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Consider the permutation T = (taqgblvxh)(n sk w fue)(ycodjr)(pzmi). (a) Showing your working, and working entirely in disjoint cycle notation, give the disjoint cycle notations for 1 and for 7-1, and then compute aª(x) and -1(c). (b) Justifying your answer, find two positive powers a and ß such that Tª = T = (c) Explain how a monoalphabetic substitution cipher works. Illustrate your explana- tion by using the permutation T above to encrypt the plaintext It is not that secrets are never needed in security, but they are never desirable.

Consider the permutation T = (taqgblvxh)(n sk w fue)(ycodjr)(pzmi). (a) Showing your working, and working entirely in disjoint cycle notation, give the disjoint cycle notations for 1 and for 7-1, and then compute aª(x) and -1(c). (b) Justifying your answer, find two positive powers a and ß such that Tª = T = (c) Explain how a monoalphabetic substitution cipher works. Illustrate your explana- tion by using the permutation T above to encrypt the plaintext It is not that secrets are never needed in security, but they are never desirable.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 72E
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Consider the permutation (taqgblvxh)(n skw fue)(ycodjr)(pz mi). (a) Showing your working, and working entirely in disjoint cycle notation, give the disjoint cycle notations for T and for T-1, and then compute T*(x) and -1(c). (b) Justifying your answer, find two positive powers a and B such that n° = T = T (c) Explain how a monoalphabetic substitution cipher works. Illustrate your explana- tion by using the permutation 7 above to encrypt the plaintext It is not that secrets are never needed in security, but they are never desirable.
Transcribed Image Text:Consider the permutation (taqgblvxh)(n skw fue)(ycodjr)(pz mi). (a) Showing your working, and working entirely in disjoint cycle notation, give the disjoint cycle notations for T and for T-1, and then compute T*(x) and -1(c). (b) Justifying your answer, find two positive powers a and B such that n° = T = T (c) Explain how a monoalphabetic substitution cipher works. Illustrate your explana- tion by using the permutation 7 above to encrypt the plaintext It is not that secrets are never needed in security, but they are never desirable.
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