Check elements are distinct in simple lottery. (#111)

## Content

Found another issue with the simple lottery. We need to check that
elements in the proof are distinct. I guess the simple lottery is not so
simple. :)

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src/centralized_telescope/algorithm.rs

@@ -12,6 +12,8 @@ use blake2::{Blake2s256, Digest};
 /// Calls up to setup.max_retries times the prove_index function and returns an empty
 /// proof if no suitable candidate is found.
 pub(super) fn prove(setup: &Setup, prover_set: &[Element]) -> Option<Proof> {
+    debug_assert!(crate::utils::misc::check_distinct(prover_set));
+
     // Run prove_index up to max_retries times
     (0..setup.max_retries).find_map(|retry_counter| prove_index(setup, prover_set, retry_counter).1)
 }

src/simple_lottery/algorithm.rs

@@ -8,12 +8,15 @@ use crate::utils::types::Element;
 use blake2::{Blake2s256, Digest};
 
 pub(super) fn prove(setup: &Setup, prover_set: &[Element]) -> Option<Proof> {
+    debug_assert!(crate::utils::misc::check_distinct(prover_set));
+
     let mut element_sequence = Vec::with_capacity(setup.proof_size as usize);
     for &element in prover_set {
         if lottery_hash(setup, element) {
             element_sequence.push(element);
         }
         if prover_set.len() as u64 >= setup.proof_size {
+            element_sequence.sort_unstable();
             return Some(Proof { element_sequence });
         }
     }
@@ -23,6 +26,7 @@ pub(super) fn prove(setup: &Setup, prover_set: &[Element]) -> Option<Proof> {
 
 pub(super) fn verify(setup: &Setup, proof: &Proof) -> bool {
     (proof.element_sequence.len() as u64 == setup.proof_size)
+        && proof.element_sequence.is_sorted_by(|a, b| a < b)
         && proof
             .element_sequence
             .iter()

src/utils/misc.rs

@@ -0,0 +1,8 @@
+use super::types::Element;
+
+/// Returns true iff all elements in the slice are distinct.
+pub(crate) fn check_distinct(elements: &[Element]) -> bool {
+    let mut elements = elements.to_vec();
+    elements.sort_unstable();
+    elements.is_sorted_by(|a, b| a < b)
+}

src/utils/mod.rs

@@ -1,3 +1,5 @@
 pub(crate) mod sample;
 
 pub(crate) mod types;
+
+pub(crate) mod misc;