Private Key Extraction. The receiver Xxx 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 Xxxxx encrypts her plaintext message M and obtains a ciphertext C. Decryption: Upon receiving the ciphertext C from Xxxxx, Xxx decrypts it using his private key skIDBob to recover the plaintext M. As a mirror image of the above identity-based encryption, one can consider an identity-based Signature (IBS) scheme. In this scheme, the xxxxxx Xxxxx first obtains a signing (private) key associated with her identifier information from the PKG. She then signs a message using the Signing key. The verifier Xxx now uses Alice's identifier information to verify Bob's signature. {No needs for Xxx to get Alice's certificate. More precisely, an IBS scheme can be described Using the following steps. (Figure illustrates a schematic outline of an IBS scheme). key pair, which we denote by skPKG and pkPKG respectively.
Private Key Extraction. The xxxxxx Xxxxx authenticates herself to the PKG and obtains a private key skIDAlice associated with her identity IDAlice. Signature Generation: Using her private key skIDAlice, Xxxxx creates a signature ¾ on her message M. Signature Verification: Having obtained the signature ¾ and the message M from Xxxxx, the verifier Xxx checks whether ¾ 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". Further studies in IDE
Private Key Extraction. The receiver Bob authenticates himself to the private key generator and obtains his private key skBob which is associated with his identity IDBob.
Private Key Extraction. The xxxxxx, Xxxxx, authenticates herself to the private key generator and obtains her private key skAlice which is associated with her identity IDAlice.
Private Key Extraction. Xxxxx chooses identity information. The private key generator computes the point PAlice = H1(IDAlice) ∈ E(Fq) where PAlice is Xxxxx’s public key. The private key generator sends the point QAlice = s PAlice ∈ E(Fq) to Xxxxx. This QAlice is Xxxxx’s private key.
Private Key Extraction. A user submits his identity information ID to private key generator. Then private key generator computes the user’s public key as QID = H1(ID), and returns his private key SID = sQID.
Private Key Extraction. Each user obtains the private keys; SK1i and SK2i from a private key generator. Figure 4.1 shows the value of braids in the setup and private key extraction phases. The detail of the values prepared by the private key generator for Xxxxx, Xxx, and Xxxxxxx is shown in the following. For Xxxxx:
1) The private key generator encodes Xxxxx’s identity XXX into a braid in group g1, then divides this braid into left and right braids; g1l and g1r
2) The private key generator prepares private keys SK1A and SK2A for Xxxxx where SK1A = z1 g1l z2 and SK2A = z4 g1rz3 For Bob:
1) The private key generator encodes Bob’s identity IDB into a braid in group g2, then divides this braid into left and right braids; g2l and g2r
2) The private key generator prepares private keys SK1B and SK2B for Bob where SK1B = z1 g2l z2 and SK2B = z4 g2rz3 For Xxxxxxx:
1) The private key generator encodes Xxxxxxx’s identity IDC into a braid in group g3, then divides this braid into left and right braids; g3l and g3r
2) The private key generator prepares private keys SK1C and SK2C for Bob where SK1C = z1 g3l z2 and SK2C = z4 g3r z3 For the private key generator:
1) The private braid groups; g, z1, z2, z3, and z4
2) The public braid groups; g1, g2, g3, …, gn are for users 1st to nth where g, g1, g2, g3, …, gn must be on different braid groups.
3) The private key generator prepares public braids; Z1 = z2-1g, and Z2 = gz4-1
