Revision history [back]
 | 1 | initial version |
Yep,
thanks, that works like a magic trick. Yet I still have some minor problems. I append the whole code in below
def HFEkeyGeneration(n,q):
k = GF(q)
R = PolynomialRing(k, 'x', n)
#Initializes random affine transformations S = (A,c), T = (B,d)
A = random_matrix(k, n, n)
while A.is_singular():
A = random_matrix(k,n,n)
B = random_matrix(k,n,n)
while B.is_singular():
B = random_matrix(k,n,n)
c = random_vector(k,n)
d = random_vector(k,n)
#For now fixed secret polynomial is given
print A
print c
print B
print d
#print "setup"
#print "Affine transformation T is:"
#print A
#print c
#print "Affinte transformation S is:"
#print B
#print d
#print "Length of message is: %d" %n
#print "The secret polynomial is:"
#print p
m = vector(R,n,R.gens())
m = A*m
m = m + c
list = m.list()
list.reverse()
P.<x> = PolynomialRing(k)
g = P.irreducible_element(n)
L.<y> = PolynomialRing(R)
pol = L(list)
g = L(g)
print g
I = L.ideal([g])
Q = L.quotient_ring(I)
pol = Q(pol^6 + 1)
list = pol.list()
list.reverse()
m = vector(R,n,list)
m = B*m
m = m + d
print m
return m
The thing is, that The part, when I power the polynomial, i.e. Q(pol^6 + 1) should be randomized. That means, that I choose pseudorandom polynomial and then evaluate 'pol' in it. I was not able to achieve that. Also, the output polynomial of this operation is of very special form. The indeterminates in coefficients are of powers either x^q (where q is cardinality of field I work in) or simply x. Yet, in finite field q, the x^q = x. I would need to rewrite the polynomial, so that every term in coefficient, where x^q appears, would be written as x.
The problem is, that I've never worked with sage before and perhaps I never will in future. So I'm just putting the code together.
| | 2 | No.2 Revision |
Yep,
thanks, that works like a magic trick. Yet I still have some minor problems. I append the whole code in below
def HFEkeyGeneration(n,q):
#Initializes basic structures
k = GF(q)
R = PolynomialRing(k, 'x', n)
#Initializes random affine transformations S = (A,c), T = (B,d)
A = random_matrix(k, n, n)
while A.is_singular():
A = random_matrix(k,n,n)
B = random_matrix(k,n,n)
while B.is_singular():
B = random_matrix(k,n,n)
c = random_vector(k,n)
d = random_vector(k,n)
#For now #The general vector we encrypt
m = vector(R,n,R.gens())
#Apply S to message
m = A*m
m = m + c
#Transforms vector to list and reverses it
list = m.list()
list.reverse()
#Setup of quotient ring
P.<x> = PolynomialRing(k)
g = P.irreducible_element(n)
L.<y> = PolynomialRing(R)
pol = L(list)
g = L(g)
print g
I = L.ideal([g])
Q = L.quotient_ring(I)
#Apply of fixed secret polynomial
pol = Q(pol^(2*q) + pol^q + 1)
#Transforms polynomial is given
print A
print c
print B
print back to vector
list = pol.list()
list.reverse()
m = vector(R,n,list)
#Apply affine transformation T
m = B*m
m = m + d
#print "setup"
#print "Affine transformation T is:"
#print A
#print c
#print "Affinte transformation S is:"
#print B
#print d
#print "Length of message is: %d" %n
#print "The secret polynomial is:"
#print p
m = vector(R,n,R.gens())
m = A*m
m = m + c
list = m.list()
list.reverse()
P.<x> = PolynomialRing(k)
g = P.irreducible_element(n)
L.<y> = PolynomialRing(R)
pol = L(list)
g = L(g)
print g
I = L.ideal([g])
Q = L.quotient_ring(I)
pol = Q(pol^6 + 1)
list = pol.list()
list.reverse()
m = vector(R,n,list)
m = B*m
m = m + d
print m
return m
The thing is, that The part, when I power the polynomial, i.e. Q(pol^6 + 1) should be randomized. That means, that I choose pseudorandom polynomial and then evaluate 'pol' in it. I was not able to achieve that. Also, the output polynomial of this operation is of very special form. The indeterminates in coefficients are of powers either x^q (where q is cardinality of field I work in) or simply x. Yet, in finite field q, the x^q = x. I would need to rewrite the polynomial, so that every term in coefficient, where x^q appears, would be written as x.
The problem is, that I've never worked with sage before and perhaps I never will in future. So I'm just putting the code together.
| | 3 | No.3 Revision |
Yep,
thanks, that works like a magic trick. Yet I still have some minor problems. I append the whole code in below
def HFEkeyGeneration(n,q):
#Initializes basic structures
k = GF(q)
R = PolynomialRing(k, 'x', n)
#Initializes random affine transformations S = (A,c), T = (B,d)
A = random_matrix(k, n, n)
while A.is_singular():
A = random_matrix(k,n,n)
B = random_matrix(k,n,n)
while B.is_singular():
B = random_matrix(k,n,n)
c = random_vector(k,n)
d = random_vector(k,n)
#The general vector we encrypt
m = vector(R,n,R.gens())
#Apply S to message
m = A*m
m = m + c
#Transforms vector to list and reverses it
list = m.list()
list.reverse()
#Setup of quotient ring
P.<x> = PolynomialRing(k)
g = P.irreducible_element(n)
L.<y> = PolynomialRing(R)
pol = L(list)
g = L(g)
print g
I = L.ideal([g])
Q = L.quotient_ring(I)
#Apply of fixed secret polynomial
pol = Q(pol^(2*q) + pol^q + 1)
#Transforms polynomial back to vector
list = pol.list()
list.reverse()
m = vector(R,n,list)
#Apply affine transformation T
m = B*m
m = m + d
#print "setup"
#print "Affine transformation T is:"
#print A
#print c
#print "Affinte transformation S is:"
#print B
#print d
#print "Length of message is: %d" %n
#print "The secret polynomial is:"
#print p
print m
return m
The thing is, that The part, when I power the polynomial, i.e. Q(pol^6 Q(pol^(2*q) + pol^q + 1) should be randomized. That means, that I choose pseudorandom polynomial and then evaluate 'pol' in it. I was not able to achieve that. Also, the output polynomial of this operation is of very special form. The indeterminates in coefficients are of powers either x^q (where q is cardinality of field I work in) or simply x. Yet, in finite field q, the x^q = x. I would need to rewrite the polynomial, so that every term in coefficient, where x^q appears, would be written as x.
The problem is, that I've never worked with sage before and perhaps I never will in future. So I'm just putting the code together.
