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Discrete Mathematics & Math
Q90 / 100
What is the algebraic structure of RSA and why it works?
Correct! Well done.
Incorrect.
The correct answer is B) RSA exploits Euler's theorem: in (ℤ/nℤ)*, a^φ(n) ≡ 1 (mod n), making ed ≡ 1 (mod φ(n)) imply (m^e)^d ≡ m (mod n)
B
Correct Answer
RSA exploits Euler's theorem: in (ℤ/nℤ)*, a^φ(n) ≡ 1 (mod n), making ed ≡ 1 (mod φ(n)) imply (m^e)^d ≡ m (mod n)
Explanation
RSA: n=pq, φ(n)=(p-1)(q-1), e·d ≡ 1 (mod φ(n)), encrypt: c = m^e mod n, decrypt: m = c^d mod n = m^(ed) mod n = m^(1+kφ(n)) ≡ m (Euler's theorem). Security: factoring n to find φ(n) is believed hard.
Progress
90/100