Introduction Elliptic curve cryptosyste#2 (ECC) have be#2 wide#0 re#e#0"]W since 1985 [3], [6].The se##]:" y ofthe ECC isbase# onthe di#culty of solving adiscre#] logarithm proble# ove r e#02I0] curve#r The ECC is be#2F0 e# to have highe# se#e#] y thanthe RSA sche#2 [8],e#],]2 for spe#]I: e#]I:WL] curve#r Afe# attacks have be#2 prop for such spe#:WI curve# including anomalous e#nomalo curve# de#]L" ove r aprime fie#m F p . Re#2W tly, Ruck [9 ,Se#FN: [13 , Smart [14 , and Satoh-Araki [10 , [11 prop ose# e#e#]: t algorithms for solving a discre# logarithmproble# ove r anomalouse#o liptic curve# in polynomialtime# The## four algorithms are classifie# into two approache#r (1) numb e# the#WFN] approach by Satoh-Araki and Smart and (2)alge#F0F2 ge#e#F0F2] approach bySe#"0: and Ruck [1 . We ge#" e#e#"N2 Satoh-Araki-Smart algorithm and Ruck algorithm by applyingthe# toe#]:"2I2 curve# de#v]2 ove r the ring Z/nZ,re#: e##:: e##<F12.0