(a) (b) Let n=pq and input the numeric values of n and (n) (The Euler Phi Function) n= 73861 (n)= (c) Input your p, q, and e below. Ensure that these are correct. p=233 q=317 e= 6835 (d) E(x)= Write down the definition of E(x) according to your assigned values. Substitute numeric values for e and n where appropriate. Use the ^ sy Compute gcd($(n), e) using the Extended Euclidean Algorithm below. Replace (n) and e with the correct numeric values below. Leave unused cells blank. The last row should contain the GCD, and values x and y such that gcd($(n), e) = ax+by where a=(n) and b=e. From your results, compute d, the inverse of e as a reduced residue modu i -1 0 9₁ "₁ (n) e X₂ 1 0 yi 0 1 d= (Remember to reduce the result modulo (n) if nece To check your work, verify that de = 1 (mod (n)) Remember to replace in and o with the actual numbers

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Problem 1: On Canvas, you will find "scores" for p, q, and e. Find them in order to complete all parts of this problem.
(a)
Input your p, q, and e below. Ensure that these are correct.
(b)
(c)
(d)
p=233
q=317
e= 6835
B
E(x)=
Let n=pq and input the numeric values of n and (n) (The Euler Phi Function)
n= 73861
(n)=
i
-1
0
D
q₁
Compute gcd($(n), e) using the Extended Euclidean Algorithm below. Replace (n) and e with the correct numeric values below.
Leave unused cells blank. The last row should contain the GCD, and values x and y such that gcd($(n), e) = ax+by where a=(n) and b=e.
ri
e
Write down the definition of E(x) according to your assigned values. Substitute numeric values for e and n where appropriate. Use the symbol to indicate exponentiation.
(n)
X₁
1
0
Vi
L
0
1
M
d=
N
O
From your results, compute d, the inverse of e as a reduced residue modulo (n), i.e. 0 ≤ d < $(n).
To check your work, verify that de = 1 (mod (n))
Remember to replace (n) and e with the actual numbers.
Make sure to verify your results before you submit!!!
P
(Remember to reduce the result modulo (n) if necessary!)
Q
Transcribed Image Text:1234567 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 A C E F G H J K Problem 1: On Canvas, you will find "scores" for p, q, and e. Find them in order to complete all parts of this problem. (a) Input your p, q, and e below. Ensure that these are correct. (b) (c) (d) p=233 q=317 e= 6835 B E(x)= Let n=pq and input the numeric values of n and (n) (The Euler Phi Function) n= 73861 (n)= i -1 0 D q₁ Compute gcd($(n), e) using the Extended Euclidean Algorithm below. Replace (n) and e with the correct numeric values below. Leave unused cells blank. The last row should contain the GCD, and values x and y such that gcd($(n), e) = ax+by where a=(n) and b=e. ri e Write down the definition of E(x) according to your assigned values. Substitute numeric values for e and n where appropriate. Use the symbol to indicate exponentiation. (n) X₁ 1 0 Vi L 0 1 M d= N O From your results, compute d, the inverse of e as a reduced residue modulo (n), i.e. 0 ≤ d < $(n). To check your work, verify that de = 1 (mod (n)) Remember to replace (n) and e with the actual numbers. Make sure to verify your results before you submit!!! P (Remember to reduce the result modulo (n) if necessary!) Q
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