Public key Algorithms in Cryptography.

Public-key cryptography, or asymmetric cryptography, is an encryption scheme that uses two mathematically related, but not identical, keys — a public key and a private key.

Unlike symmetric key algorithms that rely on one key to both encrypt and decrypt, each key performs a unique function. The public key is used to encrypt and the private key is used to decrypt.

Because of this, public keys can be freely shared, allowing users an easy and convenient method for encrypting content and verifying digital signatures, and private keys can be kept secret, ensuring only the owners of the private keys can decrypt content and create digital signatures.

By encrypting only the fixed-size message hash, we remove the inefficiency of the public-key algorithm and we can efficiently authenticate any arbitrary amount of data.

Since public keys need to be shared but are too big to be easily remembered, they are stored on digital certificates for secure transport and sharing. Since private keys are not shared, they are simply stored in the software or operating system you use, or on hardware (e.g., USB token, hardware security module) containing drivers that allow it to be used with your software or operating system.

The main business applications for public-key cryptography are:

• Digital signatures — content is digitally signed with an individual’s private key and is verified by the individual’s public key
• Encryption — content is encrypted using an individual’s public key and can only be decrypted with the individual’s private key

Security Benefits of Digital Signatures

Assuming the private key has remained secret and the individual it was issued to is the only person with access to it, digitally signing documents and emails offers the following benefits.

• Authentication — since the individual’s unique private key was used to apply the signature, recipients can be confident that the individual was the one to actually apply the signature
• Non-repudiation — since the individual is the only one with access to the private key used to apply the signature, he/she cannot later claim that it wasn’t him/her who applied the signature
• Integrity — when the signature is verified, it checks that the contents of the document or message match what was in there when the signature was applied. Even the slightest change to the original document would cause this check to fail.