1. Presented by Mike Scott
Efficient and Secure Identity-Based Signatures and Signcryption from Bilinear Maps
Paulo Barreto, Benoit Libert, Noel McCullagh and Jean-Jacques Quisquater
Presented by Mike Scott

2. A new Identity-Based Signature Scheme
Based on Sakai-Kasahara construction
Generators P, Q, g=e(P,Q), Master secret s, and Qpub=sQ, hash functions H1 and H2
Keygen
D=1/(H1(ID)+s).P generates private key D from Identity ID and TA’s secret s

3. A new Identity-Based Signature Scheme
r=gx, for random x
h=H2(M,r), to sign a message M
S=(x+h)D, where D is the private key
Signature is (h,S)

4. A new Identity-Based Signature Scheme
Verification
Signature (h,S) is accepted iff
h = H2(M,e(S,H1(ID)Q+Qpub).g-h)

5. A new Identity-Based Signcryption Scheme
Parameters as before (with another hash function H3). Key generation as before.
Sign/Encrypt from Alice to Bob
r=gx for random x, c=M  H3(r)
h=H2(M,r)
S=(x+h)DA, where DA is the senders private key
T=x(H1(IDB)P+Qpub), where IDB is recipient
Ciphertext is (c,S,T)

6. A new Identity-Based Signcryption Scheme
Decrypt/Verify
Compute r = e(T,DB), M=cH3(r), h=H2(M,r)
Accept iff
r = e(S,H1(IDA)Q+Qpub)g-h

7. Features Fast and very efficient No pairings for Sign/Encrypt
“Better than all the rest” – Tina Turner
Implemented and tested
Security proofs
Anonymity support