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Commit bdcb4d0

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1 parent 6fe108f commit bdcb4d0

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+977
-1440
lines changed

‎src/NFS.py‎

Lines changed: 61 additions & 59 deletions
Original file line numberDiff line numberDiff line change
@@ -4,7 +4,7 @@
44

55
ZQDFEGSRHTDR = 35279032783773322923326661023
66

7-
import math, time, os
7+
import math, os
88
from datetime import datetime
99
import log
1010
import parse_config
@@ -30,27 +30,29 @@
3030

3131
def initialize(n):
3232

33-
d = int(pow(3*math.log(n)/math.log(math.log(n)),1/3))
34-
first_B = int(math.exp(pow((8/9)*math.log(n),1/3)*pow(math.log(math.log(n)),2/3)))
33+
d = int(pow(3*math.log(n)/math.log(math.log(n)),1/3))
34+
first_B = int(math.exp(pow((8/9)*math.log(n),1/3)*pow(math.log(math.log(n)),2/3)))
3535
B = 10*first_B//70
3636

3737
return d, B
3838

39-
def initialize_2(f_x, n, m1, d, primes, leading_coeff):
40-
pairs_used,R_p,logs,tmp = [],[],[],10*d
41-
divide_leading,pow_div = [],[]
39+
def initialize_2(f_x, m1, d, primes, leading_coeff):
40+
pairs_used,R_p,logs,tmp = [],[],[],10*d
41+
divide_leading,pow_div = [],[]
4242
for p in primes:
4343
if not leading_coeff%p:
4444
divide_leading.append(p)
4545
u = p
4646
while not leading_coeff%u: u *= p
4747
pow_div.append(u//p)
48+
4849
logs.append(round(math.log2(p)))
49-
if p > tmp: R_p.append(find_roots_poly(f_x,p))
50-
else: R_p.append(fast_roots(f_x,p))
50+
if p > tmp: R_p.append(find_roots_poly(f_x,p))
51+
else: R_p.append(fast_roots(f_x,p))
5152
if len(R_p[-1]) == d:
52-
if d&1: pairs_used.append([[leading_coeff*p],leading_coeff*pow(p,d),[[1,1]],p*m1,[1],[0,p],1])
53-
else: pairs_used.append([[leading_coeff*p],leading_coeff*p,[[1,1]],p*m1,[1],[0,p],1])
53+
if d&1: pairs_used.append([[leading_coeff*p], leading_coeff*pow(p, d), [[1,1]], p*m1, [1], [0,p], 1])
54+
else: pairs_used.append([[leading_coeff*p], leading_coeff*p, [[1,1]], p*m1, [1], [0,p], 1])
55+
5456
for p in divide_leading:
5557
for i in range(len(pairs_used)): pairs_used[i].append(True)
5658

@@ -67,9 +69,9 @@ def initialize_3(n, f_x, f_prime, const1, leading_coeff):
6769
if is_prime(q) and leading_coeff%q:
6870
if not n%q: return q, n//q
6971
else:
70-
tmp = find_roots_poly(f_x,q)
72+
tmp = find_roots_poly(f_x,q)
7173
for r in tmp:
72-
if eval_mod(f_prime,r,q): Q.append([q,r])
74+
if eval_mod(f_prime,r, q): Q.append([q,r])
7375
q += 2
7476

7577
return Q, k
@@ -81,17 +83,17 @@ def NFS(n):
8183

8284
parameters = parse_config.parse_config(CONFIG_PATH)
8385

84-
flag_use_batch_smooth_test = parameters[0].lower() in ["true"]
85-
flag_gaussian_pivot = parameters[1].lower() in ["true"]
86-
flag_lanczos = parameters[2].lower() in ["true"]
87-
flag_square_root_couveignes = parameters[3].lower() in ["true"]
88-
const = int(parameters[4])
86+
FLAG_USE_BATCH_SMOOTH_TEST = parameters[0].lower() in ["true"]
87+
FLAG_GAUSSIAN_PIVOT = parameters[1].lower() in ["true"]
88+
FLAG_LANCZOS = parameters[2].lower() in ["true"]
89+
FLAG_SQUARE_ROOT_COUVEIGNES = parameters[3].lower() in ["true"]
90+
CONST = int(parameters[4])
8991
BLOCK_SIZE = int(parameters[5])
90-
nb_poly_coarse_eval = int(parameters[6])
91-
nb_poly_precise_eval = int(parameters[7])
92-
prime_bound = int(parameters[8])
93-
nb_roots = int(parameters[9])
94-
multiplier = int(parameters[10])
92+
NB_POLY_COARSE_EVAL = int(parameters[6])
93+
NB_POLY_PRECISE_EVAL = int(parameters[7])
94+
PRIME_BOUND = int(parameters[8])
95+
NB_ROOTS = int(parameters[9])
96+
MULTIPLIER = int(parameters[10])
9597
NB_CPU_POLY_SELECTION = int(parameters[11])
9698
NB_CPU_SIEVE = int(parameters[12])
9799

