 Discrete Math Questions

Subject Mathematics Discrete Math

Question

3. Consider the coding function c = 7x + 11 mod 26.
(a) Use this function to put your name into code.
(b) Now put your coded name into code (so that you are using the coding function twice).
(c) Show that using the coding function twice is equivalent to using the coding function d = 23x + 10 mod 26 once.
(d) What is the moral of this story?

4.
(a) Use the Euclidean algorithm to find the inverse of 17 mod 26.
(b) Consider the coding function c = 17x+3. Find the decoding function.
(c) The following message was coded using c = 17x + 3. Decode the message.
Z E N K J J G T I T W S S T L N G Z R I E.
(For this question, use A = 1, B = 2, ..., Y = 25, and Z = 0.)
(d) Why?

Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

4. (a) Since gcd(17, 26) = 1, thus its multiplicative inverse exists
Now 26 = 17*1 + 9 => 9 = 26 – 17*1 …… (a)
17 = 9*1 + 8 => 8 = 17 – 9.1 …….. (b)
9 = 8*1 + 1 => 1 = 9 – 8*1   ……. (c)
From (b), put value in (a) we have 1 = 9 –(17-9*1)*1
1 = 9 – 17*1 + 9*1 = 9*2 -17*1   … (d)
Now substitute value of 9 form (a) in (d)
1 = (26-17*1)*2 – 17*1 = 26*2 – 17*3
=> 26*2 + 17*(-3) = 1 mod 26
Thus -3 is inverse of 17 but – 3 = 23 mod 26
This shows 23 is inverse of 17....

This is only a preview of the solution. Please use the purchase button to see the entire solution

Related Homework Solutions

Discrete Math Questions \$60.00
Discrete Mathematics
Permutations
Combinations
Integers
Intervals
Tables
Prime Numbers
Odd Numbers
Even Numbers
Sets
Symmetric Relations
Reflexive Relations
Transitive Relations
Discrete Math Questions \$10.00
Mathematics
Proofs
Logic
Statements
Equivalence
Tables
Even Numbers
Odd Numbers
Recurrent Sequence Question \$8.00
Recurrence
Recursive
Sequence
Induction
Proof
Formula
Discrete
Math
Iteration
Method
Guess
Integer
Binomial Theorem Questions \$18.00
Mathematics
Binomial Theorem
Numbers
Terms
Repeated Digits
Non-repeated Digits
Even Digits
Odd Digits
Discrete Mathematics Problem \$60.00
Discrete Mathematics
Division Algorithm
Mathematical Induction
Divisibility
Primality Algorithm
Live Chats