Practice question · Select all that apply
Select every statement that is TRUE.
Hints
- Check the mod 8 claim against the specific residue 2.
- Security in modern cryptography comes from a hard problem, not a hidden procedure.
Show the answer
- A. a has an inverse mod n exactly when gcd(a, n) = 1
- C. Every nonzero residue mod 7 has an inverse
- D. An ISBN check digit makes a weighted sum congruent to 0 mod 11
Why
7 is prime so every nonzero residue is coprime to it and invertible. 8 is not: 2, 4 and 6 share the factor 2 with 8 and have no inverse (2x is always even, so never 1 mod 8). RSA's algorithm is completely public; its security rests on factoring being hard.
Practise Congruences and Applications
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