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ref.py
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from params import Rq, Zq, x
def mainmul_ref(in1_poly, in2_poly):
return in1_poly * in2_poly % (x ** 1440 - 1)
def lowmul_ref(in1_poly, in2_poly):
return in1_poly * in2_poly % (x ** 81)
def main_lay1_ref(in_poly):
out_ntt = [[0 for j in range(9)] for i in range(10)]
for j in range(9):
f0 = extract(in_poly, 0, j)
f1 = extract(in_poly, 1, j)
f2 = extract(in_poly, 2, j)
f3 = extract(in_poly, 3, j)
f4 = extract(in_poly, 4, j)
f5 = extract(in_poly, 5, j)
f6 = extract(in_poly, 6, j)
f7 = extract(in_poly, 7, j)
f8 = extract(in_poly, 8, j)
f9 = extract(in_poly, 9, j)
h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 = ntt10_ref(f0, f1, f2, f3, f4, f5, f6, f7, f8, f9)
out_ntt[0][j] = h0
out_ntt[1][j] = h1
out_ntt[2][j] = h2
out_ntt[3][j] = h3
out_ntt[4][j] = h4
out_ntt[5][j] = h5
out_ntt[6][j] = h6
out_ntt[7][j] = h7
out_ntt[8][j] = h8
out_ntt[9][j] = h9
return out_ntt
def imain_lay1_ref(in_ntt):
out_poly = 0
for j in range(9):
h0 = in_ntt[0][j]
h1 = in_ntt[1][j]
h2 = in_ntt[2][j]
h3 = in_ntt[3][j]
h4 = in_ntt[4][j]
h5 = in_ntt[5][j]
h6 = in_ntt[6][j]
h7 = in_ntt[7][j]
h8 = in_ntt[8][j]
h9 = in_ntt[9][j]
f0, f1, f2, f3, f4, f5, f6, f7, f8, f9 = intt10_ref(h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
out_poly += insert(f0, 0, j)
out_poly += insert(f1, 1, j)
out_poly += insert(f2, 2, j)
out_poly += insert(f3, 3, j)
out_poly += insert(f4, 4, j)
out_poly += insert(f5, 5, j)
out_poly += insert(f6, 6, j)
out_poly += insert(f7, 7, j)
out_poly += insert(f8, 8, j)
out_poly += insert(f9, 9, j)
return out_poly
def main_lay2_ref(in_ntt):
out_ntt = [[0 for j in range(9)] for i in range(10)]
for i in range(10):
f0 = in_ntt[i][0]
f1 = in_ntt[i][1]
f2 = in_ntt[i][2]
f3 = in_ntt[i][3]
f4 = in_ntt[i][4]
f5 = in_ntt[i][5]
f6 = in_ntt[i][6]
f7 = in_ntt[i][7]
f8 = in_ntt[i][8]
h0, h1, h2, h3, h4, h5, h6, h7, h8 = ntt9_ref(f0, f1, f2, f3, f4, f5, f6, f7, f8)
out_ntt[i][0] = h0
out_ntt[i][1] = h1
out_ntt[i][2] = h2
out_ntt[i][3] = h3
out_ntt[i][4] = h4
out_ntt[i][5] = h5
out_ntt[i][6] = h6
out_ntt[i][7] = h7
out_ntt[i][8] = h8
return out_ntt
def imain_lay2_ref(in_ntt):
out_ntt = [[0 for j in range(9)] for i in range(10)]
for i in range(10):
h0 = in_ntt[i][0]
h1 = in_ntt[i][1]
h2 = in_ntt[i][2]
h3 = in_ntt[i][3]
h4 = in_ntt[i][4]
h5 = in_ntt[i][5]
h6 = in_ntt[i][6]
h7 = in_ntt[i][7]
h8 = in_ntt[i][8]
f0, f1, f2, f3, f4, f5, f6, f7, f8 = intt9_ref(h0, h1, h2, h3, h4, h5, h6, h7, h8)
out_ntt[i][0] = f0
