Public Key Encryption

Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions.

The security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security.

Application of PKC

• Encryption/Decryption
  • The sender encrypts the message using the receiver’s public key
• Digital Signature
  • The sender signs a message by encrypting the message or a transformation of the message using its private key
• Key exchange
  • Two sides cooperate to exchange a session key, typically for conventional encryption.

Condition of PKC

• Computationally easy
  • To generate public and private key pair
  • To encrypt the message using an encryption key
  • To decrypt the message using the decryption key
• Computational infeasible
  • To compute the private key using the public key
  • To recover the plaintext using ciphertext and public key
• The encryption and decryption can be applied in either order

RSA Algorithm

RSA encryption algorithm is a type of public-key encryption algorithm. Named after its inventors Rivest, Shamir, and Adelman (RSA)

RSA algorithm uses the following procedure to generate public and private keys:

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1. Choose two different large random prime numbers.
2. Calculate n = p x q