4.1. Course on Foundations of Cryptography

Try these first

1. 1.

   What is mathematical reasoning?

   Hint

   Think about the logical process in mathematics.

2. 2.

   Define combinatorial analysis.

   Hint

   It's about how we count objects in different ways.

3. 3.

   What is the main objective of mathematical reasoning?

   • To formulate proofs
   • To apply statistics
   • To teach programming

   Hint

   Recall the key role of proofs in math.

4. 4.

   True or False: Combinatorial analysis is only useful in mathematics and not in computer science.

   • True
   • False

   Hint

   Think about how counting impacts programming.

5. 5.

   Prove that the combination formula C(n, k) is equal to C(n-1, k-1) + C(n-1, k).

   Hint

   Think about ways to choose elements in different scenarios.

6. 6.

   Given a cryptographic algorithm, analyze its time complexity using recurrence relations.

   Hint

   Use common algorithms as references for how to express their time complexities.