yaole
61 lines
1.4 KiB
Python
61 lines
1.4 KiB
Python
#!/usr/bin/python3
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import math
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n = 0xB640000002A3A6F1D603AB4FF58EC74449F2934B18EA8BEEE56EE19CD69ECF25
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p = 0xB640000002A3A6F1D603AB4FF58EC74521F2934B1A7AEEDBE56F9B27E351457D
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# n = 65000549695646603732796438742359905742570406053903786389881062969044166799969
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# p = 65000549695646603732796438742359905742825358107623003571877145026864184071783
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sqrt_n = int( math.sqrt(n))
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def lamb(n):
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l = pow(2,(n-1)//3, n)
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l2 = l**2%n
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return min(l,l2)
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# return max(l,l2)
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def norm(a,b):
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return int(math.sqrt(a**2 + b**2))
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l = lamb(n)
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print("lambda=",l)
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print("lambda^2=",l**2%n)
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print("")
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# eta = pow(p-2, 2*(p-1)//3,p)
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# print("eta = ", hex(eta))
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# print("eta^2 = ", hex(eta**2%p))
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s = [1,0]
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t = [0,1]
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r = [n,l]
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while r[-1] > 1:
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d = r[-2] // r[-1]
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r.append(r[-2] - r[-1]*d)
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s.append(s[-2] - s[-1]*d)
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t.append(t[-2] - t[-1]*d)
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d = r[-2] // r[-1]
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r.append(r[-2] - r[-1]*d)
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s.append(s[-2] - s[-1]*d)
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t.append(t[-2] - t[-1]*d)
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# r[-1] < sqrt_n
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print("s * n + t * l = r")
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for i in range(len(s)):
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print("{} * n + {} * lambda = {}".format( s[i], t[i], r[i]))
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print("")
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print("sqrt(n)=",sqrt_n,"\n")
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print("norm:")
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print(norm(r[-1], t[-1]))
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print(norm(r[-2], t[-2]))
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print(norm(r[-3], t[-3]))
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print("")
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print("v1,v2:")
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for i in range(len(s)):
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print(r[i], -t[i], "\n==>", norm(r[i], t[i]), r[i] < sqrt_n)
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print("")
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# print(r[-1], -t[-1])
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# print(r[-2], -t[-2])
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# print(r[-3], -t[-3])
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# print(r[-2]*t[-3]-r[-3]*t[-2]), |