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The RSA cryptosystem is a public-key type of cryptosystem. One of the core decisions in the design of an RSA cryptosystem is the key size. Typical key sizes used in this kind of cryptosystem range from 1024 bits to 4096 bits. With a key of the length of n bits, there are 2 x n number of possible keys that can be used. This number obviously 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 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 seen to be 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 as compared to what the current computer technology offers. If an adequately sized computer capable of running the Grover’s algorithm was to become available, it could reduce a 128-bit key down to 64-bit security, which is 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.
Choice of key length is influenced by many factors, 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. Or it could be just for a HTTPS web server or some other TLS server that can be replaced every two years or so.
· It could be for a dedicated application (For example, a closed user group with all using the same software supporting 4096 bit) or it could be for a vast user base where some of the users have to use 2048 bit due to old software/hardware.
· Whether it is important to use the key in a variety of 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.
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