cpk in one page
TRANSCRIPT
CPK in One PageCombined Public Key Cryptosystem (CPK) is an Identity Based Encryption (IBE) scheme, which is a public-key cryptosystem where any string is a valid public key, such as email address [email protected]. • Users who share a public parameter (called public key matrix in CPK) can encrypt a message or verify a signature by other’s identity (such as email address) without his X.509 certificate.• CPK is based on Elliptic Curve Cryptography (ECC).
•ECC Parameters• y2=x3+ax+b mod p• p, a, b are EC parameter• G is a selected base point• points and operation on EC form a group.• n is group order.Private Key on ECC• k: an integer, 0<k<nPublic Key on ECC:• P = k*G: a point
(a+b)*G = a*G + b*G3. Communication
Alice: encrypt(message, “[email protected]”, PublicKeyFactorMatrix) =>ciphertext sign(message, alice’s PrivateKey) =>signature Bob: verify(signature, PublicKeyFactorMatrix) => verify success signer is “[email protected]” decrypt(ciphertext, Bob’s PrivateKey ) => decrypt success output message
1. CPK Center Initialization Init ECC parameters Init Private Key Factor Matrix
(SM), a 32x32 matrix of random private keys.
Init Public Key Factor Matrix (PM), PM[i][j] = SM[i][j]*G.
2. CPK Center Create User “alice” • SHA1(“[email protected]”) => 20-byte hash• 20-byte hash => 32 * 5-bit index (j1, j2, j3, ……, j32)• SM[32*index] => 32 private key factors (r1j1, r2j2, r3j3, ……, r32j32)• Private key of alice = r1j1+r2j2+…+ r32j32
• Public key of alice = r1j1G+r2j2G+… + r32j32 G • Private key is send to alice secretly.• Public key factor matrix is published publicly.
EC Point addtion R = P + QEC Point scalar multiplication k*P = P + P + … + P