Commitment scheme 里面 Setup($1^\lambda$) 的意思

[luckyyang]

In the context of a commitment scheme, Setup($1^\lambda$) refers to a probabilistic polynomial-time (PPT) algorithm that takes a security parameter $\lambda$ (in unary) and generates public parameters $pp$. The notation $1^\lambda$ means that the input to the algorithm is a string of $\lambda$ ones, which is used as the security parameter.

In computer science, unary refers to a numeral system in which each natural number is represented by a corresponding number of 1s. For example, the number 3 would be represented as "111" in unary. Therefore, in the context of a security parameter, $1^\lambda$ means that the input to the algorithm is a string of $\lambda$ ones. In the unary numeral system, the number 10 is represented by ten ones: "1111111111".