Prime Numbers
What is a prime number?
A number greater than 1 that can only be divided by 1 and itself
What are the two keys used in public key encryption?
A public key and a private key.
What does RSA stand for?
Rivest, Shamir, and Adleman
Where are prime-based systems used online?
In HTTPS, online banking, messaging apps, etc.
When was RSA invented?
In the 1970s.
Why are primes called the “atoms” of mathematics?
Because all other numbers can be built from them through multiplication.
What is the purpose of the public key?
To encrypt messages.
What is the first step in generating RSA keys?
Choose two large prime numbers, p and q.
What protocol secures websites?
SSL/TLS.
What new type of computer threatens prime-based cryptography?
Quantum computers.
Give three examples of prime numbers under 20.
2, 3, 5, 7, 11, 13, 17, 19.
What is the private key used for?
To decrypt messages.
What is n in RSA encryption?
The product of p × q.
Which popular messaging apps use encryption?
WhatsApp and Signal.
What is being developed to resist quantum attacks?
Post-quantum cryptography.
Why are prime numbers important in cryptology?
They make encryption hard to reverse (factorization is difficult).
Why can’t hackers easily find the private key?
Because it requires factoring a huge number into its prime factors.
Why is RSA secure?
Because factoring n into p and q is extremely hard.
What role do primes play in cryptocurrencies?
They help generate secure cryptographic keys.
Why are prime numbers considered “mysterious”?
Because they appear irregularly and infinitely, with no clear pattern.
What makes factoring large numbers so challenging?
Because no efficient algorithm exists to factor very large numbers quickly.
What mathematical property links the two keys?
Both are based on the same pair of large prime numbers.
In the example with p=3 and q=11, what is n?
n = 33.
What could happen if encryption based on primes stopped working?
Online transactions, messages, and data would no longer be secure.
What makes cryptology a fascinating field?
It connects pure math with real-world digital security.