Hill Cipher Encoder/Decoder
Enter a 2×2 key matrix (mod 26), check invertibility, then encrypt or decrypt text. We strip non-letters and pad with X if needed.
1. Key matrix (2×2)
Values are integers mod 26 (0–25). A common demo key is [[3, 3], [2, 5]].
2. Text
For decryption, paste ciphertext here and click “Decrypt”.
3. Actions
4. Output
Result
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Numeric vector (A=0 … Z=25)
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How the Hill cipher works (2×2)
1. Choose a 2×2 key matrix K with entries mod 26.
2. Convert text to numbers using A=0, B=1, …, Z=25, and group into 2-element column vectors.
3. For each vector P, compute C = K · P mod 26. Convert back to letters.
K = [a b; c d], det(K) = ad − bc.
K is invertible mod 26 if gcd(det(K), 26) = 1.
To decrypt, we need the inverse matrix K⁻¹ mod 26 so that P = K⁻¹ · C mod 26. This page computes that for you.
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\\]
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Formula (extracted text)
K = [a b; c d], det(K) = ad − bc. K is invertible mod 26 if gcd(det(K), 26) = 1.
Variables and units
- No variables provided in audit spec.
Sources (authoritative):
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.