Problem: [HITCTF 2021]Baby ECC
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思路
- BSGS
EXP
from sage.groups.generic import bsgs
N = 2**256-2**32-2**9-2**8-2**7-2**6-2**4-1
E = EllipticCurve(GF(N), [0, 7])
xG = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
yG = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
G = E([xG,yG])
cipher0 = E([76950424233905085841024245566087362444302867365333079406072251240614685819574 , 85411751544372518735487392020328074286181156955764536032224435533596344295845])
cipher1 = E([42965775717446397624794967106656352716523975639425128723916600655527177888618 , 32441185377964242317381212165164045554672930373070033784896067179784273837186])
cipher2 = E([26540437977825986616280918476305280126789402372613847626897144336866973077426 , 1098483412130402123611878473773066229139054475941277138170271010492372383833])
m1 = bsgs(G,cipher0,(1,1048575),operation='+')
m2 = bsgs(G,cipher1,(1,1048575),operation='+')
m3 = bsgs(G,cipher2,(1,1048575),operation='+')
print(m1,m2,m3)
n = [m1,m2,m3]
flag = "NSSCTF{" + ''.join([hex(i)[2:] for i in n])+"}"
print(flag)
总结
- 对该题的考点总结