# Tag Info

3

I'll use these common definitions and notations: $a\equiv b\pmod c$ means that $c>0$ and $c$ divides $b-a$ $a\equiv b^{-1}\pmod c$ means that $a\cdot b\equiv 1\bmod c$ $a=b\bmod c$ means that $a\equiv b\pmod c$ and $0\le a<c$ $a=b^{-1}\bmod c$ means that $a\equiv b^{-1}\pmod c$ and $0\le a<c$ $\varphi$ is the Euler totient function (also noted ...

3

The security of $\varphi$ and $\lambda$ should be equivalent since they are mathematically equivalent in the context in which they are used. (That is: the $d'$th power in $(\mathbb Z/pq\mathbb Z)^\times$ is exactly the same operation as the $d$th power.) However, the mathematically "right" modulus for computing $d$ is $\lambda(pq)$: it is precisely the ...

2

If you can select the distinct secret primes $p$ and $q$ such that $(p-1)/2$ and $(q-1)/2$ are also prime, then it becomes easy. For a random value $r$, $g = r^2$ will have order precisely $(p-1)(q-1)/4 \approx n/4$ unless $r, r-1$ or $r+1$ happens to not be relatively prime to $n$ (which, if you select $r$ randomly in the range $[2, n-2]$, happens with ...

Top 50 recent answers are included