def main():
nfspoly = poly.Poly([8, 29, 15, 1])
NF = poly.NumberField(nfspoly)
while (True):
q = primemath.generateLargePrime(10)
s = poly.getRootsModPFast(nfspoly, q)
if (len(s) > 0):
break
s = s[0]
print "special_q: f(%s) = 0 mod %s" % (s, q)
while (True):
p = primemath.generateLargePrime(7)
r = poly.getRootsModPFast(nfspoly, p)
if (len(r) > 0):
break
r = r[0]
print "p: f(%s) = 0 mod %s" % (r, p)
basis = find_sublattice_basis(q, s, p, r)
print "basis: %s" % basis
basis_r = reduce_basis(basis[0], basis[1])
a0 = basis_r[0][0]
b0 = basis_r[0][1]
a1 = basis_r[1][0]
b1 = basis_r[1][1]
print "reduced basis: %s" % [[a0, b0], [a1, b1]]
print "generating lattice points..."
for i in range(-20, 20):
for j in range(-20, 20):
a = a0 * i + a1 * j
b = b0 * i + b1 * j
if (a == 0 or b == 0):
continue
NFelement = NF(poly.Poly([a, b]))
if (NFelement.norm() % q == 0 and NFelement.norm() % p == 0):
print "%s is q-divisible and p-divisible" % [a, b]
else:
raise AssertionError("%s is not q-divisible or p-divisible" %
[a, b])
def main():
nfspoly = poly.Poly([8,29,15,1])
NF = poly.NumberField(nfspoly)
while(True):
q = primemath.generateLargePrime(10)
s = poly.getRootsModPFast(nfspoly,q)
if(len(s) > 0):
break
s = s[0]
print "special_q: f(%s) = 0 mod %s" %(s,q)
while(True):
p = primemath.generateLargePrime(7)
r = poly.getRootsModPFast(nfspoly,p)
if(len(r) > 0):
break
r = r[0]
print "p: f(%s) = 0 mod %s" %(r,p)
basis = find_sublattice_basis(q,s,p,r)
print "basis: %s" % basis
basis_r = reduce_basis(basis[0],basis[1])
a0 = basis_r[0][0]
b0 = basis_r[0][1]
a1 = basis_r[1][0]
b1 = basis_r[1][1]
print "reduced basis: %s" % [[a0,b0],[a1,b1]]
print "generating lattice points..."
for i in range(-20,20):
for j in range(-20,20):
a = a0*i+a1*j
b = b0*i+b1*j
if(a == 0 or b == 0):
continue
NFelement = NF(poly.Poly([a,b]))
if(NFelement.norm()%q == 0 and NFelement.norm()%p == 0):
print "%s is q-divisible and p-divisible" % [a,b]
else:
raise AssertionError("%s is not q-divisible or p-divisible" % [a,b])
def generatePrimes(primes,nfsPoly,couvBound): prodPrimes = 1 sumBound = 0.0 for prime in primes: sumBound += math.log(prime,2) prodPrimes *= prime while(sumBound <= couvBound): prime = primemath.generateLargePrime(64) if(not(poly.irreducibleModP(nfsPoly,prime))): continue sumBound += math.log(prime,2) primes.append(prime) prodPrimes *= prime print "%s/%s primes" % (int(sumBound/64)+1,int(couvBound/64)+1) return (primes,prodPrimes)
def generatePrimes(primes, nfsPoly, couvBound):
prodPrimes = 1
sumBound = 0.0
for prime in primes:
sumBound += math.log(prime, 2)
prodPrimes *= prime
while (sumBound <= couvBound):
prime = primemath.generateLargePrime(64)
if (not (poly.irreducibleModP(nfsPoly, prime))):
continue
sumBound += math.log(prime, 2)
primes.append(prime)
prodPrimes *= prime
print "%s/%s primes" % (int(sumBound / 64) + 1,
int(couvBound / 64) + 1)
return (primes, prodPrimes)
def main():
nfspoly = poly.Poly([8,29,15,1])
NF = poly.NumberField(nfspoly)
while(True):
q = primemath.generateLargePrime(20)
r = poly.getRootsModPFast(nfspoly,q)
if(len(r) > 0):
break
r = r[0]
print "special_q: f(%s) = 0 mod %s" %(r,q)
basis = []
b = 1
for i in range(2):
a = -b*r + i*q
basis.append([a,b])
print "basis: %s" % basis
basis_r = reduce_basis(basis[0],basis[1])
a0 = basis_r[0][0]
b0 = basis_r[0][1]
a1 = basis_r[1][0]
b1 = basis_r[1][1]
print "reduced basis: %s" % [[a0,b0],[a1,b1]]
print "generating lattice points..."
