Kernel: SageMath (stable)
In [20]:
In [2]:
5194994355689918998948375534214446732680520861354545436708195599748240133397592369029790575386462392596047460303979357256019325902210604204031
True
In [3]:
5194994355689918998948375534214446732680520861354545436708195599748240133397592369029790575386462392596047460303979357256019325902210604204031
True
In [4]:
229036002299580430864382545454534508354326861103924243886156739364802216156884115227899761308451782617967270366579042488442498132519929653698943465033139313565151784203127224027578369
In [5]:
CPU times: user 39.9 ms, sys: 0 ns, total: 39.9 ms
Wall time: 66.8 ms
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We are going to use p where p = 2^5 * 3^6 * 5 + (-1)
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Alice's secret Key is of order 3^4 where the biggest multiplicity of 3-subgroup is 6
Bob's secret Key is of order 2 where the biggest multiplicity of 2-subgroup is 5
CPU times: user 26.7 ms, sys: 542 µs, total: 27.3 ms
Wall time: 52.3 ms
In [8]:
CPU times: user 21.2 ms, sys: 8.16 ms, total: 29.4 ms
Wall time: 33.2 ms
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27
CPU times: user 4.03 ms, sys: 7 µs, total: 4.04 ms
Wall time: 3.89 ms
In [10]:
Isogeny of degree 27 from Elliptic Curve defined by y^2 = x^3 + 116638*x over Finite Field of size 116639 to Elliptic Curve defined by y^2 = x^3 + 82968*x + 70354 over Finite Field of size 116639
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CPU times: user 4.91 ms, sys: 144 µs, total: 5.05 ms
Wall time: 4.22 ms
In [13]:
CPU times: user 5.59 ms, sys: 3.61 ms, total: 9.2 ms
Wall time: 9.46 ms
In [14]:
CPU times: user 20.9 ms, sys: 142 µs, total: 21 ms
Wall time: 19.2 ms
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Have Alice and Bob arrived at the same curve?
True
In [16]:
Their shared secret key is 111162
In [17]:
116639
In [18]:
In [19]:
(1728, 90546, 111162)
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