Slide $713\mathrm{.}2$

Let GenRSA be as in the previous sections, and construct a signature scheme as follows:

$$Gen: on input $1",$ run GenRSA$(1")$ to compute $($N$,$e$,$ d$).$ The public key is $($N$,$ e$)$ and the private key is $($N$,$d$).$

As part of key generation, a function H : $\{0,1\}*->$ Z is specified, but we leave this implicit.

$$Sign: on input a private key $($N$,$d$)$ and a message m $\{0,1\}*$ compute

o :$=[$H$($m$)$ mod N$].$

$$ Vrfy: on input a public key $($N$,$ e$),$ a message m$,$ and a signature o$,$ output $1$ if and only if

$$ ZH$($m$)$ mod N$.$

The RSA$-$FDH signature scheme.

Question $1$

Consider the RSA Full Domain Hash $($FDH$)$ signature scheme in slide $7$ of module $13\mathrm{.}2.$ Is the resulting signature deterministic or randomized?

$[$Assume the function H is deterministic.$]$

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