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This comprehensive explanation has been generated from 38 GitHub source documents. All source documents are searchable here.
Last updated: October 7, 2025
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A mathematical function that is computationally easy to compute in one direction (from input to output) but computationally infeasible to invert (from output back to input), forming the foundation of cryptographic security in KERI through hash functions, key derivation, and self-certifying identifiers.
A one-way function is a fundamental cryptographic primitive characterized by asymmetric computational complexity. The function can efficiently compute an output for any given input in polynomial time, but given only the output (the "image" of the function), it is computationally infeasible to determine what the original input was. This computational asymmetry is understood within the framework of computational complexity theory, where "easy" means computable in polynomial time and "hard" means the inverse operation requires exponential or super-polynomial computational resources.
The defining property of one-way functions is irreversibility through computational hardness rather than mathematical impossibility. While theoretically it may be possible to reverse the function through exhaustive search, the computational resources required (time, energy, hardware) make such reversal practically impossible for properly designed one-way functions with sufficient cryptographic strength (typically 128 bits or more of entropy).
One-way functions serve as the mathematical foundation for numerous cryptographic operations including:
One-way functions emerged from theoretical computer science and cryptography research in the 1970s and 1980s as researchers formalized the mathematical properties required for secure cryptographic systems. The concept builds on earlier work in computational complexity theory, particularly the study of problems that are easy to verify but hard to solve (NP-complete problems).
Traditional cryptographic systems relied on one-way functions for:
KERI implementations must use cryptographically strong one-way functions that provide both:
Approved hash functions include Blake3, SHA-256, and SHA3-256, all providing 128+ bits of security.
Seeds and salts used as inputs to one-way functions must have sufficient entropy (randomness) to prevent brute-force attacks. KERI requires minimum 128 bits of entropy for cryptographic strength, though 256 bits is recommended for long-term security.
KERI uses derivation codes prepended to identifiers to specify which one-way function was used in derivation. This enables:
While one-way functions are "easy" to compute, implementations should:
One-way hash functions (unlike public key cryptography) are generally considered post-quantum secure because:
Implementations should:
The security of these systems depends entirely on the computational hardness of inverting the one-way function. If an efficient algorithm were discovered to invert the function, the entire security model would collapse. This dependency on computational hardness (rather than mathematical impossibility) distinguishes cryptographic security from information-theoretic security.
KERI leverages one-way functions as the foundational cryptographic primitive for establishing autonomic trust basis - a trust model that requires no external authorities or infrastructure. The protocol's security architecture depends on one-way functions in multiple critical ways:
KERI uses one-way functions to create self-certifying identifiers (SCIDs) where the identifier is cryptographically derived from the controller's public key. The derivation process follows:
Seed → Private Key → One-Way Function → Public Key → One-Way Function → Identifier
This double application of one-way functions ensures:
The one-way property means that while anyone can verify that a signature was created by the private key corresponding to the identifier, no one can work backwards from the identifier to discover the private key.
KERI extensively uses cryptographic hash functions (a specific type of one-way function) to create digests and Self-Addressing Identifiers (SAIDs). A digest is defined as a "verifiable cryptographic commitment" created through a collision-resistant hash of content.
The one-way property of hash functions enables:
Critically, KERI establishes that "a verifiable cryptographic commitment (such as a digital signature) to the digest of data is cryptographically equivalent to a commitment to the data itself." This equivalence property, enabled by the one-way nature of hash functions, allows ACDC credentials to use compact SAID references instead of embedding full data while maintaining cryptographic integrity.
KERI's revolutionary pre-rotation mechanism depends fundamentally on one-way functions for its security properties. In pre-rotation, the controller commits to the next set of rotation keys by publishing the cryptographic digest of those keys rather than the keys themselves.
The one-way property provides:
This approach transforms key rotation from a vulnerability (where compromised keys can be used to rotate to attacker-controlled keys) into a security feature (where unexposed pre-rotated keys enable recovery even after compromise).
The KERI specification describes using one-way functions to derive cryptographic keys from seeds (also called bran) and salts. A seed is "a cryptographic string used as a primary input for creating key material for an autonomic identifier."
The derivation process:
High-Entropy Seed + Salt → One-Way Function → Private Key → One-Way Function → Public Key
The one-way property ensures:
The KERI glossary defines cryptographic strength as the degree of resistance to attack, with 128 bits of entropy cited as the minimum for secure one-way functions. This strength requirement ensures that even with substantial computational resources, inverting the function remains infeasible.
For cryptonyms (cryptographic pseudonymous identifiers), the specification requires derivation "via a one-way cryptographic function with a sufficiently high degree of cryptographic strength (e.g., 128 bits)." This ensures that cryptonyms provide both universal uniqueness and computational security against inversion attacks.
One-way functions provide the irreplaceable security foundation for KERI's autonomic trust model. Unlike administrative trust (which depends on organizational security) or algorithmic trust (which depends on consensus mechanisms), autonomic trust depends solely on the computational hardness of inverting one-way functions. This creates a security model that:
Identifier Generation: Controllers generate AIDs by deriving identifiers from key pairs using one-way functions, creating self-certifying identifiers that prove control authority through signatures.
Content Addressing: ACDC credentials use SAIDs (self-addressing identifiers) where the identifier is the digest of the content, enabling compact references and tamper detection.
Key Event Logs: KELs use hash chaining where each event includes the digest of the previous event, creating tamper-evident logs through one-way function composition.
Witness Receipts: Witnesses sign digests of key events rather than the full events, enabling compact receipts while maintaining cryptographic binding.
Delegation Commitments: Delegators commit to delegated identifiers using digests, enabling verifiable delegation without exposing delegation details prematurely.
Computational Assumptions: Security depends on the assumption that no efficient algorithm exists to invert the one-way function. Advances in mathematics or quantum computing could potentially weaken this assumption, though KERI's pre-rotation mechanism provides some post-quantum protection.
Irreversibility: The one-way property means that if the original input (seed, private key) is lost, it cannot be recovered from the output. This places responsibility on controllers to securely backup seeds and implement recovery mechanisms.
Collision Resistance: While one-way functions prevent inversion, they must also be collision-resistant (hard to find two inputs producing the same output). KERI uses cryptographically strong hash functions like Blake3 and SHA-256 that provide both properties.
Performance Considerations: While computing one-way functions is "easy" in polynomial time, it still requires computational resources. KERI's architecture minimizes the number of hash operations required for verification to maintain performance at scale.
One-way functions enable KERI's zero-trust, end-verifiable security architecture. Because verification only requires computing one-way functions (which is efficient) rather than inverting them (which is infeasible), any party can independently verify:
This verification capability, enabled by the asymmetric computational complexity of one-way functions, forms the foundation of KERI's claim to provide "ambient verifiability" - the ability for anyone, anywhere, at any time to verify identifier control authority without depending on trusted infrastructure.