2.6 Consider all the possible sets of two square roots s, t of 1 (mod 35)...

2.6 Consider all the possible sets of two square roots s, t of 1 (mod 35) where s ≢ t (mod 35) (there are six of them, since addition is commutative (mod 35). For all possible combinations, compute gcd(s + t, 35). Which combinations give you a single prime factor of 35?

2.7 Using CRT notation, show what is going on for all the combinations you considered in #2.6. Explain why gcd(s + t, 35) sometimes gave you a factor, and it sometimes did not.

2.8 Explain how you can make a digital signature that is mathematically equivalent to factoring using the results you considered in this assignment.

Expert Solution

Colby Messinger answered 1 year ago

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