@@ -101,54 +103,54 @@ def NFS(n):
101103

102104
primes = create_smooth_primes_base(B)
103105
for p in primes:
104-
if not n%p: return p,n//p
106+
if not n%p: return p,n//p
105107

106108
prod_primes = math.prod(primes)
107109

108-
const1, const2 = const*primes[-1], const*primes[-1]*primes[-1]
110+
const1, const2 = CONST*primes[-1], CONST*primes[-1]*primes[-1]
109111

110112
if NB_CPU_POLY_SELECTION == 1:
111-
f_x,m0,m1,tmp,_ = mono_cpu_polynomial_selection.poly_search(n,primes,nb_roots,prime_bound,multiplier,
112-
int(pow(n,1/(d+1))),d,nb_poly_coarse_eval,
113-
nb_poly_precise_eval,LOG_PATH)
113+
f_x,m0,m1,tmp,_ = mono_cpu_polynomial_selection.poly_search(n,primes,NB_ROOTS, PRIME_BOUND, MULTIPLIER,
114+
int(pow(n,1/(d+1))),d, NB_POLY_COARSE_EVAL,
115+
NB_POLY_PRECISE_EVAL, LOG_PATH)
114116

115117
else:
116-
f_x,m0,m1,tmp,_ = multi_cpu_polynomial_selection.poly_search(n,primes,nb_roots,prime_bound,multiplier,
117-
int(pow(n,1/(d+1))),d,nb_poly_coarse_eval,
118-
nb_poly_precise_eval,NB_CPU_POLY_SELECTION,LOG_PATH)
118+
f_x,m0,m1,tmp,_ = multi_cpu_polynomial_selection.poly_search(n,primes,NB_ROOTS, PRIME_BOUND, MULTIPLIER,
119+
int(pow(n,1/(d+1))),d, NB_POLY_COARSE_EVAL,
120+
NB_POLY_PRECISE_EVAL, NB_CPU_POLY_SELECTION,LOG_PATH)
119121

120122
log.write_log(LOG_PATH, "poly search completed, parameters : m0 = "+str(m0)+" ; m1 = "+str(m1)+" ; d = "+str(d)+"\n")
121123

122-
f_x, m0, M = mono_cpu_polynomial_selection.evaluate_polynomial_quality(f_x,B,m0,m1,primes,LOG_PATH)
124+
f_x, m0, M = mono_cpu_polynomial_selection.evaluate_polynomial_quality(f_x,B, m0,m1,primes,LOG_PATH)
123125

124126
leading_coeff = f_x[0]
125127
zeros_f = get_complex_roots(f_x)
126128
zeros = [leading_coeff*i for i in zeros_f]
127129
f_prime = get_derivative(f_x)
128130

129131
g = [1,f_x[1]]
130-
for i in range(2,len(f_x)): g.append(f_x[i]*pow(leading_coeff,i-1))
132+
for i in range(2,len(f_x)): g.append(f_x[i]*pow(leading_coeff,i-1))
131133
g_prime = get_derivative(g)
132134

133-
g_prime_sq,g_prime_eval = div_poly(poly_prod(g_prime,g_prime),g),pow(leading_coeff, d-2, n)*eval_F(m0,m1,f_prime,d-1)%n
135+
g_prime_sq,g_prime_eval = div_poly(poly_prod(g_prime,g_prime),g),pow(leading_coeff, d-2, n)*eval_F(m0,m1,f_prime,d-1)%n
134136

