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It's not the algorithm that's more "efficient" (that's just a welcome side-effect) but the security level. Security levels are usually given in bits; to say that a cipher has 80 bits of security means that we assume it takes roughly $2^{80}$ effort to break it, for some definitions of "effort" and "break". For RSA, the main problem is factoring large ...


For all $\ell\in\mathbb N$, the cardinality of the set $\{0,1\}^\ell$ is $2^\ell$. This can be obtained inductively: We have $\{0,1\}^0=\{()\}$ (the empty tuple) which has cardinality $1=2^0$. If $\lvert\{0,1\}^\ell\rvert=2^\ell$, the elements of $\{0,1\}^{\ell+1}$ can be partitioned into two classes: The sequences that start with $0$ and those that start ...

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