3.15. Use the Miller-Rabin test on each of the following numbers. In each case, either provide a Miller-Rabin witness for the compositeness of n, or conclude that n is probably prime by providing 10 numbers that are not Miller-Rabin witnesses for n. n (c) n = 294439 (a) n = 1105. (Yes, 5 divides n, but this is just a warm-up exercise!) (b) n = 294409 (d) n = 118901509 (f) n = 118901527 (e) n = 118901521 118915387 Solution to Exercise 3.15. (a) n − 1 = 1104 = 24. 69. 60 = n = 269 = -138 (mod 1105) (mod 1105) (mod 1105) (mod 1105) Thus 1105 is composite. It factors as n = 5.13.17. 22.69 = 259 24-69-324 28-69 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

[Algebraic Cryptography] How do you solve this? Second picture is an example answer

3.15. Use the Miller-Rabin test on each of the following numbers. In each
case, either provide a Miller-Rabin witness for the compositeness of n, or
conclude that n is probably prime by providing 10 numbers that are not
Miller-Rabin witnesses for n.
n
(c) n = 294439
(a) n = 1105. (Yes, 5 divides n, but this is just a warm-up exercise!)
(b) n = 294409
(d) n = 118901509
(f) n = 118901527
(e) n = 118901521
118915387
Solution to Exercise 3.15.
(a) n − 1 = 1104 = 24. 69.
60
=
n =
269 = -138
(mod 1105)
(mod 1105)
(mod 1105)
(mod 1105)
Thus 1105 is composite. It factors as n = 5.13.17.
22.69 = 259
24-69-324
28-69 1
Transcribed Image Text:3.15. Use the Miller-Rabin test on each of the following numbers. In each case, either provide a Miller-Rabin witness for the compositeness of n, or conclude that n is probably prime by providing 10 numbers that are not Miller-Rabin witnesses for n. n (c) n = 294439 (a) n = 1105. (Yes, 5 divides n, but this is just a warm-up exercise!) (b) n = 294409 (d) n = 118901509 (f) n = 118901527 (e) n = 118901521 118915387 Solution to Exercise 3.15. (a) n − 1 = 1104 = 24. 69. 60 = n = 269 = -138 (mod 1105) (mod 1105) (mod 1105) (mod 1105) Thus 1105 is composite. It factors as n = 5.13.17. 22.69 = 259 24-69-324 28-69 1
2.
For each of the following numbers n, provide a Miller-Rabin witness for the compositeness of
n. (a) 15; (b) 21; (c) 25; (d) 35.
Transcribed Image Text:2. For each of the following numbers n, provide a Miller-Rabin witness for the compositeness of n. (a) 15; (b) 21; (c) 25; (d) 35.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,