Evaluation Key

An evaluation key is a public parameter in a fully homomorphic encryption (FHE) scheme that enables a designated party, such as a cloud server, to perform specific mathematical operations on ciphertext (encrypted data). Crucially, these operations are performed without ever accessing the underlying plaintext, preserving data privacy. The key is generated alongside a secret key during the initial setup of the cryptographic system and is required to execute the Eval function, which is the homomorphic evaluation of a circuit or function.

The evaluation key is distinct from the public key used for initial encryption. While the public key allows anyone to encrypt data, only a holder of the evaluation key can perform computations on that encrypted data. This separation of duties enhances security and control. In many FHE constructions, such as the BGV, BFV, or CKKS schemes, the evaluation key contains additional information, often called hints or encryptions of the secret key, that are necessary to manage the noise growth that inherently occurs during homomorphic operations, a process known as bootstrapping.

Practically, evaluation keys enable critical privacy-preserving applications. For instance, in secure cloud computing, a client can send encrypted data and an evaluation key to a server. The server can then run a machine learning model or a database query on the encrypted data and return an encrypted result, which only the client can decrypt with their secret key. This architecture ensures the server never sees the raw data, mitigating privacy risks in outsourced computation.

The size and management of evaluation keys present significant engineering challenges. In advanced FHE schemes, evaluation keys can be large—sometimes gigabytes in size—and their generation can be computationally intensive. Ongoing research focuses on optimizing key sizes and improving the efficiency of key-switching and modulus switching operations that rely on these keys. These optimizations are vital for making FHE practical for real-world, large-scale deployments.

In zero-knowledge proof systems, particularly zk-SNARKs, an evaluation key (often called a proving key) is a public parameter generated during a trusted setup ceremony. It contains encoded information about the specific circuit or program being verified. A prover uses this key to generate a proof that they have executed the circuit correctly on some private witness data, without revealing that data. The complementary verification key is used by the verifier to check the proof's validity. This separation of keys is fundamental to the succinctness and efficiency of SNARKs.

Within fully homomorphic encryption (FHE), an evaluation key serves a different but analogous purpose. It is a public key derived from the secret key that enables anyone to perform arbitrary computations (addition and multiplication) on ciphertexts. When an evaluator applies a function to encrypted data using the evaluation key, the resulting ciphertext remains encrypted and can be decrypted with the original secret key to reveal the output of the function as if it were run on the plaintext. This enables privacy-preserving cloud computing.

The security of an evaluation key is paramount. In zk-SNARKs, if the toxic waste from the trusted setup used to create the evaluation and verification keys is not destroyed, a malicious actor could generate fraudulent proofs. In FHE schemes like BGV or CKKS, the evaluation key's structure often introduces "noise" growth during computation, which must be managed through techniques like bootstrapping. Proper generation and handling of this key are therefore critical operational details for any system deploying these advanced cryptographic protocols.

An Evaluation Key is the public output of a trusted setup ceremony, a critical preparatory phase for many zero-knowledge proof systems like zk-SNARKs. This ceremony involves multiple participants collaboratively generating a set of public parameters, which includes the Evaluation Key and a corresponding Verification Key. The process uses a secret value, often called the toxic waste or tau, which must be securely discarded. The security of the entire system hinges on the assumption that this secret is permanently erased and cannot be reconstructed by any party.

The primary function of the Evaluation Key is to allow a prover to generate a proof. In systems such as Groth16, the key contains precomputed elliptic curve points that encode the constraints of the specific program or circuit being verified. When creating a proof, the prover uses this key to perform cryptographic operations that bind their secret witness data to the public statement, resulting in a short, easily verifiable proof. Importantly, the Evaluation Key is specific to a single arithmetic circuit; a new setup is required for each different program.

While the Evaluation Key is public, its creation is a point of vulnerability. If the secret toxic waste used to generate it is not properly destroyed, a malicious actor could create fraudulent proofs. To mitigate this, modern implementations use multi-party computation (MPC) ceremonies, like Perpetual Powers of Tau, where multiple participants contribute randomness. This decentralizes trust, as the final parameters are secure as long as at least one participant was honest and destroyed their secret share. The resulting structured reference string (SRS), which includes the Evaluation Key, is then considered safe for public use.

In practice, developers and networks treat a finalized Evaluation Key as a common reference point. For example, a zk-rollup like zkSync or a privacy-focused blockchain like Zcash will publish a specific Evaluation Key for its core circuit. All provers (e.g., rollup operators) must use this exact key to generate valid proofs that the network's verifiers, using the paired Verification Key, will accept. This creates a standardized, trust-minimized framework for executing and verifying complex computations off-chain.