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L = = (lij) and b = (b₁,...,bm), then l1,1 1,2 l2,1 12,2 l2,m -**-- lm, 1 lm, 2 lm.m Suppose Oscar has learned that the plaintext (y₁,...,Ym) = (x₁,...,xm) adisplayedequation is encrypted to give the ciphertext DSRMSIOPLXLJBZULLM +(b₁,...,bm). and Oscar also knows that m = 3. Determine the key, showing all computa- tions.

L = = (lij) and b = (b₁,...,bm), then l1,1 1,2 l2,1 12,2 l2,m -**-- lm, 1 lm, 2 lm.m Suppose Oscar has learned that the plaintext (y₁,...,Ym) = (x₁,...,xm) adisplayedequation is encrypted to give the ciphertext DSRMSIOPLXLJBZULLM +(b₁,...,bm). and Oscar also knows that m = 3. Determine the key, showing all computa- tions.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2.24 An Affine-Hill Cipher is the following modification of a Hill Cipher: Let m be a positive integer, and define P = C = (Z26)". In this cryptosystem, a key K consists of a pair (L, b), where L is an m x m invertible matrix over Z26, and b € (Z26). For x = (x₁,...,xm) ≤ P and K = (L, b) ≤ K, we compute € y = ek (x) = (y₁ym) by means of the formula y = xL + b. Hence, if
Transcribed Image Text:2.24 An Affine-Hill Cipher is the following modification of a Hill Cipher: Let m be a positive integer, and define P = C = (Z26)". In this cryptosystem, a key K consists of a pair (L, b), where L is an m x m invertible matrix over Z26, and b € (Z26). For x = (x₁,...,xm) ≤ P and K = (L, b) ≤ K, we compute € y = ek (x) = (y₁ym) by means of the formula y = xL + b. Hence, if
L = (li,j) and b = (b₁,..., bm), then (y₁, ym) = (x₁,...,xm) l1,1 1,2 l2,1 2,2 ... ⠀ ⠀ lm, 1 lm, 2 Suppose Oscar has learned that the plaintext adisplayedequation is encrypted to give the ciphertext DSRMSIOPLXLJBZULLM l1,m l2,m : lm,m + (b₁,...,bm). and Oscar also knows that m = 3. Determine the key, showing all computa- tions.
Transcribed Image Text:L = (li,j) and b = (b₁,..., bm), then (y₁, ym) = (x₁,...,xm) l1,1 1,2 l2,1 2,2 ... ⠀ ⠀ lm, 1 lm, 2 Suppose Oscar has learned that the plaintext adisplayedequation is encrypted to give the ciphertext DSRMSIOPLXLJBZULLM l1,m l2,m : lm,m + (b₁,...,bm). and Oscar also knows that m = 3. Determine the key, showing all computa- tions.
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