06-Public Key Encryption

Public-Key Cryptography

A cryptographic approach that uses a pair of private and public keys, allowing secure communication between parties without a shared secret.

RSA Encryption

A public-key encryption algorithm developed in 1977 by Rivest, Shamir, and Adleman, widely used for secure communication.

ElGamal Encryption

An encryption scheme based on the Diffie-Hellman key exchange algorithm, providing a method for secure communication.

Elliptic Curve Cryptography

A type of public-key cryptography that uses the algebraic structure of elliptic curves to secure communication and transactions.

Passive Attack

An attack that attempts to learn or use information from a system without affecting system resources.

Active Attack

An attack that attempts to alter system resources or affect their operation.

Key Exchange

The process of securely exchanging secret keys between endpoints for secure communication.

Symmetric Key Encryption

Encryption where the sender and receiver share a secret key for encrypting and decrypting messages.

Public-Key Encryption Scheme

A system consisting of key generation, encryption, and decryption algorithms for secure communication using public and private keys.

Symmetric vs

A comparison between symmetric and asymmetric encryption methods based on key generation, key size, and performance.

RSA Mathematical Background

Concepts related to prime numbers, greatest common divisors, and the integer factorization problem in the context of RSA encryption.

Totient Function

A function denoted by φ(n) that calculates the number of relative prime numbers less than a given integer n.

RSA Key Generation

The process of generating public and private key pairs for RSA encryption, involving prime number selection and calculation of key components.

Example

A step-by-step illustration of RSA key generation using prime numbers, totient calculation, and selection of public and private keys.

RSA Encryption

A method of encrypting and decrypting data using a public-private key pair, where the encryption is done using the public key and decryption using the private key.

Euler’s Theorem

A theorem stating that if 'a' and 'n' are relatively prime, then 'a' raised to the power of Euler's totient function of 'n' is congruent to 1 modulo 'n'.

Public Key

A key used for encryption in asymmetric cryptography, shared publicly.

Private Key

A key used for decryption in asymmetric cryptography, kept private.

Diffie-Hellman

A key exchange protocol that allows two parties to establish a shared secret over an insecure channel.

Semi-Prime Numbers

Numbers that are the product of two prime numbers, often used in RSA encryption for the modulus.

Discrete Logarithm Problem

In ElGamal encryption, the challenge of finding an exponent when given a base, result, and modulus.

Primitive Root modulo n

A number 'g' that is a generator of the multiplicative group of integers modulo 'n'.