mirror of https://github.com/zcash/pasta.git
Refactor to generate the 'primes' file rather than relying on it as input.
Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood
parent
3513811d0f
commit
a7aea2312c
124
verify.sage
124
verify.sage
|
|
@ -1,5 +1,8 @@
|
|||
import os
|
||||
import sys
|
||||
from errno import ENOENT, EEXIST
|
||||
from sortedcontainers import SortedSet
|
||||
|
||||
|
||||
def readfile(fn):
|
||||
fd = open(fn,'r')
|
||||
|
|
@ -42,6 +45,82 @@ def requirement(fn,istrue):
|
|||
return istrue
|
||||
|
||||
def verify():
|
||||
|
||||
try:
|
||||
s = set(map(Integer, readfile('primes').split()))
|
||||
except IOError, e:
|
||||
if e.errno != ENOENT: raise
|
||||
s = set()
|
||||
|
||||
needtofactor = SortedSet()
|
||||
V = SortedSet() # distinct verified primes
|
||||
verify_primes(V, s, needtofactor)
|
||||
verify_pass(V, needtofactor)
|
||||
|
||||
old = V
|
||||
needtofactor.update(V)
|
||||
while len(needtofactor) > len(old):
|
||||
k = len(needtofactor) - len(old)
|
||||
sys.stdout.write('Factoring %d integer%s' % (k, '' if k == 1 else 's'))
|
||||
sys.stdout.flush()
|
||||
for x in needtofactor:
|
||||
if x not in old:
|
||||
for (y, z) in factor(x):
|
||||
s.add(y)
|
||||
sys.stdout.write('.')
|
||||
sys.stdout.flush()
|
||||
|
||||
print('')
|
||||
|
||||
old = needtofactor.copy()
|
||||
verify_primes(V, s, needtofactor)
|
||||
|
||||
writefile('primes', '\n'.join(map(str, s)) + '\n')
|
||||
writefile('verify-primes', '<html><body>\n' +
|
||||
''.join(('2\n' if v == 2 else
|
||||
'<a href=proof/%s.html>%s</a>\n' % (v,v)) for v in V) +
|
||||
'</body></html>\n')
|
||||
|
||||
verify_pass(V, needtofactor)
|
||||
|
||||
|
||||
def verify_primes(V, s, needtofactor):
|
||||
for n in sorted(s):
|
||||
if not n.is_prime() or n in V: continue
|
||||
needtofactor.add(n-1)
|
||||
if n == 2:
|
||||
V.add(n)
|
||||
continue
|
||||
for trybase in primes(2,10000):
|
||||
base = Integers(n)(trybase)
|
||||
if base^(n-1) != 1: continue
|
||||
proof = 'Primality proof for n = %s:\n' % n
|
||||
proof += '<p>Take b = %s.\n' % base
|
||||
proof += '<p>b^(n-1) mod n = 1.\n'
|
||||
f = factor(1)
|
||||
for v in reversed(V):
|
||||
if f.prod()^2 <= n:
|
||||
if n % v == 1:
|
||||
u = base^((n-1)/v)-1
|
||||
if u.is_unit():
|
||||
if v == 2:
|
||||
proof += '<p>2 is prime.\n'
|
||||
else:
|
||||
proof += '<p><a href=%s.html>%s is prime.</a>\n' % (v,v)
|
||||
proof += '<br>b^((n-1)/%s)-1 mod n = %s, which is a unit, inverse %s.\n' % (v,u,1/u)
|
||||
f *= factor(v)^(n-1).valuation(v)
|
||||
if f.prod()^2 <= n: continue
|
||||
if n % f.prod() != 1: continue
|
||||
proof += '<p>(%s) divides n-1.\n' % f
|
||||
proof += '<p>(%s)^2 > n.\n' % f
|
||||
proof += "<p>n is prime by Pocklington's theorem.\n"
|
||||
proof += '\n'
|
||||
writefile('../../../proof/%s.html' % n,proof)
|
||||
V.add(n)
|
||||
break
|
||||
|
||||
|
||||
def verify_pass(V, needtofactor):
|
||||
p = Integer(readfile('p'))
|
||||
k = GF(p)
|
||||
kz.<z> = k[]
|
||||
|
|
@ -51,7 +130,6 @@ def verify():
|
|||
x1 = Integer(readfile('x1'))
|
||||
y1 = Integer(readfile('y1'))
|
||||
shape = readfile('shape').strip()
|
||||
s = readfile('primes')
|
||||
rigid = readfile('rigid').strip()
|
||||
|
||||
safefield = True
|
||||
|
|
@ -66,48 +144,16 @@ def verify():
|
|||
safecomplete = True
|
||||
safeind = True
