Security parameter
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 formula_1 and formula_2, 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. formula_1 is expressed as a string of formula_1 formula_5s, formula_6, conventionally written as formula_7 - so that the time complexity of the cryptographic algorithm is polynomial in the size of the input. Computational security. The security of cryptographic primitives relies on the hardness of some hard problems. One sets the computational security parameter formula_1 such that formula_9 computation is considered intractable. Statistical security. Security in cryptography often relies on the fact that statistical distance between is small. We formalise this using the statistical security parameter by saying that the distributions are "statistically close" if the  statistical distance between distributions can be expressed as a negligible function in the security parameter. One sets the statistical security parameter formula_13 such that formula_14 is considered a "small enough" chance of the adversary winning. Consider the following two broad categories of attack of adversaries on a given cryptographic scheme: attacks in which the adversary tries to learn secret information, and attacks in which the adversary tries to convince an honest party to accept a false statement as true (or vice versa). In the first case, for example a public-key encryption scheme, an adversary may be able to obtain  a large amount of information from which he can attempt to learn secret information, e.g. by examining the distribution of ciphertexts for a fixed plaintext encrypted under different randomness. In the second case, it may be that the adversary must guess a challenge or a secret and can do so with some fixed probability; in this we can talk about distributions by considering the algorithm for sampling the challenge in the protocol. In "both" cases, we can talk about the chance of the adversary "winning" in a loose sense, and can parameterise the statistical security by requiring the distributions to  be statistically close in the first case or defining a challenge space dependent on the statistical security parameter in the second case.