Cryptography Basics — CyberHacks

knowledge

Overview

Cryptography ensures secure communication in the presence of adversaries by transforming information into unreadable formats for unauthorized users. It provides confidentiality, integrity, authentication, and non-repudiation — implemented using symmetric and asymmetric encryption and underpinned by mathematical operations like XOR and modulo arithmetic.

Terminology

Term	Definition
Symmetric Encryption	Uses the same key for both encryption and decryption
Asymmetric Encryption	Uses a key pair — public key to encrypt, private key to decrypt
Plaintext	Original unencrypted data
Ciphertext	Encrypted output of a plaintext message
Key	Secret value used to encrypt or decrypt data
XOR (Exclusive OR)	Bitwise operation fundamental to many encryption algorithms
Modulo (mod)	Returns the remainder of division; used in cryptographic computations

Core Concepts

Symmetric Encryption (Private Key Cryptography)

Uses the same key for both encryption and decryption. Fast but requires secure key exchange.

Algorithm	Key Size	Notes
DES	56-bit	Legacy; considered insecure
3DES (Triple DES)	168-bit (effective ~112-bit)	Applies DES three times
AES	128, 192, or 256-bit	Current standard; widely used

Asymmetric Encryption (Public Key Cryptography)

Uses a key pair — public key encrypts, private key decrypts. Slower but solves key distribution problem. See Public Key Basics

Algorithm	Key Size	Notes
RSA	2048, 3072, 4096-bit	Most widely used asymmetric algorithm
Diffie-Hellman	2048-bit minimum (3072/4096 recommended)	Key exchange protocol
ECC (Elliptic Curve Cryptography)	256-bit	Comparable security to 3072-bit RSA at smaller key size

XOR Operation (Exclusive OR)

Fundamental bitwise operation used in many encryption schemes.

Truth Table

A	B	A ⊕ B
0	0	0
0	1	1
1	0	1
1	1	0

Key Properties:

A ⊕ A = 0
A ⊕ 0 = A
Commutative and associative

Reversibility — How XOR Decryption Works: Let P = plaintext, K = key, C = ciphertext

Encrypt: C = P ⊕ K
Decrypt: C ⊕ K = (P ⊕ K) ⊕ K = P ⊕ (K ⊕ K) = P ⊕ 0 = P

Modulo Operator (mod / %)

Returns the remainder of division. Used extensively in cryptographic algorithms.

Syntax: X % Y = remainder when X is divided by Y
Example: 25 % 5 = 0 because 25 = 5 × 5 + 0

Properties:

Result always falls in range 0 to Y - 1 for positive Y
Not reversible — X % 5 = 4 has infinite possible values of X
This irreversibility is what makes modulo useful in cryptography

References / Images

Symmetric vs asymmetric key usage diagrams
XOR operation truth table illustrations
Modulo arithmetic examples