Cryptography uses math operations to make data harder to understand without a key. Some operations are simple but powerful tools for mixing and transforming data. Even modern encryption algorithms depend on them.

XOR (Exclusive OR)

XOR is a bitwise operation used to compare two binary values. It returns 1 if the bits are different, and 0 if they are the same.

  • Common in symmetric encryption (e.g., AES, stream ciphers)
  • Reversible: A ⊕ B ⊕ B = A (can get the original value back)
  • Also used in hash functions and error detection

XOR Truth Table:

ABA ⊕ B
000
011
101
110

Example:

A:  1101
B:  1011
-------------
A⊕B: 0110

Modulo Operation

Modulo gives the remainder when one number is divided by another. It’s written as a mod n.

  • Modular arithmetic is used in RSA, Diffie-Hellman, and ECC
  • Helps with looping values inside a fixed range
  • Keeps numbers within specific limits in math-based encryption

Example:

17 mod 5 = 2  (because 17 ÷ 5 = 3 with remainder 2)

AND, OR, NOT (Bitwise Operations)

These logical operations work on individual bits. They are often used in masking, shifting, and low-level data handling.

Bitwise AND:

Returns 1 only if both bits are 1.

A:  1101
B:  1011
A & B: 1001

Bitwise OR:

Returns 1 if either bit is 1.

A:  1101
B:  1011
A | B: 1111

Bitwise NOT:

Flips each bit (1 becomes 0, and 0 becomes 1).

A:    1101
~A:   0010