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Identity-Based Cryptography
 

Identity-Based Cryptography

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Cryptography, Network Security

Cryptography, Network Security

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  • Public key as email or IP addresses

Identity-Based Cryptography Identity-Based Cryptography Presentation Transcript

  • Presented By: Arif Ahmed(12-25-109) Under the Guidance Of Sabyasachi Abhadhan Identity Based Cryptography using Bilinear pairing 8/18/2013arifch2009@gmail.com
  • Project Title Identity Based Cryptography using Bilinear pairing 8/18/2013arifch2009@gmail.com
  • Outline  Introduction to IBC  Proposed Existing Schemes  Bilinear Pairing  Security Assumption in IBC  Advantages of Using IBC  Applications Using IBC  Current Research in IBC  Time Plan for Future 8/18/2013arifch2009@gmail.com
  • Introduction to IBC IBC is a public-key Cryptography system in which an arbitrary string can be used as the public key. In particular, Email ID, IP addresses and Phone number can be used as public keys. The concept was first proposed by Adi Shamir in 1984. First usable IBE schemes was first implemented in 2001by Boneh and Franklin [crypto 2001, SIAM J. of computing 2003] 8/18/2013arifch2009@gmail.com
  • Existing schemes - Identity-Based Encryption - Identity-Based Signature - Identity-Based Signcryption - Short Signatures - Group Signatures 8/18/2013arifch2009@gmail.com
  • Figure 1: Identity-Based Encryption Identity-Based Encryption 8/18/2013arifch2009@gmail.com
  •  Setup: The PKG creates its master (private) and public key pair, which we denote by skPKG and pkPKG respectively.  Private Key Extraction: The receiver Bob authenticates himself to the PKG and obtains a private key skIDBob associated with his identity IDBob.  Encryption: Using Bob's identity IDBob and the PKG's pkPKG, the sender Alice encrypts her plaintext message M and obtains a cipher text C.  Decryption: Upon receiving the cipher text C from Alice, Bob decrypts it using his private key skIDBob to recover the plaintext M. Identity-Based Encryption 8/18/2013arifch2009@gmail.com
  • Figure 2: Identity-Based Signature Identity-Based Signature 8/18/2013arifch2009@gmail.com
  • Identity-Based Signature  Setup: The Private Key Generator (PKG), which is a trusted third party, creates its master (private) and public key pair, which we denote by skPKG and pkPKG respectively.  Private Key Extraction: The signer Alice authenticates herself to the PKG and obtains a private key skIDAlice associated with her identity IDAlice.  Signature Generation: Using her private key skIDAlice , Alice creates a signature on her message M.  Signature Verification: Having obtained the signature µ and the message M from Alice, the verifier Bob checks whether µ is a genuine signature on M using Alice's identity IDAlice and the PKG's public key pkPKG. If it is, he returns “Accept". Otherwise, he returns “Reject". 8/18/2013arifch2009@gmail.com
  • Definition of the Bilinear Pairing. The admissible bilinear pairing e is defined over two groups of the same prime-order q denoted by G and F, e :G*G-> F has following properties :  Bilinear: e (aR1,bR2)= e (R1,R2) ^ab  Non-degenerate : e does not send all pairs of points in G*G to the identity in F.  Computable: For all R1;R2 in G, the map e(R1;R2) is efficiently computable. 8/18/2013arifch2009@gmail.com
  • Security Assumptions The bilinear Pair, above motioned gave rise of following computational Problem, Bilinear Diffie- Hellman(BDH Problem ) : Give (G, q, ^e, P, aP, bP, cP) where a, b, c are chose at radom from Zq, the Computational of ^e(P, P)^abc  Conclusion : Note that the security of many identity- based cryptographic schemes in the current literature depends on the BDH assumption 8/18/2013arifch2009@gmail.com
  • Pairing-based IBE schemes Setup : • PKG Specifies a group G generated by P G^* and Bilinear Pairing • Two Hash Function H1: {0,1}*->G* H2: F-> {0,1}l , l=length of the plain text • PKG pick a master key S Zq*(Randomly) and computes Ppkg=sP • PKG publishes Ppkg, H1, H2, G, F 8/18/2013arifch2009@gmail.com
  • Pairing-based IBE schemes Extraction : The receiver Bob contact PKG to get Private Key, DID=sQID where QID = H1(ID) Encryption : The sender Alice now encrypt message M using Bob’s public key U=rP V= The Resulting cipher text C=(U,V) is sent to Bob Decryption: Bob decrypts C by computing 8/18/2013arifch2009@gmail.com
  • Advantages of Using IBC  Public Key Size is small  No PKI management or certificate database  Inherent key escrow, though a drawback, allows for some additional benefits:  No client-side installation required; PKG can encrypt and sign messages for the user, in a web- based messaging application, for example.  Users’ keys may be kept on the PKG, which is more secure than users’ workstations.  “Chameleon” signatures – only recipient can verify 8/18/2013arifch2009@gmail.com
  • Notable Applications Using IBC  IBE email system developed by Volt-age Security provides plug-ins for Outlook, pine, hotmail, and Yahoo.  Researchers from Hewlett Packard Lab in Bristol, developed a health care information system that facilitates an IBE capability. 8/18/2013arifch2009@gmail.com
  • Time Plan for Future May Basics Of Cryptography over June Number Theory & Abstract Algebra over July Literature Survey on ECC, Bilinear Pairing and Identity based Cryptography over August Search a topic Gone through the journals and gambit guide N/A September Proposing IBS and IBE Scheme N/A 8/18/2013arifch2009@gmail.com
  • References  D. Boneh and M. Franklin, Identity-Based Encryption from the Weil Pairing, Proceedings of CRYPTO 2001, LNCS 2139, pages 213-229,Springer-Verlag, 2001.  J. Baek, J. Newmarch, R . Safavi-Naini, . W Susilo, A Survey of Identity-Based Cryptography, Proc. of Australian Unix Users Group Annual Conference, 2004  D . Boneh, A Brief Look at Pairings Based Cryptography, FOCS’07 48th Annual IEEE Symposium on 2007  http://crypto.stanford.edu/ibe/  Modern Cryptography Theory & Practice, Wenbo Mao, Low Price Edition, hp Company  Cryptography and Network Security, W. Stalligngs, 5th Edition, Pearson 8/18/2013arifch2009@gmail.com