160 lines
3.2 KiB
Python
160 lines
3.2 KiB
Python
from random import randint
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from tqdm import tqdm
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f_size = 3301
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F = GF(f_size, names=("z", ))
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f_a = list(F)
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# m = 32
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# n = 80
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m = 44
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n = 112
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# m = 72
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# n = 184
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# m = 8
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# n = 20
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# m = 2
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# n = 5
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O = random_matrix(F, (n - m), m)
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output = ""
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poly_m = []
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d = n / (m * log(f_size, 2).n())
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N = ceil(sqrt((n + 1)/4)) + 1
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print("d: ", d)
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print("N: ", N)
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z = zero_matrix(F, m, (n - m))
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for i in tqdm(range(m)):
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P1 = random_matrix(F, (n - m), (n - m))
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for j in range(0, len(P1.rows())):
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for k in range(0, j):
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P1[j, k] = 0
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P2 = random_matrix(F, (n - m), m)
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P3 = -O.T * P1 * O - O.T * P2
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for j in range(0, len(P3.rows())):
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for k in range(j+1, len(P3.rows())):
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P3[j, k] += P3[k, j]
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P3[k, j] = 0
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for i in P1:
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for j in i:
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output += hex(f_a.index(j))[2:]
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for i in P2:
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for j in i:
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output += hex(f_a.index(j))[2:]
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for i in P3:
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for j in i:
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output += hex(f_a.index(j))[2:]
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P = block_matrix([ [P1, P2], [z, P3]])
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poly_m.append(P)
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v = matrix(F, n, 1, [randint(0, 1) for i in range(n)])
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oil_basis = block_matrix(F, 2, 1, [O, identity_matrix(F, m)])
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o1 = zero_matrix(F, n, 1)
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o2 = zero_matrix(F, n, 1)
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for i in oil_basis.columns():
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o1 += F.random_element() * matrix(F, n, 1, list(i))
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o2 += F.random_element() * matrix(F, n, 1, list(i))
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o_hat1 = v + o1
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# o_hat2 = v + o2
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print("o1 :", [i[0] for i in o1])
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# print("o2 :", [i[0] for i in o2])
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print("v :", [i[0] for i in v])
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print("o1+v :", [i[0] for i in o_hat1])
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# print("o2+v :", [i[0] for i in o_hat2])
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print()
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# for P in poly_m:
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# print("oPo:", o1.T * P * o1)
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# print("vPv:", v.T * P * v)
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# print("qPq:", o_hat.T * P * o_hat)
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# correction = o_hat.T * (P.T + P) * v
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# print("oPx:", correction)
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# print("tot:", v.T * P * v + o_hat.T * P * o_hat - correction)
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# print()
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# print()
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# P = poly_m[0]
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vec = [[(o_hat1.T * (P.T + P))[0][i] for i in range(n)] for P in poly_m]
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s = [(v.T * P * v + o_hat1.T * P * o_hat1)[0][0] for P in poly_m]
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# print("s: ", (v.T * P * v + o_hat.T * P * o_hat)[0][0])
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# print("k: ", vec)
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# out = 0
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# for i in range(len(vec)):
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# out += int(vec[i]) * int(v[i][0])
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#
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# t = matrix(QQ, 1, len(vec) + 2, [int(i[0]) for i in v] + [-(out // 3301), -1])
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# print("t: ", t)
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d = n / (m * log(f_size, 2).n())
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N = ceil(sqrt((n + 1)/4)) + 1
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print("d: ", d)
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print("N: ", N)
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b1 = identity_matrix(QQ, n)
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b2 = zero_matrix(QQ, n, 1)
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b3 = matrix(QQ, m, n, [[N * int(i) for i in j] for j in vec]).T
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b4 = zero_matrix(QQ, m, n)
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b5 = zero_matrix(QQ, m, 1)
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b6 = N * f_size * identity_matrix(QQ, m)
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b7 = matrix(QQ, 1, n, [1/2]*n)
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b8 = matrix(QQ, 1, 1, [1/2])
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b9 = matrix(QQ, 1, m, [N * int(i) for i in s])
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B = block_matrix([[b1, b2, b3], [b4, b5, b6], [b7, b8, b9]])
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print(B)
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print()
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BH = B.LLL()
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BH = matrix(ZZ, 2 * BH)
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print(BH)
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for beta in tqdm(range(0, 10)):
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BH = BH.BKZ(block_size=beta + 1, fp='rr', precision=200)
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BH = 1/2 * matrix(QQ, BH)
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print(BH)
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print()
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for out_vec in BH:
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if abs(out_vec[-(m + 1)]) == 1/2:
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if out_vec[-(m + 1)] == -1/2:
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testvec = [i + 1/2 for i in out_vec]
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else:
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testvec = [i + 1/2 for i in -out_vec]
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print(testvec)
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print()
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print([i[0] for i in v])
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