Transcribed TextTranscribed Text

1. Prove the following: If P and q are primes, p t q. p|d, and q|d, then pq|d. (I stated this fact without proof in the RSA notes.) 6. Recall our discussion of partial information on RSA. We defined the functions, o parify(2° mod n) = if I mod n is even 1 if I mod n is odd half(2" mod n) o if x mod n < n/2 = 1 if x mod n > n/2 Here e and n are the usual RSA public key parameters, and I is an RSA plaintext message, which means that it's an integer less than n. Prove the following: if half(2° mod n) = 1, then parify((2x) mod n) = 1. 7. Let p be prime. Prove that if I2 III 1 mod P and I # (p - 1) mod p. then 2 III 1 mod p. [Note that (p - 1) III (mod p)] 8. Suppose that p is prime, l' > 0, a III 1 mod p. and god(r.p - 1) = d. Prove that ad III 1 mod p.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    50% discount

    $18.00 $9.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Cryptography Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats