Algorithm 8  Heuristicallyparameterise RNS-CKKS scheme using expected cost of computation.

Require: c: Integer maximal cost of this cyphertext group.

Require: s: Integer scale power, the scale of the cyphertext. Default: $s=40$. We advise not to go below 30 due to noise accumulation and lack of prime availability.

Require: p: Float special prime multiplier, the multiplier that dictates the scale-stabilised special primes in the coefficient modulus chain. Default: $p=1.5$

Ensure: $\mathit{parms}$: MS-SEAL RNS-CKKS parameter dictionary/map.

function parameterise(c, s, p)

$\mathit{parms}\leftarrow \mathrm{dict}\left(\right)$

$\mathit{parms}\left[″\mathrm{scheme}″\right]\leftarrow 2$            ▹ 2 is CKKS in MS-SEAL

$\mathit{parms}\left[″\mathrm{scale}″\right]\leftarrow \mathrm{pow}(2,s)$              ▹ scale power

$m\leftarrow \left[s\mathrm{for}i\mathrm{in}\mathrm{range}\right(c+2\left)\right]$

$m\left[0\right]\leftarrow \mathrm{int}\left(m\right[0]\ast p)$             ▹ Mult first special prime

$m[-1]\leftarrow \mathrm{int}\left(m\right[-1]\ast p)$            ▹ Mult last special prime

$b\leftarrow 27$

while $b<\mathrm{sum}\left(m\right)$ do

$b\leftarrow b\ast 2$

$\mathit{parms}\left[″\mathrm{poly}\_\mathrm{modulus}\_\mathrm{degree}″\right]\leftarrow \mathrm{int}(1024\ast (b/27\left)\right)$

return $\mathit{parms}$