Given an ordered set $S$ of positive integers (eg. $S=\{503, 503, 520, 551...N\}$) I want to be able to reveal the percentile rank (eg. 503 is in the top 10th percentile) for each element of a contiguous subset of $S$ (ie. $\{s_i,s_{i+1},... s_k\} \;|\; i \ge 0, k \lt N$). However I don't want to leak information that can be used to efficiently deduce $N$.
Using the formula for calculating a percentile rank of a given score from wikipedia:
$$P = \frac{\text{# values below score } s - (0.5 \times \text{# of scores with value }s)}{N}$$
We should be able to solve for $N$ with two percentiles $p_1$ and $p_2$ and the number of scores between them, $n$ using this formula.
$$
N = \frac{n}{p_2-p_1}
$$
As a demonstration, given a randomly generated dataset of $N$ of $10,000$ and values
$p_1=0.0751, p_2 = 0.0951 \text{ and } n=200$
$$N = \frac{200}{0.0951-0.0751}=10,000$$
Is there anything that can be done to maintain as much accuracy as possible while preventing the efficient determination of $N$ (something like differential privacy)? If this is possible I'm assuming I'll need to introduce some randomness, however I'm not sure how to formulate how much will be required.
