Mathematics, 26.02.2020 19:01, AM28

2.25. Suppose n = pq with p and q distinct odd primes. (a) Suppose that gcd(a, pq) = 1. Prove that if the equation x2 ≡ a (mod n) has any solutions, then it has four solutions. (b) Suppose that you had a machine that could find all four solutions for some given a. How could you use this machine to factor n?Hoffstein, Jeffrey. An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) (p. 112). Springer New York. Kindle Edition.

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2.25. Suppose n = pq with p and q distinct odd primes. (a) Suppose that gcd(a, pq) = 1. Prove that i...