135137
delta = []
136138
for r in range(d):
137139
tmp = []
138140
for i in range(d):
139141
delt = 0
140142
for j in range(d-i):
141-
if zeros[r].real == 0 or zeros[r].imag == 0 or j == 0: delt += (abs(g[-i-j-2])*pow(leading_coeff,j)*pow(my_norm(zeros_f[r]),j))
142-
else: delt += (abs(g[-i-j-2])*pow(leading_coeff,j)*pow(my_norm(zeros_f[r]),j))+1
143+
if zeros[r].real == 0 or zeros[r].imag == 0 or j == 0: delt += (abs(g[-i-j-2])*pow(leading_coeff,j)*pow(my_norm(zeros_f[r]),j))
144+
else: delt += (abs(g[-i-j-2])*pow(leading_coeff,j)*pow(my_norm(zeros_f[r]),j))+1
143145
tmp.append(delt)
144146
delta.append(tmp)
145147

146148

147149
inert_set = []
148150
for p in primes:
149-
if m1%p and leading_coeff%p and irreducibility(g,p): inert_set.append(p)
151+
if m1%p and leading_coeff%p and irreducibility(g,p): inert_set.append(p)
150152

151-
pairs_used, R_p, logs, divide_leading, pow_div, B_prime = initialize_2(f_x, n, m1, d, primes, leading_coeff)
153+
pairs_used, R_p, logs, divide_leading, pow_div, B_prime = initialize_2(f_x, m1, d, primes, leading_coeff)
152154

153155
Q, k = initialize_3(n, f_x, f_prime, B, leading_coeff)
154156

@@ -157,63 +159,63 @@ def NFS(n):
157159

158160
if NB_CPU_SIEVE <= 1:
159161
if NB_CPU_SIEVE < 1: print("NB_CPU parameter incorrectly set. Must be > 0. Sieving with 1 CPU.")
160-
pairs_used, V = mono_cpu_sieve.find_relations(f_x,leading_coeff,g,primes,R_p,Q,B_prime,divide_leading,
161-
prod_primes,pow_div,pairs_used,const1,const2,logs,m0,m1,
162-
M,d,n,flag_use_batch_smooth_test,LOG_PATH)
162+
pairs_used, V = mono_cpu_sieve.find_relations(f_x,leading_coeff,g, primes,R_p,Q, B_prime,divide_leading,
163+
prod_primes,pow_div,pairs_used,const1,const2,logs,m0,m1,
164+
M,FLAG_USE_BATCH_SMOOTH_TEST,LOG_PATH)
163165

164166
else:
165-
pairs_used, V = multi_cpu_sieve.find_relations(f_x,leading_coeff,g,primes,R_p,Q,B_prime,divide_leading,
166-
prod_primes,pow_div,pairs_used,const1,const2,logs,m0,m1,
167-
M,d,n,flag_use_batch_smooth_test,LOG_PATH,NB_CPU_SIEVE)
167+
pairs_used, V = multi_cpu_sieve.find_relations(f_x,leading_coeff,g, primes,R_p,Q, B_prime,divide_leading,
168+
prod_primes,pow_div,pairs_used,const1,const2,logs,m0,m1,
169+
M,FLAG_USE_BATCH_SMOOTH_TEST, LOG_PATH,NB_CPU_SIEVE)
168170

169171
print("")
170172
log.write_log(LOG_PATH, "sieving complete, building matrix...")
171-
if flag_gaussian_pivot:
173+
if FLAG_GAUSSIAN_PIVOT:
172174
matrix = build_dense_matrix(pairs_used, primes, R_p, Q, divide_leading)
173175
length = len(matrix[0])
174176
matrix, N, U = siqs_build_matrix_opt(matrix)
175177
log.write_log(LOG_PATH, "matrix built "+str(len(matrix))+"x"+str(len(pairs_used))+" finding kernel...")
176178
else:
177-
matrix = build_sparse_matrix(pairs_used,primes,R_p,Q,divide_leading)
179+
matrix = build_sparse_matrix(pairs_used,primes,R_p,Q, divide_leading)
178180
matrix = transpose_sparse(matrix, V)
179181
log.write_log(LOG_PATH, "matrix built "+str(len(matrix))+"x"+str(len(pairs_used))+" reducing...")
180-
if not flag_gaussian_pivot:
182+
if not FLAG_GAUSSIAN_PIVOT:
181183
matrix, pairs_used = reduce_sparse_matrix(matrix, pairs_used)
182184
log.write_log(LOG_PATH, "matrix built "+str(len(matrix))+"x"+str(len(pairs_used))+" finding kernel...")
183185

