def gauss_samp(B, sigma, mean, n, q):
Bg = gramschmidt.gs(B)
current_center = mean
e = np.zeros(n)
#print max([np.linalg.norm(np.array(Bg[:,i].T)[0]) for i in range(n)])
print B
#print sigma
# iterate i = n - 1 ... 0
for i in range(0,n)[::-1]:
# get the i^th gram schmidt vector
bg_i = np.array(Bg[:,i].T)[0]
cp_i = np.dot(current_center.T, bg_i) / np.dot(bg_i, bg_i)
sp_i = sigma/np.linalg.norm(bg_i)
#print "s_i, c_i: ", sp_i, cp_i
z_i = gauss_samp_1D(sp_i, cp_i, n) % q
# get the i^th basis vector
b_i = np.array(B[:,i].T)[0]
zb = z_i*b_i
e = np.mod(np.add(e, zb), q)
current_center = np.mod(np.subtract(current_center, zb), q)
return e
def gauss_samp(B, sigma, mean, n, q):
Bg = gramschmidt.gs(B)
current_center = mean
e = np.zeros(n)
#print max([np.linalg.norm(np.array(Bg[:,i].T)[0]) for i in range(n)])
print B
#print sigma
# iterate i = n - 1 ... 0
for i in range(0, n)[::-1]:
# get the i^th gram schmidt vector
bg_i = np.array(Bg[:, i].T)[0]
cp_i = np.dot(current_center.T, bg_i) / np.dot(bg_i, bg_i)
sp_i = sigma / np.linalg.norm(bg_i)
#print "s_i, c_i: ", sp_i, cp_i
z_i = gauss_samp_1D(sp_i, cp_i, n) % q
# get the i^th basis vector
b_i = np.array(B[:, i].T)[0]
zb = z_i * b_i
e = np.mod(np.add(e, zb), q)
current_center = np.mod(np.subtract(current_center, zb), q)
return e
W = np.concatenate((W,nextrow),axis=0)
return W[1:]
def trapdoor_G(n,q,k):
Tg = np.diagflat(2*np.ones(k))+np.diagflat(-1*np.ones(k-1),-1)
Tg[:,-1] = [int(b) for b in np.binary_repr(q,k)[::-1]]
T = np.kron(np.eye(n),Tg)
return T
def gen_basis(n, q, m, A, R):
k = int(np.ceil(np.log2(q)))
m0=m-n*k
M1 = np.concatenate((np.concatenate((np.eye(m0),np.zeros((n*k,m0))),axis=0),R),axis=1)
Tg = trapdoor_G(n,q,k)
A0 = np.mod(-A[:,:m0],q)
W = binary_decomp(A0,k)
M2 = np.concatenate((np.concatenate((np.eye(m0),W),axis=0),np.concatenate((np.zeros((m0,n*k)),Tg),axis=0)),axis=1)
return np.mod(M1*M2,q)
if __name__ == "__main__":
n=32
q=2053
k=int(np.ceil(np.log2(q)))
m=2*n*k
A,R = gen_trap(n,q,m)
B = gen_basis(n,q,m,A,R)
print np.amax(np.amax(np.mod(A*B,q)))
Bg = gramschmidt.gs(B)
print "Max Gram-Schmidt: ", max([np.linalg.norm(np.array(Bg[:,i].T)[0]) for i in range(m)])
return T
def gen_basis(n, q, m, A, R):
k = int(np.ceil(np.log2(q)))
m0 = m - n * k
M1 = np.concatenate((np.concatenate(
(np.eye(m0), np.zeros((n * k, m0))), axis=0), R),
axis=1)
Tg = trapdoor_G(n, q, k)
A0 = np.mod(-A[:, :m0], q)
W = binary_decomp(A0, k)
M2 = np.concatenate((np.concatenate((np.eye(m0), W), axis=0),
np.concatenate((np.zeros((m0, n * k)), Tg), axis=0)),
axis=1)
return np.mod(M1 * M2, q)
if __name__ == "__main__":
n = 32
q = 2053
k = int(np.ceil(np.log2(q)))
m = 2 * n * k
A, R = gen_trap(n, q, m)
B = gen_basis(n, q, m, A, R)
print np.amax(np.amax(np.mod(A * B, q)))
Bg = gramschmidt.gs(B)
print "Max Gram-Schmidt: ", max(
[np.linalg.norm(np.array(Bg[:, i].T)[0]) for i in range(m)])
