def generate_primitive_root(n, q):
for i in xrange(q):
if Prime.is_prime(i):
s = set()
for j in range(q):
s.add(i**j % q)
if s == set(range(q)) - {0}:
return i
return None
def generate_primitive_root(n, q):
if q == 2**64 - 2**32 + 1:
return 7
not_approved = []
for i in xrange(q):
if Prime.is_prime(i):
s = set()
for j in range(q):
s.add(i**j % q)
if s == set(range(q)) - {0}:
return i
return None
def generate_primitive_root(n,q):
not_approved = []
r = None
while r is None:
k = generate_k(n,not_approved)
for i in xrange(q):
if Prime.is_prime(i):
s = set()
for j in range(q):
s.add(i**j % q)
if s == set(range(q))-{0}:
r = i
if r is None:
# print "%d not approved" % k
not_approved.append(k)
return r,k
def get_a_proper_prime(N): # We need a special prime p of the form p = k*N + 1, for some integer k k = 1 while not Prime.is_prime(k * N + 1): k = k + 1 return k * N + 1
def generate_k(n,not_approved=[]):
k = 1
while (not Prime.is_prime(k*n+1)) or (k in not_approved):
k+=1
return k
