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You want to find a 2 2 enciphering matrix A in Z 30 . You have two plaintext/ciphertext digraphpairs(ina 30 -letteralphabet),whichenablesyoutowrite A P = C
You want to find a 22 enciphering matrix A in Z30. You have two plaintext/ciphertext digraphpairs(ina30-letteralphabet),whichenablesyoutowrite AP=C(mod30), where
P=(3235), C=(178829).
- Workingmodulo10,writeAintheformAJ+10L(mod30),whereLisan unknown matrix modulo3(whose entries are0,1or2) andJis a matrix you know from yourmod10computations (note thatAJ(mod10)).Find the matrixJsuch that all of its entries are between0and29and are divisible by3.
- Working modulo3, find the second column of the matrixL.
- How many possibilities are there for the original matrixA? List them all.
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Linear Algebra A Modern Introduction
Authors: David Poole
4th edition
1285463242, 978-1285982830, 1285982835, 978-1285463247
