BLS Signatures

1. Boneh–Lynn–Shacham
(BLS) Signatures and Key
Sharing
Prof Bill Buchanan, The Cyber Academy
http://asecuritysite.com

2. Public and private keys with ECC
Private key:
3000435645222292238384993377803994445231
5749064290473682127167271568896730865
Public key:
((510349466858130011708174351023534141234
70700731734176493660185826748147116266,6
4210743524728530290185905551942812616400
571488225773882109119010482573127691),
(154347787600214066669276686400572148050
94329177828734336347158339868964471406,1
6458834280993920926797344108664633448008
87723192890577720280731380716208522))

3. Bilinear mapping

4. Boneh–Lynn–Shacham
(BLS) Signatures
Prof Bill Buchanan, The Cyber Academy
http://asecuritysite.com

5. Pair mapping in elliptic curve

6. BLS Signature

7. BLS Signature Message: Hello name=BN254 curve
order=1679810873101583228494080414223173390975957960340475274902
8378864165570215949
-----Signature Test----
secretKey
3e6a4c7dae8f3563fabb9b57d04b4b21d3f2b9f4544adc7bedc6cbb36f036b10
publicKey
a96fee792a1b933badbbadb9613ecd7f9903da5edfd100209622dc3402739b13d
f01cbb184ce620dc474d08bd83b47ac1a394e1ab652839b6232555a9be25499
signature
424d9ebf795d85e8abbbbddc264b110550afcb627dc90608e357d0cd3c2d7f08

8. BLS Signature Message: Hello name=BN254 curve
order=1679810873101583228494080414223173390975957960340475274902
8378864165570215949
-----Signature Test----
secretKey
3e6a4c7dae8f3563fabb9b57d04b4b21d3f2b9f4544adc7bedc6cbb36f036b10
publicKey
a96fee792a1b933badbbadb9613ecd7f9903da5edfd100209622dc3402739b13d
f01cbb184ce620dc474d08bd83b47ac1a394e1ab652839b6232555a9be25499
signature
424d9ebf795d85e8abbbbddc264b110550afcb627dc90608e357d0cd3c2d7f08
Message: Hello
Private key:
2aabe11b7f965e8b16f525127efa01833f12ccd84daf9748373b66838520cdb7
pub: EC Point x: 39516301f4c81c21fbbc97ada61dee8d764c155449967fa6b02655a4664d1562 y:
d9aa170e4ec9da8239bd0c151bf3e23c285ebe5187cee544a3ab0f9650af1aa6
Public key: EC Point x: 39516301f4c81c21fbbc97ada61dee8d764c155449967fa6b02655a4664d1562 y:
d9aa170e4ec9da8239bd0c151bf3e23c285ebe5187cee544a3ab0f9650af1aa6
Signature: Signature {
r: BN: 905eceb65a8de60f092ffb6002c829454e8e16f3d83fa7dcd52f8eb21e55332b,
s: BN: 8f22e3d95beb05517a1590b1c5af4b2eaabf8e231a799300fffa08208d8f4625, recoveryParam: 0 }

9. BLS Signature Aggregation

10. BLS Key Aggregation and N-of-N Multisignature (multisig)

11. Key Sharing with
Crypto Pairs
Prof Bill Buchanan, The Cyber Academy
http://asecuritysite.com

12. Key share

13. Tripartite Key Share import bn256
a,_ = bn256.g2_random()
b,_ = bn256.g2_random()
c,_ = bn256.g2_random()
print "a:",a print "b:",b print "c:",c
pa = bn256.g1_scalar_base_mult(a)
qa = bn256.g2_scalar_base_mult(a)
print "Pa (generated from G1):",pa
print "Qa: (generated from G2)",qa
pb = bn256.g1_scalar_base_mult(b)
qb = bn256.g2_scalar_base_mult(b)
pc = bn256.g1_scalar_base_amult(c)
qc = bn256.g2_scalar_base_mult(c)
k1= bn256.optimal_ate( qc,pb)
v1 =k1.exp(a)
print "Key1:",
v1.x k2= bn256.optimal_ate( qa,pc)
v2 =k2.exp(b)
#print "Key2:",v2.x
k3= bn256.optimal_ate( qb,pa)
v3 =k3.exp(c)
#print "Key3:",v3.x
if (v1==v2 == v3):

14. Tripartite Key Share a:
606360743810913691978275367595286157330984168617581986083
66189372866965005041
b:
112470929226171079981303075008501844092160735162102556422
19825916479131083134
c:
242884733589679234288833987702141844686310533263025067207
36367961192472481050
pa (generated from G1):
(86105122028063057751813726031967023093967819126418021244
60940919865940423719,
370343612508781080007527750365119374781311320881562655896
18251393353249913293)
qa: (generated from G2)
((5976954856244468135363683841384682617853280824656397988
8615064998271775750431,3219378630704500599430065426421728
4966051268717356168670774189430830488090370),
(37811650259301145322109276722276205627276211121476528136
991019224758641910695,48576140729896170279426296298748686
639125993076539153704602345157165462229))

15. Boneh–Lynn–Shacham
(BLS) Signatures and Key
Sharing
Prof Bill Buchanan, The Cyber Academy
http://asecuritysite.com