'''
**Hess Identity-Based Signature (Hess02)**
*Authors:* F. Hess
| **Title:** "Efficient Identity Based Signature Schemes Based on Pairings"
| **Published in:** Selected Areas in Cryptography, 2002
| **Available from:** LNCS Vol. 2595, pages 310-324
| **Notes:**
.. rubric:: Scheme Properties
* **Type:** signature (identity-based)
* **Setting:** bilinear groups (asymmetric)
* **Assumption:** BDH
.. rubric:: Implementation
:Authors: J. Ayo Akinyele
:Date: 11/2011
'''
from charm.toolbox.pairinggroup import PairingGroup,ZR,G1,G2,pair
from charm.toolbox.PKSig import PKSig
#import gc
#gc.disable()
#gc.set_debug(gc.DEBUG_LEAK)
debug = False
[docs]
class Hess(PKSig):
"""
>>> from charm.toolbox.pairinggroup import PairingGroup
>>> group = PairingGroup('SS512')
>>> hess = Hess(group)
>>> (master_public_key, master_secret_key) = hess.setup()
>>> ID = "janedoe@email.com"
>>> (public_key, secret_key) = hess.keygen(master_secret_key, ID)
>>> msg = "this is a message!"
>>> signature = hess.sign(master_public_key, secret_key, msg)
>>> hess.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...")
h, s = group.random(G1), group.random(ZR)
S1 = pair(h,pk['g2']) ** s
a = H2(M, S1)
S2 = (sk ** a) * (h ** s)
return {'S1':S1, 'S2':S2}
# return (S1, 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(pk, mpk['P']) ** a) * S1:
return True
return False
[docs]
def main():
groupObj = PairingGroup('SS512')
chch = Hess(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(mpk, 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()