|
||||
|
||||
V = [] # distinct verified primes
|
||||
for line in s.split():
|
||||
n = Integer(line)
|
||||
if not n.is_prime(): continue
|
||||
if n == 2:
|
||||
if not n in V: V += [n]
|
||||
continue
|
||||
for trybase in primes(2,10000):
|
||||
base = Integers(n)(trybase)
|
||||
if base^(n-1) != 1: continue
|
||||
proof = 'Primality proof for n = %s:\n' % n
|
||||
proof += '<p>Take b = %s.\n' % base
|
||||
proof += '<p>b^(n-1) mod n = 1.\n'
|
||||
f = factor(1)
|
||||
for v in reversed(V):
|
||||
if f.prod()^2 <= n:
|
||||
if n % v == 1:
|
||||
u = base^((n-1)/v)-1
|
||||
if u.is_unit():
|
||||
proof += '<p><a href=%s.html>%s is prime.</a>\n' % (v,v)
|
||||
proof += '<br>b^((n-1)/%s)-1 mod n = %s, which is a unit, inverse %s.\n' % (v,u,1/u)
|
||||
f *= factor(v)^(n-1).valuation(v)
|
||||
if f.prod()^2 <= n: continue
|
||||
if n % f.prod() != 1: continue
|
||||
proof += '<p>(%s) divides n-1.\n' % f
|
||||
proof += '<p>(%s)^2 > n.\n' % f
|
||||
proof += "<p>n is prime by Pocklington's theorem.\n"
|
||||
proof += '\n'
|
||||
writefile('../../../proof/%s.html' % n,proof)
|
||||
if not n in V: V += [n]
|
||||
break
|
||||
|
||||
writefile('verify-primes',''.join('<a href=proof/%s.html>%s</a>\n' % (v,v) for v in V))
|
||||
|
||||
pstatus = 'Unverified'
|
||||
if not p.is_prime(): pstatus = 'False'
|
||||
needtofactor.add(p)
|
||||
if p in V: pstatus = 'True'
|
||||
if pstatus != 'True': safefield = False
|
||||
writefile('verify-pisprime',pstatus + '\n')
|
||||
|
||||
pstatus = 'Unverified'
|
||||
if not l.is_prime(): pstatus = 'False'
|
||||
needtofactor.add(l)
|
||||
if l in V: pstatus = 'True'
|
||||
if pstatus != 'True': safebase = False
|
||||
writefile('verify-lisprime',pstatus + '\n')
|
||||
|
|
@ -130,6 +176,7 @@ def verify():
|
|||
if gcdlpis1 and l.is_prime():
|
||||
u = Integers(l)(p)
|
||||
d = l-1
|
||||
needtofactor.add(d)
|
||||
for v in V:
|
||||
while d % v == 0: d /= v
|
||||
if d == 1:
|
||||
|
|
@ -146,6 +193,7 @@ def verify():
|
|||
writefile('verify-trace','%s\n' % t)
|
||||
f = factor(1)
|
||||
d = (p+1-t)/l
|
||||
needtofactor.add(d)
|
||||
for v in V:
|
||||
while d % v == 0:
|
||||
d //= v
|
||||
|
|
@ -156,6 +204,7 @@ def verify():
|
|||
writefile('verify-cofactor','Unverified\n')
|
||||
|
||||
D = t^2-4*p
|
||||
needtofactor.add(D)
|
||||
for v in V:
|
||||
while D % v^2 == 0: D /= v^2
|
||||
if prod([v for v in V if D % v == 0]) != -D:
|
||||
|
|
@ -178,6 +227,7 @@ def verify():
|
|||
|
||||
twistl = 'Unverified'
|
||||
d = p+1+t
|
||||
needtofactor.add(d)
|
||||
for v in V:
|
||||
while d % v == 0: d /= v
|
||||
if d == 1:
|
||||
|
|
@ -201,6 +251,7 @@ def verify():
|
|||
writefile('expand2-twistl','<br>= %s\n' % expand2(twistl))
|
||||
f = factor(1)
|
||||
d = (p+1+t)/twistl
|
||||
needtofactor.add(d)
|
||||
for v in V:
|
||||
while d % v == 0:
|
||||
d //= v
|
||||
|
|
@ -214,6 +265,7 @@ def verify():
|
|||
if gcdtwistlpis1 and twistl.is_prime():
|
||||
u = Integers(twistl)(p)
|
||||
d = twistl-1
|
||||
needtofactor.add(d)
|
||||
for v in V:
|
||||
while d % v == 0: d /= v
|
||||
if d == 1:
|
||||
|
|
@ -231,6 +283,8 @@ def verify():
|
|||
|
||||
precomp = 0
|
||||
joint = l
|
||||
needtofactor.add(p+1-t)
|
||||
needtofactor.add(p+1+t)
|
||||
for v in V:
|
||||
d1 = p+1-t
|
||||
d2 = p+1+t
|
||||
|
|
|
|||
Loading…
Reference in New Issue