Over the course of building the power siphon, word gets out to other nations and

Question

Over the course of building the power siphon, word gets out to other nations and the UN is upset you did this behind their back. The NSA is not happy and wants answers. Not knowing who leaked this information, you set out to find the culprit. Special agent Kim is here to help. She has intercepted an RSA encrypted message with a ciphertext of 278 and a public key of N-323, e 7. She also notes that the last two letters of the culprit' s name are ry. After decrypting the message and adding the last two letters, who is the culprit? (Note: numbers in the decrypted message encode letters)

Explanation / Answer

N= 323 = 17*19

PHI(N) = (17-1)*(19-1) = 16*18 = 288

e=7

Now we have to find d such that:

ed = 1 mod PHI(N)

or

7d = 1 mod 288

we get d=247

Now let P denote plain text and C denote cipher text.

Then P = C247 mod N = 278247 mod 323 = 31

Therefore P = 31

Now 3 means c and 1 means a

So, the culprit is cary.

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