3 Hill cipher
Hiteishi Diwanji
Multiletter cipher – Hill Cipher:
- M – Square Matrix
- M-1 – Inverse square matrix
- M(M-1 ) = M-1 M = I – I is the identity matrix where only diagonal elements are 1 from upper left to lower right and all other elements are zero.
- Every time inverse of the matrix does not exist.
M(M-1 ) = I:
- [1] Cryptography and Network Security By William Stallings
Calculation of inverse of matrix:
- If determinant of a square matrix is nonzero, then the inverse of matrix is computed as [A-1]ij = (det A)-1 (-1)i+j (Dji) where (Dji) is the subdeterminant obtained by deleting the jth row and the ith column of A. det(A) is the determinant of A and (det A)-1 is multiplicative inverse of (det A) mod 26.
Hill Algorithm:
- C = PK mod 26
- C – ciphertext row vector of length 3
- P – plaintext row vector of length 3
- K is 3×3 matrix of encryption key.
Hill algorithm example:
Strength of Hill cipher:
- Completely hides single – letter frequency
- 3×3 Hill cipher hides two-letter frequecy.
- Protect against ciphertext only attack.
- Weak against known plaintext attack.
- Given m Plaintext-ciphertext pairs of length m.
- C=PK. P and C are known hence K can be obtained.
Evaluation of Known plaintext attack:
you can view video on Hill Cipher |
Suggested Reading:
- Cryptography and Network Security Principles and Practice by William Stallings, sixth Edition, PEARSON.
- Security in Computing by Charles Pfleeger & Shari Lawrence Pfleeger, fourth Edition, PEARSON.
- Network Security by Charlie Kaufman, Radia Perlman, Mike Speciner, second Edition, PHI.
- The Complete Reference – Network Security by Roberta Bragg, Mark Rhodes-Ousley & Keith Strassberg, Tata McGraw Hill
- Network Security Bible by Eric Cole, Ronald Krutz, James Conley, Wiley
- Hacking 6 Exposed by Stuart McClure, Joel Scambray & George Kurtz , Tata McGraw Hill .
- www.snort.org
- https://nmap.org