Secure E-Voting: Homomorphic Vote Tallying

Cast a Ballot

Auto-cast batch size 10

Live Readouts

Ballots cast

Modulus n

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Combined ciphertext C mod n²

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Election result

🔒 sealed — not yet decrypted

How it works

This runs a real (toy-sized) Paillier cryptosystem, the textbook additively-homomorphic scheme. Key generation picks primes p, q, sets n = p·q, g = n+1, and λ = lcm(p−1, q−1):

Encrypt:  c = (1 + m·n) · r^n  mod n²      (r random, gcd(r,n)=1)
Combine:  C = c₁ · c₂ · … · c_k  mod n²  = Enc(m₁ + m₂ + … + m_k)
Decrypt:  m = L(C^λ mod n²) · μ  mod n,   L(x) = (x−1)/n

The combine step is pure ciphertext multiplication — no key is involved and no individual m_i is ever recovered. Because Paillier is additively homomorphic, multiplying ciphertexts together produces the encryption of the sum of the plaintexts. That is exactly what an election authority needs: every voter encrypts their own ✓/✗ ballot (1 or 0) with the authority's public key (n, g), ballots are multiplied together as they arrive, and only the final product is ever decrypted with the private key (λ, μ) — revealing the tally without ever exposing a single vote.

Yes / No + Encrypt & Cast — encrypts one ballot with a fresh random blinding factor r and multiplies it into the running ciphertext (the glowing sphere at the ring's center).
Cast Random Batch — simulates many voters at once, each producing an independent ciphertext, positioned around the ring by its value mod n².
Tally Election — runs the actual decryption formula above on the combined ciphertext and reveals the sum of Yes votes.

Real deployments (Paillier-based e-voting trials, Google's private ad-conversion measurement, encrypted database aggregation) use 2048-bit primes instead of the small demo primes here, but the arithmetic is identical.

Encrypted Yes ballot Encrypted No ballot Combined ciphertext (ballot box)

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