The basic principle of asymmetric cryptography

The biggest disadvantage of the symmetric password is that the key management is difficult, because the two sides of the communication must reserve the same key after the encryption, and in the network environment, the key should be replaced frequently, so in the case of more users, the number of keys and management difficulty will be increased correspondingly, and symmetric password is not easy to achieve digital signature

1. Basic Ideas

A) Public key password, that is, asymmetric cryptosystem, the basic idea is to say the key of symmetric password K is divided into encryption key ke and decryption key KD, with encryption key KE control encryption, decryption key KD control decrypt, and because of computational complexity to ensure that encryption key ke in the computation cannot eject the decryption key KD, This will not expose the KD even if Ke is exposed, because the encryption key is public and fundamentally overcomes the difficulty of the traditional password in key distribution

b) using the public key when encrypting, using the private key when decrypting, this shows that the encryption algorithm E and decryption algorithm D is a reversible operation, namely: D (E (m)) =m

2. Application

A) in an asymmetric cipher, the cryptographic and decryption operations are exchangeable D (E (m)) =e (d (M)) =m, which can apply an asymmetric cipher to a digital signature, following the process of digital signatures:

I. Having a public key ke and a private key KD can execute decryption algorithm to derive signature sig

II. To verify that a signature information is identical, the signature information can be encrypted using the public key Ke, and the same signature will be the same when the encrypted content is identical.

3. Security

A) Asymmetric cryptography is based on a difficult mathematical problem, such as the factorization of a

The problem that the scale of solving problem can solve in polynomial time complexity is called P class problem, and the problem that the computer can not solve in the polynomial complexity is that the NP,NP problem is a kind of difficult problem, the most difficult one is NPC problem.

Ii. The essence of design cryptography is to find a problem that is difficult to solve, which explains the interdependence between the security of cryptography and computational complexity.

4. Pros and cons

A) The advantage is that fundamentally customer service is the difficulty of distributing key in symmetric cryptosystem, and it is easy to realize digital signature

b) The disadvantage is that the computation time is long, the time complexity is high, and the encryption and decryption efficiency is reduced.

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