'''
**Cha-Cheon Identity-Based Signature (CHCH03)**
*Authors:* J. C. Cha, J. H. Cheon
| **Title:** "An Identity-Based Signature from Gap Diffie-Hellman Groups"
| **Published in:** PKC, 2003
| **Available from:** LNCS Vol. 2567, pages 18-30
| **Notes:**
.. rubric:: Scheme Properties
* **Type:** signature (identity-based)
* **Setting:** bilinear groups (asymmetric)
* **Assumption:** Gap-DH
.. rubric:: Implementation
:Authors: J. Ayo Akinyele
:Date: 11/2011
'''
from charm.toolbox.pairinggroup import PairingGroup,ZR,G1,G2,GT,pair
from charm.toolbox.PKSig import PKSig
debug = False
[docs]
class CHCH(PKSig):
"""
>>> from charm.toolbox.pairinggroup import PairingGroup
>>> group = PairingGroup('SS512')
>>> chch = CHCH(group)
>>> (master_public_key, master_secret_key) = chch.setup()
>>> ID = "janedoe@email.com"
>>> (public_key, secret_key) = chch.keygen(master_secret_key, ID)
>>> msg = "this is a message!"
>>> signature = chch.sign(public_key, secret_key, msg)
>>> chch.verify(master_public_key, public_key, msg, signature)
True
"""
def __init__(self, groupObj):
global group,H1,H2
group = groupObj
H1 = lambda x: group.hash(x, G1)
H2 = lambda x,y: group.hash((x,y), ZR)
[docs]
def setup(self):
g2, alpha = group.random(G2), group.random(ZR)
msk = alpha
P = g2 ** alpha
mpk = {'P':P, 'g2':g2}
return (mpk, msk)
[docs]
def keygen(self, msk, ID):
alpha = msk
sk = H1(ID) ** alpha
pk = H1(ID)
return (pk, sk)
[docs]
def sign(self, pk, sk, M):
if debug: print("sign...")
s = group.random(ZR)
S1 = pk ** s
a = H2(M, S1)
S2 = sk ** (s + a)
return {'S1':S1, 'S2':S2}
[docs]
def verify(self, mpk, pk, M, sig):
if debug: print("verify...")
(S1, S2) = sig['S1'], sig['S2']
a = H2(M, S1)
if pair(S2, mpk['g2']) == pair(S1 * (pk ** a), mpk['P']):
return True
return False
[docs]
def main():
groupObj = PairingGroup('SS512')
chch = CHCH(groupObj)
(mpk, msk) = chch.setup()
_id = "janedoe@email.com"
(pk, sk) = chch.keygen(msk, _id)
if debug:
print("Keygen...")
print("pk =>", pk)
print("sk =>", sk)
M = "this is a message!"
sig = chch.sign(pk, sk, M)
if debug:
print("Signature...")
print("sig =>", sig)
assert chch.verify(mpk, pk, M, sig), "invalid signature!"
if debug: print("Verification successful!")
if __name__ == "__main__":
debug = True
main()