Field reference
Cryptography glossary
Short definitions for terms used throughout the guide.
Mathematical base
- Modulus
- The number at which arithmetic wraps. Modulo 7 keeps only the residues 0 through 6.
- Congruent
- Two integers are congruent modulo n when they leave the same remainder after division by n.
- Finite field
- A finite set with addition, subtraction, multiplication, and division by every nonzero element, all staying inside the set.
- Group
- A set with one combination rule, an identity, inverses, and predictable grouping of operations.
- Generator
- A group element whose repeated combination produces every element in the relevant subgroup.
- Subgroup
- A smaller group contained inside a larger group, using the same operation. Cryptographic protocols usually work inside a chosen prime-order subgroup.
- Order
- The number of elements in a group or subgroup. The order of a point is the number of additions needed to return to the identity.
- Discrete logarithm
- The reverse of repeated group combination: given G and Q = kG, recover k.
Elliptic curves
- Elliptic curve
- A set of points satisfying a curve equation over a chosen field, plus a special identity point.
- Scalar multiplication
- Repeatedly adding one elliptic-curve point to itself. Written Q = kG.
- Private key
- A secret scalar used to derive a public key and authorize signatures.
- Public key
- A curve point derived from the private scalar. It can verify signatures without exposing the scalar.
- Off-curve
- A byte string that does not decode to a valid point on the chosen elliptic curve. Solana deliberately requires this for PDAs.
- Signer privilege
- A runtime property saying an account may authorize the current instruction. A transaction signature or valid PDA derivation can supply it.
- Cross-program invocation
- One Solana program calling an instruction in another program while passing account privileges into the child instruction.
Zero knowledge
- Statement
- The public claim that a verifier checks.
- Witness
- Private information that makes the public statement true.
- Constraint
- An arithmetic rule that valid witness values must satisfy.
- Circuit
- A fixed computation expressed as connected operations or arithmetic constraints.
- Completeness
- An honest prover with a valid witness can convince the verifier.
- Soundness
- A dishonest prover cannot convince the verifier of a false statement except with a small bounded probability.
- Zero knowledge
- The proof reveals no usable information beyond the truth of its statement, under the system's formal definition.
- SNARK
- A succinct, non-interactive argument of knowledge. Each word describes a separate property that we will test later.
Quantum algorithms
- Grover's algorithm
- A quantum method that searches an unstructured space using roughly the square root of the classical number of oracle queries.
- Shor's algorithm
- A quantum method for factoring integers and computing discrete logarithms in polynomial time on a suitable quantum computer.
Primary definitions: RFC 8032, SEC 1, GMR, Shor, and Grover.