def _generate_x(self):
# generate an "x" (1 < x < q), where q is (p-1)/2.
# p is a 128-byte (1024-bit) number, where the first 64 bits are 1.
# therefore q can be approximated as a 2^1023. we drop the subset of
# potential x where the first 63 bits are 1, because some of those
# will be larger than q (but this is a tiny tiny subset of
# potential x).
while 1:
x_bytes = os.urandom(128)
x_bytes = byte_mask(x_bytes[0], 0x7f) + x_bytes[1:]
if (x_bytes[:8] != b7fffffffffffffff and
x_bytes[:8] != b0000000000000000):
break
self.x = util.inflate_long(x_bytes)
def _generate_x(self):
# generate an "x" (1 < x < (p-1)/2).
q = (self.p - 1) // 2
qnorm = util.deflate_long(q, 0)
qhbyte = byte_ord(qnorm[0])
byte_count = len(qnorm)
qmask = 0xff
while not (qhbyte & 0x80):
qhbyte <<= 1
qmask >>= 1
while True:
x_bytes = os.urandom(byte_count)
x_bytes = byte_mask(x_bytes[0], qmask) + x_bytes[1:]
x = util.inflate_long(x_bytes, 1)
if (x > 1) and (x < q):
break
self.x = x
def _roll_random(n):
"""returns a random # from 0 to N-1"""
bits = util.bit_length(n - 1)
byte_count = (bits + 7) // 8
hbyte_mask = pow(2, bits % 8) - 1
# so here's the plan:
# we fetch as many random bits as we'd need to fit N-1, and if the
# generated number is >= N, we try again. in the worst case (N-1 is a
# power of 2), we have slightly better than 50% odds of getting one that
# fits, so i can't guarantee that this loop will ever finish, but the odds
# of it looping forever should be infinitesimal.
while True:
x = os.urandom(byte_count)
if hbyte_mask > 0:
x = byte_mask(x[0], hbyte_mask) + x[1:]
num = util.inflate_long(x, 1)
if num < n:
break
return num