Generate random numbers

This document explains how to generate cryptographically secure random encrypted numbers fully on-chain using the FHE library in fhevm. These numbers are encrypted and remain confidential, enabling privacy-preserving smart contract logic.

Key notes on random number generation

• On-chain execution: Random number generation must be executed during a transaction, as it requires the pseudo-random number generator (PRNG) state to be updated on-chain. This operation cannot be performed using the eth_call RPC method.

• Cryptographic security: The generated random numbers are cryptographically secure and encrypted, ensuring privacy and unpredictability.

Random number generation must be performed during transactions, as it requires the pseudo-random number generator (PRNG) state to be mutated on-chain. Therefore, it cannot be executed using the eth_call RPC method.

Basic usage

The FHE library allows you to generate random encrypted numbers of various bit sizes. Below is a list of supported types and their usage:

// Generate random encrypted numbers
ebool rb = FHE.randEbool();       // Random encrypted boolean
euint8 r8 = FHE.randEuint8();     // Random 8-bit number
euint16 r16 = FHE.randEuint16();  // Random 16-bit number
euint32 r32 = FHE.randEuint32();  // Random 32-bit number
euint64 r64 = FHE.randEuint64();  // Random 64-bit number
euint128 r128 = FHE.randEuint128(); // Random 128-bit number
euint256 r256 = FHE.randEuint256(); // Random 256-bit number

Example: Random Boolean

function randomBoolean() public returns (ebool) {
  return FHE.randEbool();
}

Bounded random numbers

To generate random numbers within a specific range, you can specify an upper bound. The specified upper bound must be a power of 2. The random number will be in the range [0, upperBound - 1].

// Generate random numbers with upper bounds
euint8 r8 = FHE.randEuint8(32);      // Random number between 0-31
euint16 r16 = FHE.randEuint16(512);  // Random number between 0-511
euint32 r32 = FHE.randEuint32(65536); // Random number between 0-65535

Example: Random number with upper bound

function randomBoundedNumber(uint16 upperBound) public returns (euint16) {
  return FHE.randEuint16(upperBound);
}

Security Considerations

• Cryptographic security: The random numbers are generated using a cryptographically secure pseudo-random number generator (CSPRNG) and remain encrypted until explicitly decrypted.

• Gas consumption: Each call to a random number generation function consumes gas. Developers should optimize the use of these functions, especially in gas-sensitive contracts.

• Privacy guarantee: Random values are fully encrypted, ensuring they cannot be accessed or predicted by unauthorized parties.