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CPK In One Page

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CPK In One Page

  1. 1. CPK in One Page 2. CPK Center Create User “alice” • SHA1(“alice@pku.cn”) => 20-byte hash • 20-byte hash => 32 * 5-bit index Combined Public Key •ECC Parameters (j1, j2, j3, ……, j32) Cryptosystem (CPK) is an • y2=x3+ax+b mod p Identity Based Encryption (IBE) • p, a, b are EC parameter • SM[32*index] => 32 private key factors scheme, which is a public-key • G is a selected base point (r1j1, r2j2, r3j3, ……, r32j32) cryptosystem where any string • points and operation on EC • Private key of alice is a valid public key, such as form a group. = r1j1+r2j2+…+ r32j32 email address alice@pku.cn. • n is group order. • Public key of alice • Users who share a public Private Key on ECC = r1j1G+r2j2G+… + r32j32 G parameter (called public key • k: an integer, 0<k<n • Private key is send to alice secretly. matrix in CPK) can encrypt a Public Key on ECC: • Public key factor matrix is published message or verify a signature • P = k*G: a point publicly. by other’s identity (such as email address) without his X. (a+b)*G = a*G + b*G 3. Communication 509 certificate. • CPK is based on Alice: Elliptic Curve Cryptography encrypt(message, “bob@pku.cn”, (ECC). PublicKeyFactorMatrix) =>ciphertext sign(message, alice’s PrivateKey) =>signature Bob: verify(signature, PublicKeyFactorMatrix) => verify success 1. CPK Center Initialization signer is “alice@pku.cn” Init ECC parameters decrypt(ciphertext, Bob’s PrivateKey ) Init Private Key Factor Matrix => decrypt success (SM), a 32x32 matrix of output message random private keys. EC Point addtion Init Public Key Factor Matrix R=P+Q (PM), PM[i][j] = SM[i] EC Point scalar multiplication [j]*G. k*P = P + P + … + P

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