Prime Numbers in Cryptography: Uses & Benefits

Click For Summary

Discussion Overview

The discussion focuses on the usage of large prime numbers in cryptography, particularly in the context of RSA encryption, as well as exploring potential applications outside of cryptography.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about the usage of large primes in cryptography.
  • Another participant explains that large primes are essential for RSA encryption, highlighting the ease of modular arithmetic with them and the difficulty of factoring their product for decryption.
  • A specific example is provided regarding the RSA-200 semiprime, noting the extensive computational effort required to factor it.
  • Some participants question whether there are applications for large primes outside of cryptography.
  • Responses suggest various uses outside cryptography, including numerical algorithms, pseudorandom number generation, and private information retrieval schemes.

Areas of Agreement / Disagreement

The discussion presents multiple viewpoints regarding the applications of large primes, with some participants agreeing on their significance in cryptography while others explore additional uses, indicating that the conversation remains open-ended without a definitive consensus.

Contextual Notes

Some claims about the difficulty of factoring large primes and the computational resources required are presented without detailed mathematical justification, leaving assumptions about the complexity and feasibility of these tasks unresolved.

hadi amiri 4
Messages
98
Reaction score
1
What is yhe usage of big primes in Cryptography?
 
Physics news on Phys.org
One major use is for RSA. Encrypting with RSA requires finding large random primes and doing modular arithmetic with them, which are easy. Decrypting RSA can be performed by factoring the product of the primes, which is believed to be hard.

As an example: the 663-bit semiprime RSA-200 was factored by a cluster of computers; the lattice sieving alone was the equivalent of 55 years of work on a single processor. I multiplied the factors together on my computer; according to Pari, this took 0 ms.
 
are there any uses outside cryptography?
 
soandos said:
are there any uses outside cryptography?

Numerical algorithms (e.g. factorial computation), pseudorandom number generation (e.g. Mersenne twister), private information retrieval schemes (see Yekhanin's Ph.D thesis), etc.
 

Similar threads

Graduate Discussion on Astronomical Prime Numbers and Re-evaluating the Primali
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Which Mathematician's Theorem Linked Prime Numbers to Cryptography?
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad What are some applications of prime numbers other than cryptography
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Frequency of prime number gaps according to (p-1)/(p-2)
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Localising a non integral domain at a prime
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad How to Prove a Congruence Relation for Prime Numbers?
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Which Mathematicians Pioneered Prime Numbers for Cryptography?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Fundamental theorem of arithmetic from Jordan-Hölder theorem
  • · Replies 5 ·
Replies
5
Views
3K
Python Who can find the largest prime number with their own programmed code?
  • · Replies 28 ·
Replies
28
Views
5K
Undergrad Logical representation of prime numbers
  • · Replies 19 ·
Replies
19
Views
4K