init: v1.0.0

sm/sm9/internal/bn256/scripts/gfp12_lattice.py

@@ -0,0 +1,30 @@
+import math
+
+n = 0xB640000002A3A6F1D603AB4FF58EC74449F2934B18EA8BEEE56EE19CD69ECF25
+p = 0xB640000002A3A6F1D603AB4FF58EC74521F2934B1A7AEEDBE56F9B27E351457D
+
+p0=p%n
+n2 = int(math.sqrt(n))
+
+# n = 65000549695646603732796438742359905742570406053903786389881062969044166799969
+# p = 65000549695646603732796438742359905742825358107623003571877145026864184071783
+b = [13037178982157583874, 13037178982157583875, 13037178982157583875, 13037178982157583875]
+a = [v*(p**i) % n for i,v in enumerate(b)]
+print(a)
+print(sum(a)%n)
+
+# x = sum(out[i]*(p**i))
+def padic(x):
+    m = p % n
+    print(m)
+    b=[]
+    while x > 0:
+        b.append(x%m)
+        x = x // m
+    return b
+print(padic(n))
+
+print("----------")
+for m in [n*(n//4+n2+i) for i in range(1,10)]:
+    print(padic(m))
+    print("")

sm/sm9/internal/bn256/scripts/lattice.py

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

sm/sm9/internal/bn256/scripts/matrix.py

@@ -0,0 +1,33 @@
+#!/usr/bin/env sage
+
+from sage.all import *
+
+n = 0xB640000002A3A6F1D603AB4FF58EC74449F2934B18EA8BEEE56EE19CD69ECF25
+p = 0xB640000002A3A6F1D603AB4FF58EC74521F2934B1A7AEEDBE56F9B27E351457D
+# n = 65000549695646603732796438742359905742570406053903786389881062969044166799969
+# p = 65000549695646603732796438742359905742825358107623003571877145026864184071783
+# p_inv = pow(p, n - 2, n)
+# a = matrix(ZZ, 4, 4, [
+#     [n, 0, 0, 0],
+#     [0, p, -1, 0],
+#     [0, 0, p, -1],
+#     [0, 0, 0, n],
+# [n - 1, p_inv, 0, 0],
+# [n - 2, p_inv, p_inv ** 2 % n, 0],
+# [n - 3, p_inv, p_inv ** 2 % n, p_inv ** 3 % n]
+# ])
+# print(a.BKZ())
+x = 0x600000000058F98A
+t = 6*x*x+1
+r = p+1-t
+# x = 6518589491078791937
+v = [[x + 1, x, x, -2 * x],[2 * x + 1, -x, -(x + 1), -x],[2 * x, 2 * x + 1, 2 * x + 1, 2 * x + 1],[x - 1, 4 * x + 2, -(2 * x - 1), x - 1]]
+mv = matrix(ZZ, 4,4,v)
+print(mv.det())
+print()
+print(-3*r)
+for l in v:
+    print("bigFromBase10(\"{}\"),bigFromBase10(\"{}\"),bigFromBase10(\"{}\"),bigFromBase10(\"{}\")".format(l[0],l[1],l[2],l[3]))
+    # a = [v * (p ** i) % n for i, v in enumerate(l)]
+    # print(sum(a) % n)
+print(2*x*x+3*x+1, 12*x*x*x+8*x*x+x, 6*x*x*x+4*x*x+x, -2*x*x-x)