Prime Numbers in Cryptography: Uses & Benefits

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SUMMARY

Prime numbers play a crucial role in cryptography, particularly in RSA encryption, which relies on large random primes for secure communication. The difficulty of factoring the product of these primes underpins the security of RSA. For instance, the RSA-200 semiprime, a 663-bit number, was factored using extensive computational resources, demonstrating the complexity involved. Additionally, prime numbers find applications beyond cryptography, including numerical algorithms, pseudorandom number generation, and private information retrieval schemes.

PREREQUISITES
  • Understanding of RSA encryption and decryption processes
  • Familiarity with modular arithmetic
  • Knowledge of numerical algorithms and their applications
  • Basic concepts of pseudorandom number generation
NEXT STEPS
  • Research the RSA algorithm and its implementation in cryptographic systems
  • Explore modular arithmetic techniques used in encryption
  • Learn about the Mersenne Twister algorithm for pseudorandom number generation
  • Investigate private information retrieval schemes as outlined in Yekhanin's Ph.D. thesis
USEFUL FOR

Cryptographers, security engineers, computer scientists, and anyone interested in the applications of prime numbers in secure communications and algorithm development.

hadi amiri 4
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What is yhe usage of big primes in Cryptography?
 
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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.
 

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