Hawkynt

Hill Cipher

Classical polygraphic substitution cipher using linear algebra with matrix multiplication modulo 26. Encrypts blocks of letters using matrix operations. Invented by Lester S. Hill in 1929, requires matrix to be invertible mod 26.

Properties

Property	Value
Category	Classical Ciphers
Sub-category	Classical Cipher
Security status	🎓 Educational Only
Complexity	Expert
Inventor	Lester S. Hill
Year	1929
Origin	🇺🇸 United States
Source	algorithms/classical/hill.js

Security

Status: 🎓 Educational Only

Known vulnerabilities

Issue	Description	Mitigation
If enough plaintext-ciphertext pairs are known, the key matrix can be recovered using linear algebra	—	Requires n known plaintext blocks for n×n matrix, but still vulnerable
While more resistant than monoalphabetic ciphers, still vulnerable to advanced frequency analysis	—	Educational use only - modern ciphers provide much better security

Documentation

• Wikipedia Article
• Original Paper
• Mathematical Background

References

• DCode Implementation
• Educational Tutorial
• Matrix Algebra

Test vectors

4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — Wikipedia worked 2x2 example - HELP under [[3,3],[2,5]]

Field	Value
key	332c332c322c35
input	48454c50
expected	48494154

Vector 2 — Wikipedia worked 3x3 example - ACT under [[6,24,1],[13,16,10],[20,17,15]]

Field	Value
key	362c32342c312c31332c31362c31302c32302c31372c3135
input	414354
expected	504f48

Vector 3 — Wikipedia worked 3x3 example - CAT under the same matrix

Field	Value
key	362c32342c312c31332c31362c31302c32302c31372c3135
input	434154
expected	46494e

Vector 4 — Padding case - odd-length text filled out to the block size with X. No published source carries this value; it is here to keep the padding path covered

Field	Value
key	332c322c352c37
input	48454c4c4f
expected	444c44434b58

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