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Questions

I am very new to cryptography and so I am looking for feedback on this question on RSA. Please let me know if I have made any mistakes, Thank you!

(a).

RSA Algorithm:

-choose two primes p,q

-compute n = p * q

-compute phi = (p-1)*(q-1)

-choose e such that 1 < e < phi and gcd(e,phi) = 1 where gcd is greatest common divisor

-e is the public key

-calculate d such that d = phi * k + 1 / e for some integer k

-d is private key

-cipher text c for plain text

-m is computed as: c = m^e mod n

-plain text m for cipher text c is computed as m = c^d mod n

  p = 83 ; q = 89 then,

  n = 7387

  phi = 7216

  e = 193

  d = 4811

  c = 4336 => 2^193 mod 7387

b)

No, 11 is not a valid private key

Cipher text using 11 as private key is "2048".

Where as decrypting using d = 4811 is 2404 which is not equal to original 2

c)

private key "d = 4811" for public key 25

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  • $\begingroup$ b) Instead of decryption find $\gcd(11,7216)$ where $7217 = 2*2*2*2*11*41$ c) show the steps? Notes 1) Please learn $\LaTeX$, 2) Include you all details. Some ways are giving link from wolfram alpha or Sagemath. $\endgroup$ – kelalaka May 21 at 11:17
  • $\begingroup$ Really sorry about the layout, I will learn! $\endgroup$ – John May 21 at 11:19
  • $\begingroup$ Using MathJax / TEX on the Cryptography site $\endgroup$ – kelalaka May 21 at 11:22
  • $\begingroup$ So for b) gcd(11, 7216) = 11. Therefore, gcd does not equal 1 so 11 is not a private key. Is this correct? $\endgroup$ – John May 21 at 11:23
  • $\begingroup$ for a) I do not think I calculated d correctly, please confirm $\endgroup$ – John May 21 at 11:26

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