RSA

lastmod 2026-06-25created 2015-02-068 edits

RSA is a public-key cryptosystem and is known as the first algorithm capable of digital signatures as well as encryption. RSA's digital signature capability made it widely used in areas that require authentication, such as e-commerce.

It was formalized in 1977 through the work of Ron Rivest, Adi Shamir, and Leonard Adleman, and the name RSA comes from the initials of these three. The three inventors received the 2002 Turing Award for this achievement.

The security of the RSA cryptosystem rests on the difficulty of factoring large numbers into primes. So if an algorithm that can factor large numbers dramatically faster is found, this cryptosystem will lose its value. In 1993, Peter Shor published Shor's algorithm, a method for factoring an arbitrary integer in polynomial time using a quantum computer. So once quantum computers are put into practical use in earnest, the RSA algorithm will become useless. However, it seems it will still take many more years for quantum computers to become practical at this level.

The RSA encryption algorithm was patented in the United States in 1983 by the Massachusetts Institute of Technology (MIT), where the inventors worked, and the patent expired on September 21, 2000.

How to generate an RSA public key

If you use ssh, use ssh-keygen as below.

$ ssh-keygen -t rsa

See also

• PKI
• SSL
• OpenSSL
• EdDSA
  • Ed25519

Favorite site

• Wikipedia (en) description of RSA
• Naver Knowledge Encyclopedia: RSA algorithm
• [Recommended] Encryption and signing with RSA ¹

References