A cryptographic system requires two individual keys and is commonly called as the public-key cryptography. **These two keys are:**

- Public key
- The secret key

– There exists a mathematical link between these two keys even though they are different.

– Out of these, one is used for encrypting or locking the plain text and other one is used for decrypting or unlocking the cipher text.

– Any of the functions can be performed one of the keys alone.

– This key might be published without making any compromising with the security.

– The key cannot be revealed to someone who does not has authorization for reading the messages.

**– Asymmetric key algorithms are used for public key cryptography and this is referred to as the asymmetric key cryptography.**

**– Public key cryptography** uses the algorithms that are based on some mathematical relationships such as the discrete logarithm and integer factorization problems which previously were not known to have an efficient solution.

– The intended recipient can easily generate the private and public keys computationally for decrypting the message using the keys.

– It is easy even for the senders for encrypting the message.

– Based on one’s knowledge of only the public keys, one cannot derive the private key.

– This is because the public key algorithm unlike symmetric key algorithms does not call for a secure initial exchange of the secret keys between the recipient and the sender.

**– Using these algorithms a digital signature can be created for the message with the help of a private key that later can be used for checking the authenticity of the message.**

– This can be later verified by the public key.

– In practical implementation, for the purpose of the signature verification encryption is done only for the hash of the message typically.

– The public key cryptography has found a wide use in the field of the crypto–systems and cryptographic algorithms.

– It is used for underpinning the PGP, GPG and TLS (transport layer security) i.e., the internet standards.

**We have three primary public key systems:**

- Digital signature systems
- Public key distribution systems
- Public key crypto – systems

– These systems are used for performing digital signature and public key distribution services.

– The public key distribution system that is used widely is the diffie – hellman key exchange and the digital signature system used widely is the digital signature algorithm.

**– Public key cryptography uses a technique called the distinguishing technique and it involves using the asymmetric key algorithms.**

– Here, the key is used for encrypting the message and this is not the same as the decryption process.

**A pair of cryptographic keys is provided to each user namely:**

- A public encryption key and
- A private decryption key

– The public key for encryption is widely distributed.

– The private decrypting key remains safe with the proprietor.

– The parameters are chosen for the mathematical relation such that it is either prohibitively expensive or almost impossible.

– On the other hand, the symmetric key algorithms makes use of the single secret key that is shared as well as kept private among the receiver and the sender for the purpose of both encryption and decryption.

– A key has to be shared securely in advance by the receiver and the sender for using the symmetric encryption scheme. – Using a key – exchange algorithm is common while using the symmetric key algorithms.

– Plus, they do not require much intensive computation when compared to the asymmetric algorithms.

– The data is then transmitted using a symmetric key algorithm and the key.

– This procedure is then used by the family of schemes called as SSL/ TLS and the PGP.

**– We call these systems as the hybrid crypto – systems.**

**– Apart from public key encryption, another purpose of public – key cryptography is digital signatures.**

– Here, the private key of the sender is used for signing the messages.

– Anyone who has access to his public key can verify this message.

– This is the proof of sender having the private key and thus it is him who is associated with the public key as well.

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