Security parameter

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In cryptography, a security parameter is a way of measuring of how "hard" it is for an adversary to break a cryptographic scheme. There are two main types of security parameter: computational and statistical, often denoted by ${\displaystyle \kappa }$ and ${\displaystyle \lambda }$, respectively. Roughly speaking, the computational security parameter is a measure for the input size of the computational problem on which the cryptographic scheme is based, which determines its computational complexity, whereas the statistical security parameter is a measure of the probability with which an adversary can break the scheme (whatever that means for the protocol).

Security parameters are usually expressed in unary representation - i.e. ${\displaystyle \kappa }$ is expressed as a string of ${\displaystyle \kappa }$ ${\displaystyle 1}$s, ${\displaystyle \kappa =1\cdots 1}$, conventionally written as ${\displaystyle 1^{\kappa }}$ - so that the time complexity of the cryptographic algorithm is polynomial in the size of the input.