Summa

Privacy-Preserving Smart Contracts on Polkadot PVM

Summa is a Somewhat Homomorphic Encryption (SHE) library that enables confidential computation on the Polkadot Virtual Machine. Smart contracts can perform arithmetic on encrypted data without ever seeing the plaintext values.

┌────────────────────────────────────────────────────────────────────┐
│                                                                    │
│   Encrypt(100) + Encrypt(50) = Encrypt(150)                       │
│                                                                    │
│   The contract computes the sum without knowing either value.      │
│                                                                    │
└────────────────────────────────────────────────────────────────────┘

Live Demo

Try it now on Passet Hub Testnet:

Contract	Address
Confidential Asset	0x68d64d2b645ff6da083ef35a90f3b3931ea20b29

# Setup
export ETH_RPC_URL="https://testnet-passet-hub-eth-rpc.polkadot.io"
export CONTRACT="0x68d64d2b645ff6da083ef35a90f3b3931ea20b29"

# Query an encrypted balance
cast call $CONTRACT "0xdef45678c4B24396670D89CB02d525E3F8fa979839c19503"

See DEPLOYED.md for full deployment details and example calls.

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How It Works

Twisted ElGamal Encryption

Summa uses Twisted ElGamal on the JubJub curve. The "twist" encodes messages in the exponent, enabling:

• Additive Homomorphism: Enc(a) + Enc(b) = Enc(a + b)
• Scalar Multiplication: k × Enc(a) = Enc(k × a)

Encryption:
    C₁ = r × G
    C₂ = m × G + r × Y    (Y = public key)

Homomorphic Add:
    (C₁ₐ + C₁ᵦ, C₂ₐ + C₂ᵦ) = Enc(a + b)

Zero-Knowledge Range Proofs

Without range proofs, an attacker could send Enc(-1000) and underflow their balance. Summa includes Bulletproofs-style range proofs that verify 0 ≤ value < 2⁶⁴ without revealing the value.

Advanced Cryptographic Primitives

• DLEQ Proofs: Proves that two elliptic curve points share the same discrete log. Used for nullifier verification.
• Shielded Notes: Support for UTXO-style private transfers using nullifiers to prevent double-spending.

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Use Cases

1. Confidential Assets (Private ERC-20)

The flagship demo contract. Token balances are encrypted - only the holder can decrypt their balance.

// On-chain: Contract adds encrypted balances
let new_balance = old_balance.add_encrypted(&deposit)?;

// Off-chain: Only you can decrypt
let balance = wallet.decrypt(&encrypted_balance)?;

2. Shielded Transfers (UTXO Mode)

Move from account-based to note-based privacy. Spend notes anonymously by revealing nullifiers.

4. Sealed-Bid Voting

Submit Enc(votes) during voting period. Sum homomorphically. Decrypt only after deadline. Prevents herd behavior.

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Quick Start

Prerequisites

# Rust 1.84+
rustup update stable

# RISC-V target for PVM
rustup target add riscv64gc-unknown-none-elf

# Polkatool for linking
cargo install polkatool@0.26

# Foundry for deployment
curl -L https://foundry.paradigm.xyz | bash && foundryup

Build

git clone https://github.com/MontaQLabs/summa
cd summa
make all

Deploy

export PRIVATE_KEY=0x<your_key>
./deploy.sh --network testnet

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Project Structure

summa/
├── summa/                        # Core cryptographic library
│   ├── src/
│   │   ├── curve.rs             # JubJub elliptic curve primitives
│   │   ├── keys.rs              # Key generation, encryption, decryption
│   │   ├── ciphertext.rs        # Homomorphic operations
│   │   ├── range_proof.rs       # Zero-knowledge range proofs
│   │   ├── dleq.rs              # DLEQ proofs for nullifiers
│   │   ├── shielded.rs          # Note/UTXO primitives
│   │   ├── veil.rs              # Proof of Personhood primitives
│   │   └── client.rs            # Wallet and calldata utilities
│   └── README.md
├── contracts/
│   └── confidential-asset/       # Private token contract (PVM)
│       ├── src/main.rs          # Contract logic with new features
│       └── Summa.sol            # Solidity router for EVM integration
├── tools/
│   └── gen-ciphertext/           # CLI for encryption/decryption
├── docs/
│   ├── TECHNICAL.md             # Detailed technical documentation
│   ├── benchmark.md             # Performance benchmarks
├── DEPLOYED.md                   # Live deployment addresses
├── deploy.sh                     # Multi-network deployment script
└── Makefile

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Performance

Detailed benchmarks are available in docs/benchmark.md.

Operation	Gas (approx.)	Time
Encryption (client)	N/A	~2ms
Homomorphic Add	~20,000	~0.05ms
Range Proof Verify	~500,000	~12ms

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License

MIT License - see LICENSE for details.

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Built for Polkadot 🔴
Enabling confidential computation on public blockchains