s ?? ??rt?????r ?? st??? ?? s?? ????? ??r ??r? s ,
??????r? ?? ??s? t?? ?r??? ?????r?s?? ?? t?? ??tt?r ???r?? ???? t?? ??st ?? t?? ?P?? ?r t?? ?P?? r?s???t?????? ?r? ???s???r??? ??? r?s??ts s??? t??t ? s??t??r? ,
?s???t?? ??? ????r t??? 20 ??r??s s???? t? ?s? t????s? ????s???t???ss ??t? ???? ?r???????t?? ?????? t??s ?st???t? s??????t ??ss???st??? ?ss?, p.40 ,