10 Questions
Which of the following is a prime number?
11
Which of the following is a composite number?
9
What does it mean to factor a number?
To write a number as a product of other numbers
What is the product of the prime numbers 2 and 3?
6
What is the value of Euler's totient function for a prime number?
2
Which of the following is a prime number?
23
What is the value of Euler's totient function for the prime number 7?
6
What is the result of the Chinese Remainder Theorem?
It solves a system of congruences.
Which key exchange algorithm is used in the Diffie Hellman key exchange?
Elliptic curve arithmetic
What is the product of the prime numbers 2 and 3?
6
Study Notes
Prime Numbers
- A prime number is a positive integer that is divisible only by itself and 1.
Composite Numbers
- A composite number is a positive integer that has more than two distinct positive divisors.
Factoring
- To factor a number means to express it as a product of prime numbers.
- Factoring is the reverse of multiplication.
Prime Number Products
- The product of the prime numbers 2 and 3 is 6.
Euler's Totient Function
- Euler's totient function for a prime number is the number itself minus 1.
- Euler's totient function for the prime number 7 is 6.
Chinese Remainder Theorem
- The Chinese Remainder Theorem is a theorem in number theory that provides a unique solution to a system of congruences.
Cryptography
- The Diffie-Hellman key exchange algorithm uses the difficulty of computing discrete logarithms in a group to establish a shared secret key.
- The key exchange algorithm used in the Diffie-Hellman key exchange is modular exponentiation.
Test your knowledge on asymmetric ciphers and the mathematics behind asymmetric key cryptography in this quiz. Explore topics such as primes, primality testing, factorization, Euler's totient function, Fermat's and Euler's theorem, Chinese Remainder Theorem, exponentiation, and logarithm.
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