Euler's Theorem

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Network Security: Euler's Theorem
Topics discussed:
1) Euler’s Theorem - Statement and Explanation.
2) Explanation on finding the Euler’s Totient Function or Phi Function.
3) Solved examples to prove Euler’s theorem holds true for a given set of values.
4) Solved examples to prove Euler’s theorem does not hold true for a given set of values.
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#NetworkSecurityByNeso #Cryptography #NetworkSecurity #EulersTheorem

Опубликовано:

19 окт 2021

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Комментарии : 33

@user-yi8ej9qj2p Год назад

Great video, Thanks!

@azizbiabani6787 2 года назад

Good explanation

@mandadirohitreddy8086 10 месяцев назад

Both are not relatively prime numbers because 33 is divisible by 11

@preeti4534 2 года назад

Please explain the homework question.

@kmdkhaleeluddin6257 11 месяцев назад

Last question is not relatively prime no. Because gcd is not getting as 1

@aestheticism3898 6 месяцев назад

Please answer the hw problem They are not relatively prime..but the case still satisfy the congruence

@agbaiobasi7390 5 месяцев назад

This does not hold true because the GCD (11,33) does not equal 1 but equals 11. To prove this, we first find the Phi value of 33, but the distinct prime numbers of 33 are 3 and 11, hence to find the Phi value, (3 - 1) * (11 - 1) = 20. Therefore, 11^20 Congruence 1 mod 33. This becomes 22 congruence 1 mod 33, and since 22 does not equal 1, this proves that Euler's theorem does not hold true here.

@SequinBrain 6 месяцев назад

11 is not relatively prime to 33 since the GCD = 11, not 1. a = 11, n = 33. We need Phi(n) or Phi(33). The two primes composing 33 = 3, 11. 3-1=2, 11-1=10, 2*10 = 20 = Phi(33). 11^20 ≡ 1 (mod 33) is false. 11^20 = a 21 digit number ending in 1, but subtracting 1 and dividing by 33 doesn't give 0, so it is false.

@agbaiobasi7390 5 месяцев назад

You are swapping a and n values. You got up till the 2*10=20. The next phase should be 11^20 Congruence to 1 mod 33, and 11^20 is still a giant number. I don't know if it's right though, that's my suggestion.

@SequinBrain 5 месяцев назад

@@agbaiobasi7390 we just had to prove whether 11 is relatively prime to 33, which they aren't. I'll relook at the #s and return, I do make mistakes every year or so. You were correct, thx, I fixed the post which should read correctly now.