for i in range(-2,2):
for j in range(-2,2):
a = a0*i+a1*j
b = b0*i+b1*j
if(a == 0 or b == 0):
continue
NFelement = NF(poly.Poly([a,b]))
if(NFelement.norm()%q == 0):
print "%s is q-divisible" % [a,b]
else:
raise AssertionError("%s is not q-divisible" % [a,b])
def main():
nfspoly = poly.Poly([8, 29, 15, 1])
NF = poly.NumberField(nfspoly)
while (True):
q = primemath.generateLargePrime(20)
r = poly.getRootsModPFast(nfspoly, q)
if (len(r) > 0):
break
r = r[0]
print "special_q: f(%s) = 0 mod %s" % (r, q)
basis = []
b = 1
for i in range(2):
a = -b * r + i * q
basis.append([a, b])
print "basis: %s" % basis
basis_r = reduce_basis(basis[0], basis[1])
a0 = basis_r[0][0]
b0 = basis_r[0][1]
a1 = basis_r[1][0]
b1 = basis_r[1][1]
print "reduced basis: %s" % [[a0, b0], [a1, b1]]
print "generating lattice points..."
for i in range(-2, 2):
for j in range(-2, 2):
a = a0 * i + a1 * j
b = b0 * i + b1 * j
if (a == 0 or b == 0):
continue
NFelement = NF(poly.Poly([a, b]))
if (NFelement.norm() % q == 0):
print "%s is q-divisible" % [a, b]
else:
raise AssertionError("%s is not q-divisible" % [a, b])
import poly
import nfspolygen
import etcmath
import primemath
import math
if __name__ == '__main__':
semiprimeSize = 100
n = primemath.generateLargePrime(semiprimeSize/2)*primemath.generateLargePrime(semiprimeSize/2)
print "n = %s" % (n)
d = 3
(m,nfsPoly) = nfspolygen.generateNFSPoly(n,d)
print "Using poly %s, m = %s" % (nfsPoly,m)
B = M = etcmath.calculateB(n)
print "Using bound %s" % B
prefactorBase = primemath.generatePrimes(B)
K = (int)(3*math.log(n,10)) # for quadratic characters
afBaseFile = open("afbase.txt", "w")
rfBaseFile = open("rfbase.txt", "w")
print "Generating af and rf bases..."
for p in prefactorBase:
if(p > B): break
rfBaseFile.write(str([m%p,p])+"\n")
K += 1
roots = poly.getRootsModPFast(nfsPoly,p)
for root in roots:
afBaseFile.write(str([root,p])+"\n")
K += 1
import poly
import nfspolygen
import etcmath
import primemath
import math
if __name__ == '__main__':
semiprimeSize = 64
n = primemath.generateLargePrime(semiprimeSize/2)*primemath.generateLargePrime(semiprimeSize/2)
print "n = %s" % (n)
d = 3
(m,nfsPoly) = nfspolygen.generateNFSPoly(n,d)
print "Using poly %s, m = %s" % (nfsPoly,m)
B = M = etcmath.calculateB(n)
print "Using bound %s" % B
prefactorBase = primemath.generatePrimes(B)
K = (int)(3*math.log(n,10)) # for quadratic characters
afBaseFile = open("afbase.txt", "w")
rfBaseFile = open("rfbase.txt", "w")
print "Generating af and rf bases..."
for p in prefactorBase:
if(p > B): break
rfBaseFile.write(str([m%p,p])+"\n")
K += 1
roots = poly.getRootsModPFast(nfsPoly,p)
for root in roots:
afBaseFile.write(str([root,p])+"\n")
K += 1
