Efficient and Secure Identity-Based Signatures and

Signcryption from Bilinear Maps

Paulo Barreto, Benoit Libert, Noel McCullagh and Jean-Jacques

QuisquaterPresented by Mike Scott

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

A new Identity-Based Signature Scheme

• Signature– 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)

A new Identity-Based Signature Scheme

• Verification– Signature (h,S) is accepted iff

– h = H2(M,e(S,H1(ID)Q+Qpub).g-h)

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)

A new Identity-Based Signcryption Scheme

• Decrypt/Verify– Compute r = e(T,DB), M=cH3(r), h=H2(M,r)

– Accept iff

– r = e(S,H1(IDA)Q+Qpub)g-h

Features

• Fast and very efficient

• No pairings for Sign/Encrypt

• “Better than all the rest” – Tina Turner

• Implemented and tested

• Security proofs

• Anonymity support