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Math Help - RSA algorithm check if ive done it right please

  1. #1
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    RSA algorithm check if ive done it right please

    Using an RSA code with the encryption integer e = 3 and distinct primes 3, 41 encode the message M = 5. Determine the decryption integer and check your encoded message by decoding it.

    to get the decryption integer:

    mod n (3-1) * (41-1) = 80

    e*d = 1 mod 80

    3*d = 1 mod 80

    d = 27

    to check message

    im not sure how to do any help please?
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  2. #2
    Super Member Bacterius's Avatar
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    Say p = 3, q = 41, so n = 123, and \varphi{(n)} = (p - 1)(q - 1) = 80.
    Say e = 3. Use the extended Euclidian algorithm to find that d = 27 (because 27 \times 3 \equiv 1 \pmod{\varphi{(n)}}.
    Now, M = 5, so C \equiv 5^e \pmod{123}, so C = 2.
    Now, C = 2, so M \equiv 2^d \pmod{123}, so M = 5.

    Thus this is correct.
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