Key Size and Encryption System
Encryption systems are often grouped into families. Common families include symmetric systems (e.g. AES) and asymmetric systems (e.g. RSA); they may alternatively be grouped according to the central algorithm used (e.g. elliptic curve cryptography).
As each of these is of a different level of cryptographic complexity, it is usual to have different key sizes for the same level of security, depending upon the algorithm used. For example, the security available with a 1024-bit key using asymmetric RSA is considered approximately equal in security to an 80-bit key in a symmetric algorithm (Source: RSA Security).
The actual degree of security achieved over time varies, as more computational power and more powerful mathematical analytic methods become available. For this reason cryptologists tend to look at indicators that an algorithm or key length shows signs of potential vulnerability, to move to longer key sizes or more difficult algorithms. For example as of May 2007, a 1039 bit integer was factored with the special number field sieve using 400 computers over 11 months. The factored number was of a special form; the special number field sieve cannot be used on RSA keys. The computation is roughly equivalent to breaking a 700 bit RSA key. However, this might be an advanced warning that 1024 bit RSA used in secure online commerce should be deprecated, since they may become breakable in the near future. Cryptography professor Arjen Lenstra observed that "Last time, it took nine years for us to generalize from a special to a nonspecial, hard-to-factor number" and when asked whether 1024-bit RSA keys are dead, said: "The answer to that question is an unqualified yes."
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