Practical unexposed public key encrypting system
A public key encryption and non-extensible technology, which is applied to the public key and key distribution of secure communication, can solve the problems of unproven security, insecurity, impracticality, etc.
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specific Embodiment approach 1
[0200] When there is only one trusted center, the proposed identity-based public key cryptosystem is used for secure communication, assuming that user B sends information m to user A. Then B first encrypts m with A's public key, and sends the encrypted ciphertext to A. After A obtains the ciphertext, he recovers m with his own private key. Specific steps are as follows:
[0201] The first part trusted center establishes system parameters:
[0202] (a) Generate the first cyclic group G 1 and the second cyclic group G 2 , where G 1 is an additive group of points on a supersingular elliptic curve or Abelian variety, G 2 is a multiplicative group of finite fields;
[0203] (b) Pick a feasible pairing e: G 1 ×G 1 →G 2 , which can be formed by the first cyclic group G 1 The two elements of generate the second cyclic group G 2 an element of
[0204] (c) Randomly choose a generator P∈G 1 ;
[0205] (d) randomly select x, y, z∈Z q , calculate P 1 =xP,P 2 =yP,P 3 = zP;...
specific Embodiment approach 2
[0230] When there are n trusted centers, where n≥2, and the proposed identity-based public key cryptosystem is used for secure communication, it is assumed that user B sends information m to user A. Then B first encrypts m with A's public key, and sends the encrypted ciphertext to A. After A obtains the ciphertext, he recovers m with his own private key. Specific steps are as follows:
[0231] The first part n trusted centers establish system parameters:
[0232] (a) Generate the first cyclic group G 1 and the second cyclic group G 2 , where G 1 is an additive group of points on a supersingular elliptic curve or Abelian variety, G 2 is a multiplicative group of finite fields;
[0233] (b) Pick a feasible pairing e: G 1 ×G 1 →G 2 , which can be formed by the first cyclic group G 1 The two elements of generate the second cyclic group G 2 an element of
[0234] (c) Randomly choose a generator P∈G 1 ;
[0235] (d) Randomly pick x i ,y i ,z i ∈ Z q , calculate P ...
specific Embodiment approach 3
[0268] When the proposed general public key cryptosystem is used for secure communication, it is assumed that user A sends information m to user B. A encrypts m with B's public key, and sends the encrypted ciphertext to B. After B obtains the ciphertext, he recovers m with his own private key. Specific steps are as follows:
[0269] The first part generates a key pair:
[0270] Establish a cyclic group G of order q with a large prime number.
[0271] User B chooses a primitive g in the cipher group G, and in Z q Randomly select the first index x, the second index y and the third index z, and reserve (x, y, z) as the private key; use the following formula to calculate the first group element c, the second group element element d, the third group element h:
[0272] c=g x ,
[0273] d=g y ,
[0274] h=g z ,
[0275] Use (g, c, d, h) as the public key and make it public;
[0276] The second part is encrypted:
[0277] User A obtains user B's public key (g, c, d, h) f...
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