PDA Derivation

Background

Solana Keypair values are points on the Ed25519 curve. A keypair consists of a public key (used as the account address) and a secret key (used to produce signatures). Anyone with the secret key can sign transactions for that address.

Two accounts with on-curve addresses

A PDA is intentionally derived to fall off the Ed25519 curve. Because it is not a valid curve point, no secret key exists, and no external party can produce a signature. Only the deriving program can authorize operations on the PDA through invoke_signed.

Off Curve Address

PDA vs keypair accounts

Optional Seeds

The optional seeds are user-defined byte strings that serve as inputs to the PDA derivation. They create unique, deterministic addresses scoped to a program. For example, using ["user", user_pubkey] as seeds derives a different PDA for each user.

Seeds must follow these constraints:

• Maximum 16 seeds per derivation (MAX_SEEDS)
• Maximum 32 bytes per seed (MAX_SEED_LEN)

Bump Seed

The bump seed is a single byte (0-255) appended to the optional seeds during derivation. find_program_address searches from 255 down to 0, calling create_program_address with each value until the result falls off the Ed25519 curve. The first value that succeeds is the canonical bump.

Programs should always use the canonical bump to ensure a unique, deterministic mapping from seeds to address.

PDA Derivation

Derivation Algorithm

The PDA derivation is implemented in the SDK's create_program_address function. The algorithm works as follows:

1. Validate that the number of seeds does not exceed MAX_SEEDS (16) and no individual seed exceeds MAX_SEED_LEN (32 bytes). If either check fails, return PubkeyError::MaxSeedLengthExceeded.
2. SHA-256 hash all seeds, the program ID, and the string "ProgramDerivedAddress" together to produce a 32-byte result.
3. Check if the result is a valid point on the Ed25519 curve.
4. If the result IS on the curve, return PubkeyError::InvalidSeeds (the address would have a corresponding private key, which violates the PDA security property).
5. If the result is NOT on the curve, return it as the PDA.

Compute Unit Costs

The on-chain syscall for create_program_address charges 1,500 CUs per call.

The try_find_program_address syscall charges 1,500 CUs on entry (before the loop), then an additional 1,500 CUs for each failed bump attempt within the loop.

Common Seed Patterns

Seeds are application-specific. Common patterns include:

Examples: Derive a PDA

Deriving a PDA computes an address only. It does not create an on-chain account at that address. The account must be explicitly created through a separate instruction (typically create_account via CPI).

The Solana SDKs provide functions for PDA derivation. Each function takes:

• Program ID: The address of the program used to derive the PDA. This program can sign on behalf of the PDA.
• Optional seeds: Predefined inputs such as strings, numbers, or other account addresses.

The examples below derive a PDA using the Solana SDKs. Click ▷ Run to execute the code.

Derive a PDA with a string seed

The example below derives a PDA using a program ID and an optional string seed.

import { Address, getProgramDerivedAddress } from "@solana/kit";

const programAddress = "11111111111111111111111111111111" as Address;
const seeds = ["helloWorld"];
const [pda, bump] = await getProgramDerivedAddress({
  programAddress,
  seeds
});

console.log(`PDA: ${pda}`);
console.log(`Bump: ${bump}`);

import { Address, getProgramDerivedAddress } from "@solana/kit";

const programAddress = "11111111111111111111111111111111" as Address;
const seeds = ["helloWorld"];
const [pda, bump] = await getProgramDerivedAddress({
  programAddress,
  seeds
});

console.log(`PDA: ${pda}`);
console.log(`Bump: ${bump}`);

Derive a PDA with an address seed

The example below derives a PDA using a program ID and an optional address seed.

