Source code for pksig_schnorr91

'''
**Schnorr Signature (Schnorr91)**

*Authors:* C. P. Schnorr

| **Title:** "Efficient Signature Generation by Smart Cards"
| **Published in:** Journal of Cryptology, 1991
| **Available from:** https://link.springer.com/article/10.1007/BF00196725
| **Notes:**

.. rubric:: Scheme Properties

* **Type:** signature (public key)
* **Setting:** integer groups
* **Assumption:** Discrete Logarithm

.. rubric:: Implementation

:Authors: Charm Developers
:Date: 2011
'''
from charm.toolbox.integergroup import IntegerGroupQ
from charm.toolbox.PKSig import PKSig

debug = False


class SchnorrSig(PKSig):
    """
    >>> from charm.core.math.integer import integer
    >>> p = integer(156816585111264668689583680968857341596876961491501655859473581156994765485015490912709775771877391134974110808285244016265856659644360836326566918061490651852930016078015163968109160397122004869749553669499102243382571334855815358562585736488447912605222780091120196023676916968821094827532746274593222577067)
    >>> q = integer(78408292555632334344791840484428670798438480745750827929736790578497382742507745456354887885938695567487055404142622008132928329822180418163283459030745325926465008039007581984054580198561002434874776834749551121691285667427907679281292868244223956302611390045560098011838458484410547413766373137296611288533)    
    >>> pksig = SchnorrSig()
    >>> pksig.params(p, q)
    >>> (public_key, secret_key) = pksig.keygen()
    >>> msg = "hello world."
    >>> signature = pksig.sign(public_key, secret_key, msg)
    >>> pksig.verify(public_key, signature, msg)
    True
    """
    def __init__(self):
        PKSig.__init__(self)
        


    def params(self, p=0, q=0, bits=1024):
        global group
        group = IntegerGroupQ(0)
        if p == 0 or q == 0:
            group.paramgen(bits)
        else:
            group.p, group.q, group.r = p, q, 2

    


    def keygen(self):
        p = group.p
        x, g = group.random(), group.randomGen()
        y = (g ** x)
        return ({'y':y, 'g':g}, x)

    


    def sign(self, pk, x, M):
        p,q = group.p, group.q
        k = group.random()
        r = (pk['g'] ** k) % p
        e = group.hash(M, r)
        s = (k - x*e) % q

        return {'e':e, 's':s }

    


    def verify(self, pk, sig, M):
        p = group.p
        r = ((pk['g'] ** sig['s']) * (pk['y'] ** sig['e'])) % p
        if debug: print("Verifying...")
        e = group.hash(M, r)
        if debug: print("e => %s" % e)
        if debug: print("r => %s" % r)
        if e == sig['e']:
            return True
        else:
            return False
        return None