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I often see the notation of powers of 1 in cryptography papers. For example, let $n$ be security parameter, then what does $1^n$ mean??

From high school student perspective, powers of one is always one.... But I hope this is not. Is this a bit string of length $n$? If so why don’t they write it as $\{0,1\}^n$?

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Is this a bit string of length $n$? If so why don’t they write it as $\{0,1\}^n$?

$\{0,1\}^n$ is not "a string of length $n$", it is the set of all strings of length $n$ (formally, the Cartesian product of $n$ copies of the set $\{0,1\}$). $1^n$ is an element of this set; namely the one where all bits are $1$.

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