In a public key cryptosystem, different keys are used for encryption and decryption, and there is a mutual dependence between the two keys: that is, information encrypted with either key can only be decrypted with the other key. . This allows both parties to communicate confidentially without exchanging keys in advance. The encryption key and algorithm are open to the public, and everyone can use this key to encrypt the file and send it to the recipient. This encryption key is also called the public key; after the recipient receives the encrypted file, it can use his The decryption key is decrypted. This key is privately managed by himself and does not need to be distributed, so it is also called a private key, which solves the problem of key distribution.
The main public key algorithms are:
RSA
,
DSA
,
DH
and
ECC
.
An
RSA
algorithm
The most famous and widely used public key system RSA is in 1978 by
Rivest
,
Shamir
and
Adleman
of the Massachusetts Institute of Technology (MIT) in the paper entitled "Methods for Obtaining Digital Signatures and Public Key Cryptosystems" Proposed. It is an asymmetric (public key) cryptosystem based on number theory and a block cipher system. Its name comes from the initials of the three inventors. Its security is based on the difficulty of factoring large integers, and the problem of factoring large integers is a well-known problem in mathematics. So far, there is no effective method to solve it, so the security of the RSA algorithm can be ensured.
The RSA system is the most typical method of the public key system. Most products and standards that use public key cryptography for encryption and digital signatures use the RSA algorithm.
The RSA algorithm is the first algorithm that
can
be used for both data encryption and
digital
signature , so it provides a basic method for the encryption and authentication of information on public networks. It usually generates a pair of RSA keys first, one of which is a secret key, which is kept by the user; the other is a public key, which can be disclosed to the outside world, and can even be registered in a network server. People use the public key to encrypt files and send them to individuals , the individual can use the private key to decrypt and accept. To improve confidentiality, the RSA key should be at least 500 bits long, and 1024 bits are generally recommended.
Two
DSA
Algorithms
DSA (Digital Signature Algorithm, used as part of the digital signature standard), it is another public key algorithm, it
cannot be
used for encryption, only for digital signature . DSA uses the public key to verify the
integrity
of the
data
and the identity of the sender of the data for the recipient . It can also be used by third parties to determine the authenticity of signatures and signed data. The security of DSA algorithm is based on the difficulty of solving discrete logarithms. This type of signature standard has greater compatibility and applicability, and has become one of the basic components of the network security system.
Three Diffie-Hellman key exchanges
The DH algorithm was proposed by
W.Diffie
and
M.Hellman
. This algorithm is the earliest public key algorithm. It is essentially a protocol for key agreement between two communicating parties: any one of the two entities uses its own private key and the other entity's public key to obtain a symmetric key, which cannot be calculated by other entities. . The security of the DH algorithm is based on the difficulty of computing discrete logarithms over finite fields. The research status of discrete logarithm shows that the DH key used needs at least 1024 bits to ensure sufficient medium and long-term security.
Four Elliptic Curve Cryptosystem (
ECC
)
In 1985, N. Koblitz and V. Miller independently proposed the Elliptic Curve Cryptosystem (ECC), which was based on the intractability of the discrete logarithm problem defined on the elliptic curve point group.
The discrete logarithm solution is very difficult. Elliptic curve discrete logarithm problems are more difficult to solve than discrete logarithm problems over finite fields.