Term Paper: The RSA Cryptosystem

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The RSA cryptosystem is a public-key type of cryptosystem. One of the core decisions in its design is the key size, which typically ranges from 1024 bits to 4096 bits.

With a key of length n bits, 2 x n possible keys can be used. This number grows rapidly with increasing values of n. Key lengths of 80 bits are usually considered the minimum for strong security in symmetric encryption algorithms.

128-bit keys are used commonly and are considered to be very strong. The very large number of operations required, i.e., 2128, to try out all the possible 128-bit keys is out of reach for most conventional digital computing techniques for the near future.

However, experts expect alternative computing technologies to arrive soon that may have superior processing power compared to current computer technology.

If an adequately sized computer capable of running Grover’s algorithm became available, it could reduce a 128-bit key to 64-bit security, roughly a (Date Encryption Standard) DES equivalent. This is one of the reasons why the Advanced Encryption System (AES) supports a 256-bit key length.

Many factors influence the choice of key length, some of the most important ones are discussed in the following:

  • Key lifetime: The key could be a long-life key, like an X.509 root for an in-house CA or an OpenPGP primary key. It could be just for an HTTPS web server or another TLS server that can be replaced every two years.
  • It could be for a dedicated application (For example, a closed user group with all the same software supporting 4096 bits) or for a vast user base where some users have to use 2048 bits due to old software/hardware.
  • It is important to use the key in various smart card readers.
  • Whether it is to be used in a mobile application (where battery conservation is an issue) or a server that will probably experience heavy load.