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- q = 1021
- K = GF(q)
- E = EllipticCurve(K, [905, 100])
- print(E)
- print(f"Group order is: {E.cardinality()}")
- P = E(1006, 416)
- assert P.additive_order() == E.cardinality()
- Q = E(612, 827)
- matches = {}
- for j, m in factor(E.cardinality()):
- assert m == 1
- P_j = int(E.cardinality() / j) * P
- Q_j = int(E.cardinality() / j) * Q
- for k in range(j):
- if k * P_j == Q_j:
- #print(f"Match found for j = {j}!")
- matches[j] = k
- break
- k = crt(list(matches.values()), list(matches.keys()))
- print(f"k = {k} mod {E.cardinality()}")
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