Can Anyone Help with These RSA Encryption Questions?

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SUMMARY

This discussion focuses on two RSA encryption problems. The first involves decrypting a ciphertext message using the RSA key (5, 2881) and requires calculating C^1109 mod 2881 for the ciphertext blocks. The second problem addresses the recovery of a plaintext message P encrypted with an exponent of 3 by three different users with distinct moduli, leading to the congruences c_i ≡ P^3 (mod n_i). The solution for the first problem involves using repeated squaring and modular reduction, while the second problem hints at the necessity of recovering P^3 before proceeding.

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buzzmath
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I'm trying to figure out these two questions

1. I have a ciphertext message produced by RSA encryption with key (e,n)=(5,2881) and I'm trying to find the plain text message of
0504 1874 0347 0515 2088 2356 0736 0468
I found the euler-phi function to be 42*66=2772 and found the modular inverse to be 1109 but I'm having trouble finding C^1109(mod2881) for each block of four. can anyone help with this?

2. I'm trying to show that if the encryption exponent 3 is used for the RSA cryptosystem by 3 different people with different moduli, and a plaintext message P encrypted usin each of their keys can be recovered from the resulting 3 ciphertext messages.
I've set it up to the congruences c_i congruent to P^3(mod n_i), i = 1,2,3 but I'm not really sure where to go from here. can anyone help?

thanks
 
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buzzmath said:
i'm having trouble finding C^1109(mod2881) for each block of four. can anyone help with this?

Use repeated squaring and reduce mod 2881 at each stage. That is find C^2 mod 2881, C^4 mod 2881, C^8 mod 2881, etc. then multiple the appropriate ones to get C^1109, reducing mod 2881 as necessary to keep the numbers small.

buzzmath said:
2. I'm trying to show that if the encryption exponent 3 is used for the RSA cryptosystem by 3 different people with different moduli, and a plaintext message P encrypted usin each of their keys can be recovered from the resulting 3 ciphertext messages.
I've set it up to the congruences c_i congruent to P^3(mod n_i), i = 1,2,3 but I'm not really sure where to go from here. can anyone help?

small hint- P will be less than each n_i. Do you have any way of first recovering P^3?
 

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