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Find multiplicative inverse of 5 mod 31 using extended Euclidea... | Filo
Solution For Find multiplicative inverse of 5 mod 31 using extended Euclidean algorithm
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SOLVED: (a) (i) Use Euclid s algorithm to find multiplicative inverse of 23 modulo 80, and hence solve the linear congruence 231 = 7 (mod 80) Explain why the following linear congruence has no solutions: 30r = 49 (mod 80). (iii) Solve the linear congruence 321 = 48 (mod 80) (b) The affine cipher E is given by E(z) = 19x 5 (mod 26) . The conversion table for letters and numbers is shown below . E 1 | 2 3 4 5 | 6 J K 8 9 10 11 12 P Q R U W X 13 14 15 | 16 17 18 19 20 21 | 22 23 24 25 Show that 1
SOLVED: (a) (i) Use Euclid s algorithm to find multiplicative inverse of 23 modulo 80, and hence solve the linear congruence 231 = 7 (mod 80) Explain why the following linear congruence has no solutions: 30r = 49 (mod 80). (iii) Solve the linear congruence 321 = 48 (mod 80) (b) The affine cipher E is given by E(z) = 19x 5 (mod 26) . The conversion table for letters and numbers is shown below . E 1 | 2 3 4 5 | 6 J K 8 9 10 11 12 P Q R U W X 13 14 15 | 16 17 18 19 20 21 | 22 23 24 25 Show that 1
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SOLVED: (a) (i) Use Euclid s algorithm to find multiplicative inverse of 23 modulo 80, and hence solve the linear congruence 231 = 7 (mod 80) Explain why the following linear congruence has no solutions: 30r = 49 (mod 80). (iii) Solve the linear congruence 321 = 48 (mod 80) (b) The affine cipher E is given by E(z) = 19x 5 (mod 26) . The conversion table for letters and numbers is shown below . E 1 | 2 3 4 5 | 6 J K 8 9 10 11 12 P Q R U W X 13 14 15 | 16 17 18 19 20 21 | 22 23 24 25 Show that 1
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