Use the data provided to find values of a and b satisfying a² = 6² (mod N). Then factorize N via using the gcd(N, a - b). N = 198103 11892 = 27000 (mod 198103) 1605²686 (mod 198103) 2378² = 108000 (mod 198103) 2815² 105 (mod 198103) and and and and 27000 23.33.53 686 = 2.7³ 108000 = 25.33.53 105 = 3.5.7
Use the data provided to find values of a and b satisfying a² = 6² (mod N). Then factorize N via using the gcd(N, a - b). N = 198103 11892 = 27000 (mod 198103) 1605²686 (mod 198103) 2378² = 108000 (mod 198103) 2815² 105 (mod 198103) and and and and 27000 23.33.53 686 = 2.7³ 108000 = 25.33.53 105 = 3.5.7
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 85E
Related questions
Question
![Use the data provided to find values of a and b satisfying a² = 6² (mod N). Then factorize N via
using the gcd(N, a - b).
N 198103
1189² = 27000 (mod 198103)
16052686 (mod 198103)
23782 108000 (mod 198103)
28152 105 (mod 198103)
and
and
and
and
2³.33.53
27000 =
686 = 2.7³
108000 = 25.3³.5³
105 3.5.7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F808f9065-30b7-479f-996c-044b45dfbd96%2Ffaf2990e-cc4a-49d8-9245-0b4411a8e157%2F9kk2179_processed.png&w=3840&q=75)
Transcribed Image Text:Use the data provided to find values of a and b satisfying a² = 6² (mod N). Then factorize N via
using the gcd(N, a - b).
N 198103
1189² = 27000 (mod 198103)
16052686 (mod 198103)
23782 108000 (mod 198103)
28152 105 (mod 198103)
and
and
and
and
2³.33.53
27000 =
686 = 2.7³
108000 = 25.3³.5³
105 3.5.7
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