184186
time_1 = datetime.now()
185187

186-
if flag_gaussian_pivot:
188+
if FLAG_GAUSSIAN_PIVOT:
187189
null_space = siqs_solve_matrix_opt(matrix, N, U)
188190
log.write_log(LOG_PATH, str(len(null_space))+" kernel vectors found")
189191
for vec in null_space:
190192
vec = compute_solutions.convert_to_binary(vec, length)
191-
flag, res = compute_solutions.compute_factors(pairs_used,vec,n,primes,f_x,g,g_prime,g_prime_sq,g_prime_eval,
192-
m0,m1,leading_coeff,d,inert_set,zeros,delta,M,flag_square_root_couveignes,
193-
time_1,LOG_PATH)
193+
flag, res = compute_solutions.compute_factors(pairs_used,vec,n, primes,g, g_prime,g_prime_sq,g_prime_eval,
194+
m0,m1,leading_coeff,d,inert_set,zeros,delta,M, FLAG_SQUARE_ROOT_COUVEIGNES,
195+
time_1,LOG_PATH)
194196
if flag: return res
195197

196198
else:
197-
if flag_lanczos:
199+
if FLAG_LANCZOS:
198200
while True:
199-
null_space = block_lanczos(matrix,len(pairs_used),BLOCK_SIZE, LOG_PATH)
201+
null_space = block_lanczos(matrix,len(pairs_used),BLOCK_SIZE, LOG_PATH)
200202

201203
log.write_log(LOG_PATH, str(len(null_space))+" kernel vectors found")
202204
for vec in null_space:
203205
vec = compute_solutions.convert_to_binary_lanczos(vec, len(pairs_used))
204-
flag, res = compute_solutions.compute_factors(pairs_used,vec,n,primes,f_x,g,g_prime,g_prime_sq,g_prime_eval,
205-
m0,m1,leading_coeff,d,inert_set,zeros,delta,M,flag_square_root_couveignes,
206-
time_1,LOG_PATH)
206+
flag, res = compute_solutions.compute_factors(pairs_used,vec,n, primes,g, g_prime,g_prime_sq,g_prime_eval,
207+
m0,m1,leading_coeff,d, inert_set,zeros,delta,M, FLAG_SQUARE_ROOT_COUVEIGNES,
208+
time_1,LOG_PATH)
207209
if flag: return res
208210

209211
else:
210212
mini_poly_estim = 1
211213
while True:
212-
null_space, mini_poly_estim = wiedemann(matrix,len(pairs_used),BLOCK_SIZE,mini_poly_estim)
214+
null_space, mini_poly_estim = wiedemann(matrix,len(pairs_used),BLOCK_SIZE,mini_poly_estim)
213215
null_space = reduce_null_space_vectors(null_space)
214216
log.write_log(LOG_PATH, str(len(null_space))+" kernel vectors found")
215217
for vec in null_space:
216-
flag, res = compute_solutions.compute_factors(pairs_used,vec,n,primes,f_x,g,g_prime,g_prime_sq,g_prime_eval,
217-
m0,m1,leading_coeff,d,inert_set,zeros,delta,M,flag_square_root_couveignes,
218-
time_1,LOG_PATH)
218+
flag, res = compute_solutions.compute_factors(pairs_used,vec,n, primes,g, g_prime,g_prime_sq,g_prime_eval,
219+
m0,m1,leading_coeff,d, inert_set,zeros,delta,M,FLAG_SQUARE_ROOT_COUVEIGNES,
220+
time_1,LOG_PATH)
219221
if flag: return res

‎src/block_lanczos.py‎

Lines changed: 25 additions & 22 deletions
Original file line numberDiff line numberDiff line change
@@ -14,14 +14,14 @@ def multiply_d(A, d):
1414

1515
# Compute W_inv and the indices for d
1616
# Basically performs gaussian elimination
17-
def block(T,N):
18-
M = concatenate(T,identity(N), N)
17+
def block(T,N):
18+
M = concatenate(T,identity(N), N)
1919
S = []
2020

2121
for j in range(N):
22-
for k in range(j,N):
22+
for k in range(j,N):
2323
if (M[k] >> 2*N - j - 1)&1 != 0:
24-
M[k],M[j] = M[j],M[k]
24+
M[k],M[j] = M[j],M[k]
2525
break
2626

