feat(quadratic voting): alternative

Author: cong-or

Cargo.lock

@@ -32,6 +32,8 @@ criterion = { version = "0.3.0", optional = true }
 rand = "0.8"
 cryptoxide = "0.4"
 tracing.workspace = true
+num-integer = "0.1"
+
 
 [features]
 property-test-api = [

src/chain-libs/chain-impl-mockchain/Cargo.toml

@@ -4,6 +4,7 @@ use crate::{
     vote::{Choice, Options},
 };
 use chain_vote::EncryptedTally;
+use num_integer::Roots;
 use std::fmt;
 use thiserror::Error;
 
@@ -166,7 +167,11 @@ impl TallyResult {
         } else {
             let index = choice.as_byte() as usize;
 
-            self.results[index] = self.results[index].saturating_add(weight);
+            // Returns the truncated principal square root of an integer – ⌊√x⌋
+            // This is solving for r in r² = x, rounding toward zero. The result will satisfy r² ≤ x < (r+1)²
+            let weight_gammad = weight.0.sqrt();
+
+            self.results[index] = self.results[index].saturating_add(Weight(weight_gammad));
 
             Ok(())
         }

src/chain-libs/chain-impl-mockchain/src/vote/tally.rs

@@ -14,6 +14,9 @@ thiserror = "1.0"
 cryptoxide = "^0.4.2"
 const_format = "0.2"
 base64 = "0.21.0"
+tracing = "0.1"
+num-integer = "0.1"
+
 
 [dev-dependencies]
 rand_chacha = "0.3"

src/chain-libs/chain-vote/Cargo.toml

@@ -11,6 +11,8 @@ use crate::{
 use base64::{engine::general_purpose, Engine as _};
 use cryptoxide::blake2b::Blake2b;
 use cryptoxide::digest::Digest;
+use num_integer::Roots;
+
 use rand_core::{CryptoRng, RngCore};
 
 /// Secret key for opening vote
@@ -155,10 +157,15 @@ impl EncryptedTally {
     pub fn add(&mut self, ballot: &Ballot, weight: u64) {
         assert_eq!(ballot.vote().len(), self.r.len());
         assert_eq!(ballot.fingerprint(), &self.fingerprint);
+
+        // Returns the truncated principal square root of an integer – ⌊√x⌋
+        // This is solving for r in r² = x, rounding toward zero. The result will satisfy r² ≤ x < (r+1)²
+        let weight_gammad = weight.sqrt();
+
         for (ri, ci) in self.r.iter_mut().zip(ballot.vote().iter()) {
-            *ri = &*ri + &(ci * weight);
+            *ri = &*ri + &(ci * weight_gammad);
         }
-        self.max_stake += weight;
+        self.max_stake += weight_gammad;
     }
 
     /// Given a single committee member's `secret_key`, returns a partial decryption of