We rely on encryption daily without even realizing it.

Encryption ensures data confidentiality and integrity, protecting sensitive information from unauthorized access or tampering during transmission or storage in digital systems.

Digital encryption works by converting plaintext (readable data) into ciphertext (unreadable data) using mathematical algorithms and keys.

An encryption key is a piece of information that controls the encryption and decryption process. It is used as input to the encryption algorithm. Keys can be symmetric (same key for both encryption and decryption) or asymmetric (public and private key pair).

More about mathematical algorithms

Encryption algorithms rely on several fundamental mathematical operations to transform plaintext into ciphertext and vice versa. Here are some key mathematical operations commonly used in encryption algorithms:

Substitution: Substitution involves replacing one piece of data with another according to a predetermined rule or key. For example, in classical ciphers like the Caesar cipher, each letter in the plaintext is shifted by a certain number of positions in the alphabet.

Permutation (Transposition): Permutation involves rearranging the order of data elements. This can be done by scrambling the order of characters, bits, or blocks of data according to a specific pattern or key.

Bitwise Operations: Bitwise operations manipulate individual bits within binary data:

• XOR (Exclusive OR): XOR combines bits according to specific rules. In encryption, XOR is often used to combine plaintext with a pseudorandom bit stream (keystream) generated by the encryption algorithm.
• AND, OR, NOT: These operations manipulate bits based on logical rules and are sometimes used in cryptographic algorithms to achieve specific transformations.

Modular Arithmetic: Modular arithmetic involves operations on integers where numbers “wrap around” upon reaching a certain value (modulus). In encryption, modular arithmetic is often used to achieve cyclic patterns or to manipulate numerical values within a specific range.

Exponentiation and Modular Exponentiation: These operations are fundamental in asymmetric encryption algorithms like RSA and ECC:

• Exponentiation: Raising a number to a power.
• Modular Exponentiation: Computing the remainder when a number is raised to a power modulo another number. This operation is crucial for efficient computation of large powers in modular arithmetic, which is essential in cryptographic key operations.

Prime Number Operations: Asymmetric encryption algorithms often involve prime number operations, such as:

• Prime Generation: Generating large prime numbers for key generation.
• Primality Testing: Checking whether a number is prime, which is essential for ensuring the security of cryptographic keys.

These mathematical operations form the basis of encryption algorithms, which combine them in intricate ways to ensure that encrypted data is secure against unauthorized access. The choice and implementation of these operations depend on the specific encryption algorithm’s design goals, security requirements, and computational efficiency considerations.

Types of encryption algorithms:

Symmetric encryption: In symmetric encryption, the same key is used for both encryption and decryption. This means both the sender and the recipient must possess the same secret key. Examples of symmetric encryption algorithms include AES (Advanced Encryption Standard), DES (Data Encryption Standard), and 3DES (Triple DES). Symmetric encryption is typically faster than asymmetric encryption but requires securely sharing the secret key.

Asymmetric Encryption: Asymmetric encryption uses a pair of keys – a public key and a private key. The public key is used for encryption, while the private key is used for decryption. Only the recipient, who holds the private key, can decrypt messages encrypted with their corresponding public key. Popular asymmetric encryption algorithms include RSA (Rivest-Shamir-Adleman) and ECC (Elliptic Curve Cryptography). Asymmetric encryption is slower than symmetric encryption but eliminates the need for secure key exchange.

Encryption Strength

The strength of an encryption algorithm depends on several factors:
Key Length: Longer keys generally provide stronger encryption because they increase the number of possible combinations, making it harder for attackers to guess the key through brute force attacks.
Complexity of Algorithm: The mathematical complexity of the algorithm determines how resistant it is to cryptanalysis – the study of breaking cryptographic systems.

Modes of operation

Encryption algorithms often operate in different modes to handle varying types of data and requirements:
ECB (Electronic Codebook): Each block of plaintext is encrypted independently, which can lead to patterns in the ciphertext.
CBC (Cipher Block Chaining): Each plaintext block is XORed with the previous ciphertext block before encryption, preventing patterns and providing better security.
CTR (Counter Mode): Encrypts plaintext by XORing it with a keystream generated by encrypting a counter value.

We use encryption algorithms extensively in various applications:

Secure Communication: Protecting emails, instant messages, and other forms of digital communication.
Data Encryption: Securing sensitive data in storage and during transmission over networks.
Digital Signatures: Ensuring data integrity and authenticity through cryptographic signing.
Payment Transactions: Encrypting financial transactions to safeguard payment information.