out_ntt[i][1] = f1
out_ntt[i][2] = f2
out_ntt[i][3] = f3
out_ntt[i][4] = f4
out_ntt[i][5] = f5
out_ntt[i][6] = f6
out_ntt[i][7] = f7
out_ntt[i][8] = f8
return out_ntt
def low_lay1_ref(in_poly):
out_ntt = [0 for i in range(10)]
f0 = extract(in_poly, 0)
f1 = extract(in_poly, 1)
f2 = extract(in_poly, 2)
f3 = extract(in_poly, 3)
f4 = extract(in_poly, 4)
h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 = ntt10_ref(f0, f1, f2, f3, f4, 0, 0, 0, 0, 0)
out_ntt[0] = h0
out_ntt[1] = h1
out_ntt[2] = h2
out_ntt[3] = h3
out_ntt[4] = h4
out_ntt[5] = h5
out_ntt[6] = h6
out_ntt[7] = h7
out_ntt[8] = h8
out_ntt[9] = h9
return out_ntt
def ilow_lay1_ref(in_ntt):
out_poly = 0
h0 = in_ntt[0]
h1 = in_ntt[1]
h2 = in_ntt[2]
h3 = in_ntt[3]
h4 = in_ntt[4]
h5 = in_ntt[5]
h6 = in_ntt[6]
h7 = in_ntt[7]
h8 = in_ntt[8]
h9 = in_ntt[9]
f0, f1, f2, f3, f4, f5, f6, f7, f8, f9 = intt10_ref(h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
out_poly += insert(f0, 0)
out_poly += insert(f1, 1)
out_poly += insert(f2, 2)
out_poly += insert(f3, 3)
out_poly += insert(f4, 4)
out_poly += insert(f5, 5)
return out_poly
def ntt10_ref(f0, f1, f2, f3, f4, f5, f6, f7, f8, f9):
fis = [f0, f1, f2, f3, f4, f5, f6, f7, f8, f9]
his = [0 for i in range(10)]
for i in range(10):
for ii in range(10):
his[i] += w10 ** (i * ii) * fis[ii]
return his[0], his[1], his[2], his[3], his[4], his[5], his[6], his[7], his[8], his[9]
def intt10_ref(h0, h1, h2, h3, h4, h5, h6, h7, h8, h9):
f0, f1, f2, f3, f4, f5, f6, f7, f8, f9 = ntt10_ref(h0, h9, h8, h7, h6, h5, h4, h3, h2, h1)
return f0 / 10, f1 / 10, f2 / 10, f3 / 10, f4 / 10, f5 / 10, f6 / 10, f7 / 10, f8 / 10, f9 / 10
def ntt9_ref(f0, f1, f2, f3, f4, f5, f6, f7, f8):
fjs = [f0, f1, f2, f3, f4, f5, f6, f7, f8]
hjs = [0 for j in range(9)]
for j in range(9):
for jj in range(9):
hjs[j] += w9 ** (j * jj) * fjs[jj]
return hjs[0], hjs[1], hjs[2], hjs[3], hjs[4], hjs[5], hjs[6], hjs[7], hjs[8]
def intt9_ref(h0, h1, h2, h3, h4, h5, h6, h7, h8):
f0, f1, f2, f3, f4, f5, f6, f7, f8 = ntt9_ref(h0, h8, h7, h6, h5, h4, h3, h2, h1)
return f0 / 9, f1 / 9, f2 / 9, f3 / 9, f4 / 9, f5 / 9, f6 / 9, f7 / 9, f8 / 9
def main_basemul_ref(in1_lay2, in2_lay2):
out_lay2 = [[0 for j in range(9)] for i in range(10)]
for i in range(10):
for j in range(9):
out_lay2[i][j] = in1_lay2[i][j] * in2_lay2[i][j] % (x ** 16 - w10 ** i * w9 ** j)
return out_lay2
def low_basemul_ref(in1_lay1, in2_lay1):
out_lay1 = [0 for i in range(10)]
for i in range(10):
out_lay1[i] = in1_lay1[i] * in2_lay1[i] % (x ** 16 - w10 ** i)
return out_lay1