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Cryptography-Oriented Modular Functions

This section focuses on modular arithmetic functions designed for cryptographic applications. These functions can handle hashing, encryption, and decryption tasks using modular techniques.

Functions Overview​

Cryptographic Modular Functions​

  • modularHash(data: string, mod: number): number
    Hashes a string using modular arithmetic.

  • modularEncryption(base: number, key: number, mod: number): number
    Performs encryption via modular exponentiation.

  • modularDecryption(encrypted: number, key: number, mod: number): number
    Decrypts an encrypted value using modular arithmetic.

Detailed Documentation​

modularHash​

Description:
Hashes a string using modular arithmetic. The hash value is computed by iterating over the characters of the input string and applying modular arithmetic.

Example:

console.log(modularHash('hello', 97)); // Output: 24
console.log(modularHash('world', 101)); // Output: 78

Validation:

  • Throws an error if data is not a string.
  • Throws an error if mod is not a positive integer.

Error Handling:

expect(() => modularHash(123, 97)).toThrow('Data must be a string.');
expect(() => modularHash('hello', -5)).toThrow('Modulus must be a positive integer.');

modularEncryption​

Description:

Encrypts a value using modular exponentiation:

Example:

console.log(modularEncryption(5, 3, 13)); // Output: 8
console.log(modularEncryption(7, 4, 10)); // Output: 1

Validation:

  • Throws an error if mod is less than or equal to 0.
  • Throws an error if base, key, or mod are not integers.

modularDecryption​

Description:

Decrypts a value using modular arithmetic. This function is typically used with encryption algorithms that rely on modular exponentiation.

Example:

console.log(modularDecryption(8, 3, 13)); // Output: 5
console.log(modularDecryption(1, 4, 10)); // Output: 7

Validation:

  • Throws an error if mod is less than or equal to 0.
  • Throws an error if encrypted, key, or mod are not integers.

Additional Notes​

Applications of modularHash​

  • Data Integrity: Used to verify the integrity of data using hash comparisons.
  • Key Derivation: Can serve as a simplified hash function for cryptographic keys.

Applications of modularEncryption and modularDecryption​

  • RSA Algorithm: Modular exponentiation is a core component of RSA encryption and decryption.
  • Secure Communication: Helps in securely encrypting and decrypting messages.