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Implementation of Elliptic-Curve Digital Signatures.
Classes and methods for elliptic-curve signatures:
private keys, public keys, signatures,
NIST prime-modulus curves with modulus lengths of
192, 224, 256, 384, and 521 bits.
Example:
# (In real-life applications, you would probably want to
# protect against defects in SystemRandom.)
from random import SystemRandom
randrange = SystemRandom().randrange
# Generate a public/private key pair using the NIST Curve P-192:
g = generator_192
n = g.order()
secret = randrange( 1, n )
pubkey = Public_key( g, g * secret )
privkey = Private_key( pubkey, secret )
# Signing a hash value:
hash = randrange( 1, n )
signature = privkey.sign( hash, randrange( 1, n ) )
# Verifying a signature for a hash value:
if pubkey.verifies( hash, signature ):
print_("Demo verification succeeded.")
else:
print_("*** Demo verification failed.")
# Verification fails if the hash value is modified:
if pubkey.verifies( hash-1, signature ):
print_("**** Demo verification failed to reject tampered hash.")
else:
print_("Demo verification correctly rejected tampered hash.")
Version of 2009.05.16.
Revision history:
2005.12.31 - Initial version.
2008.11.25 - Substantial revisions introducing new classes.
2009.05.16 - Warn against using random.randrange in real applications.
2009.05.17 - Use random.SystemRandom by default.
Written in 2005 by Peter Pearson and placed in the public domain.
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Low level ECDSA public key object.
:param generator: the Point that generates the group (the base point)
:param point: the Point that defines the public key
:param bool verify: if True check if point is valid point on curve
:raises InvalidPointError: if the point parameters are invalid or
point does not lie on the curve
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Return True if the signature is valid.
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� S( s� Return a signature for the provided hash, using the provided
random nonce. It is absolutely vital that random_k be an unpredictable
number in the range [1, self.public_key.point.order()-1]. If
an attacker can guess random_k, he can compute our private key from a
single signature. Also, if an attacker knows a few high-order
bits (or a few low-order bits) of random_k, he can compute our private
key from many signatures. The generation of nonces with adequate
cryptographic strength is very difficult and far beyond the scope
of this comment.
May raise RuntimeError, in which case retrying with a new
random value k is in order.
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