import {
  Address,
  getAddressEncoder,
  getProgramDerivedAddress
} from "@solana/kit";

const programAddress = "11111111111111111111111111111111" as Address;
const addressEncoder = getAddressEncoder();
const optionalSeedAddress = addressEncoder.encode(
  "B9Lf9z5BfNPT4d5KMeaBFx8x1G4CULZYR1jA2kmxRDka" as Address
);
const seeds = [optionalSeedAddress];
const [pda, bump] = await getProgramDerivedAddress({
  programAddress,
  seeds
});

console.log(`PDA: ${pda}`);
console.log(`Bump: ${bump}`);

import {
  Address,
  getAddressEncoder,
  getProgramDerivedAddress
} from "@solana/kit";

const programAddress = "11111111111111111111111111111111" as Address;
const addressEncoder = getAddressEncoder();
const optionalSeedAddress = addressEncoder.encode(
  "B9Lf9z5BfNPT4d5KMeaBFx8x1G4CULZYR1jA2kmxRDka" as Address
);
const seeds = [optionalSeedAddress];
const [pda, bump] = await getProgramDerivedAddress({
  programAddress,
  seeds
});

console.log(`PDA: ${pda}`);
console.log(`Bump: ${bump}`);

Derive a PDA with multiple seeds

The example below derives a PDA using a program ID and multiple optional seeds.

import {
  Address,
  getAddressEncoder,
  getProgramDerivedAddress
} from "@solana/kit";

const programAddress = "11111111111111111111111111111111" as Address;
const optionalSeedString = "helloWorld";
const addressEncoder = getAddressEncoder();
const optionalSeedAddress = addressEncoder.encode(
  "B9Lf9z5BfNPT4d5KMeaBFx8x1G4CULZYR1jA2kmxRDka" as Address
);
const seeds = [optionalSeedString, optionalSeedAddress];
const [pda, bump] = await getProgramDerivedAddress({
  programAddress,
  seeds
});

console.log(`PDA: ${pda}`);
console.log(`Bump: ${bump}`);

import {
  Address,
  getAddressEncoder,
  getProgramDerivedAddress
} from "@solana/kit";

const programAddress = "11111111111111111111111111111111" as Address;
const optionalSeedString = "helloWorld";
const addressEncoder = getAddressEncoder();
const optionalSeedAddress = addressEncoder.encode(
  "B9Lf9z5BfNPT4d5KMeaBFx8x1G4CULZYR1jA2kmxRDka" as Address
);
const seeds = [optionalSeedString, optionalSeedAddress];
const [pda, bump] = await getProgramDerivedAddress({
  programAddress,
  seeds
});

console.log(`PDA: ${pda}`);
console.log(`Bump: ${bump}`);

Iterating All Bumps

The following examples show PDA derivation using all possible bump seeds (255 to 0), illustrating how find_program_address returns the canonical bump:

import { PublicKey } from "@solana/web3.js";

const programId = new PublicKey("11111111111111111111111111111111");
const optionalSeed = "helloWorld";

// Loop through all bump seeds (255 down to 0)
for (let bump = 255; bump >= 0; bump--) {
  try {
    const PDA = PublicKey.createProgramAddressSync(
      [Buffer.from(optionalSeed), Buffer.from([bump])],
      programId
    );
    console.log("bump " + bump + ": " + PDA);
  } catch (error) {
    console.log("bump " + bump + ": " + error);
  }
}

import { PublicKey } from "@solana/web3.js";

const programId = new PublicKey("11111111111111111111111111111111");
const optionalSeed = "helloWorld";

// Loop through all bump seeds (255 down to 0)
for (let bump = 255; bump >= 0; bump--) {
  try {
    const PDA = PublicKey.createProgramAddressSync(
      [Buffer.from(optionalSeed), Buffer.from([bump])],
      programId
    );
    console.log("bump " + bump + ": " + PDA);
  } catch (error) {
    console.log("bump " + bump + ": " + error);
  }
}

bump 255: Error: Invalid seeds, address must fall off the curve
bump 254: 46GZzzetjCURsdFPb7rcnspbEMnCBXe9kpjrsZAkKb6X
bump 253: GBNWBGxKmdcd7JrMnBdZke9Fumj9sir4rpbruwEGmR4y
bump 252: THfBMgduMonjaNsCisKa7Qz2cBoG1VCUYHyso7UXYHH
bump 251: EuRrNqJAofo7y3Jy6MGvF7eZAYegqYTwH2dnLCwDDGdP
bump 250: Error: Invalid seeds, address must fall off the curve
...
// remaining bump outputs

In this example, bump 255 produces an on-curve address and fails. The first valid bump is 254, making it the canonical bump.