2727
if (M[j] >> 2*N - j -1)&1 != 0:
@@ -31,9 +31,9 @@ def block(T,N):
3131
M[k] ^= M[j]
3232
S.append(j)
3333
else:
34-
for k in range(j,N):
34+
for k in range(j,N):
3535
if (M[k] >> N - j - 1)&1 != 0:
36-
M[k],M[j] = M[j],M[k]
36+
M[k],M[j] = M[j],M[k]
3737
break
3838

3939
if (M[j] >> N - j - 1)&1 == 0:
@@ -66,26 +66,26 @@ def block_lanczos(B, nb_relations, N, LOG_PATH):
6666

6767
X = [0]*nb_relations
6868
b = transpose_sparse(B, nb_relations)
69-
Vo = sparse_multiply(b,sparse_multiply(B,Y))
69+
Vo = sparse_multiply(b,sparse_multiply(B,Y))
7070
i = 0
7171

7272
P = [0 for _ in range(nb_relations)]
7373
V = Vo
7474
d = 1
7575
while d and i <= int(len(B)/(N-0.764))+10:
76-
Z = sparse_multiply(b,sparse_multiply(B,V))
77-
vAv = dense_multiply(transpose_dense(V, N),Z)
78-
vAAv = dense_multiply(transpose_dense(Z, N),Z)
76+
Z = sparse_multiply(b,sparse_multiply(B,V))
77+
vAv = dense_multiply(transpose_dense(V, N),Z)
78+
vAAv = dense_multiply(transpose_dense(Z, N),Z)
7979

8080
W_inv, d = block(vAv,N)
8181

82-
X = add_vector(X,dense_multiply(V,dense_multiply(W_inv,dense_multiply(transpose_dense(V, N),Vo))))
82+
X = add_vector(X,dense_multiply(V,dense_multiply(W_inv,dense_multiply(transpose_dense(V, N),Vo))))
8383

8484
neg_d = switch_indices(d)
8585

8686
c = dense_multiply(W_inv, add_vector(multiply_d(vAAv, d), multiply_d(vAv, neg_d)))
8787

88-
tmp1 = multiply_d(Z,d)
88+
tmp1 = multiply_d(Z,d)
8989
tmp2 = multiply_d(V, neg_d)
9090
tmp3 = dense_multiply(V, c)
9191
tmp4 = multiply_d(vAv, d)
@@ -98,34 +98,37 @@ def block_lanczos(B, nb_relations, N, LOG_PATH):
9898
i += 1
9999

100100
log.write_log(LOG_PATH, "lanczos halted after "+str(i)+" iterations")
101-
x = add_vector(X,Y)
102-
Z = concatenate(x,V,N)
103-
matrix = transpose_dense(sparse_multiply(B, Z), 2*N)
104-
Z = transpose_dense(Z, 2*N)
105-
matrix, Z = solve(matrix,Z,len(B))
101+
x = add_vector(X, Y)
102+
Z = concatenate(x, V, N)
103+
matrix = transpose_dense(sparse_multiply(B, Z), N<<1)
104+
Z = transpose_dense(Z, N<<1)
105+
matrix, Z = solve(matrix, Z, len(B))
106+
106107
solutions = []
107108
for i in range(len(matrix)):
108109
if matrix[i] == 0 and Z[i] != 0 and Z[i] not in solutions:
109110
solutions.append(Z[i])
111+
110112
if len(solutions) == 0:
111113
solutions = block_lanczos(B,nb_relations,N<<1,LOG_PATH)
114+
112115
return solutions
113116

114117
# Performs gaussian elimination
115118
def solve(matrix, block, nb_relations):
116119
k = 0
117120

118121
for l in range(nb_relations):
119-
for i in range(k,len(matrix)):
122+
for i in range(k,len(matrix)):
120123
if (matrix[i] >> nb_relations - i - 1)&1 != 0:
121-
matrix[k],matrix[i] = matrix[i], matrix[k]
122-
block[k],block[i] = block[i], block[k]
124+
matrix[k],matrix[i] = matrix[i], matrix[k]
125+
block[k],block[i] = block[i], block[k]
123126
k += 1
124127
break
125128

126-
for z in range(i+1,len(matrix)):
129+
for z in range(i+1,len(matrix)):
127130
if (matrix[z] >> nb_relations - l - 1)&1 == 1:
128131
matrix[z] ^= matrix[k-1]
129132
block[z] ^= block[k-1]
130133

131-
return matrix,block
134+
return matrix,block

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