solve.py

from sage.all import *

key = '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'
ct = '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'
mat = []
for i in range(0, len(key), 100):
    temp = []
    curr = key[i:i+100]
    for ch in curr:
        temp.append(ord(ch) - ord('a'))
    mat.append(temp)
R = IntegerModRing(26)
inv_key = matrix(R, mat).inverse()
msg = ''
for i in range(0, len(ct), 100):
    num_ct = []
    for ch in ct[i:i+100]:
        num_ct.append(ord(ch) - ord('a'))
    vector_ct = vector(num_ct)
    pt = inv_key*vector_ct
    for num in pt:
        msg += chr(int(num) + ord('a'))
print(msg)