zkFHE

What is FHE?

Homomorphic Encryption (HE) is a powerful cryptographic method that allows computations to be performed directly on encrypted data without needing to decrypt it first. Unlike traditional public key encryption schemes, where ciphertexts cannot be mathematically manipulated, homomorphic encryption enables certain operations to be conducted while maintaining data privacy.

There are several types of homomorphic encryption schemes, each capable of performing different classes of computations over encrypted data. These computations are typically represented as either Boolean or arithmetic circuits:

• Partially Homomorphic Encryption (PHE): Supports only a single type of operation, such as either addition or multiplication.

• Somewhat Homomorphic Encryption (SHE): Can handle both addition and multiplication but only for specific, limited circuits.

• Leveled Fully Homomorphic Encryption: Capable of evaluating circuits with multiple types of operations, but only up to a pre-determined depth.

• Fully Homomorphic Encryption (FHE): The most powerful variant, allowing for unlimited computations with multiple operations on encrypted data, regardless of circuit depth.

What is zkFHE?

While FHE enables privacy-preserving computations across various applications, such as cloud computing and privacy-preserving machine learning, it has a critical limitation: unverifiability. This means that users cannot easily verify the correctness of computations performed on encrypted data. For instance, it’s difficult to ensure that the result of a machine learning prediction is not just a random value.

zkFHE (Zero-Knowledge Fully Homomorphic Encryption) addresses this issue by combining FHE with zero-knowledge proofs, particularly zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge). zkFHE ensures the integrity and correctness of computations on encrypted data, enabling verifiable privacy-preserving operations.

The design and implementation of zkFHE are complex, involving sophisticated cryptographic techniques and optimization strategies to achieve both security and performance.

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