The Beginner's Textbook for Fully Homomorphic Encryption Author: Ronny Ko arXiv ID: 2503.05136 Subjects: Cryptography and Security (cs.CR), Discrete Mathematics (cs.DM) Submission Date: First submitted on 7 Mar 2025, latest revision on 8 Sep 2025 (version 15) License: Creative Commons BY 4.0 (view license) DOI: https://doi.org/10.48550/arXiv.2503.05136 --- Overview Fully Homomorphic Encryption (FHE) is a cryptographic scheme that allows computation on encrypted data as if it were in plaintext. The result after decryption matches that of performing the same computation on the plaintext. Key features of FHE: Supports basic operations on encrypted data such as: Addition Multiplication Enables construction of more complex operations: Subtraction Division Logic gates (AND, OR, XOR, NAND, MUX) Advanced mathematical functions (ReLU, sigmoid, trigonometric functions like sin, cos) These functions can be implemented exactly or approximately to balance computational efficiency and accuracy. --- Applications Privacy-preserving machine learning: Allows servers to process encrypted data using ML models without exposing data or inference results. Only the client decrypts the output. Confidential blockchain services: Keeps smart contract sensitive data encrypted and confidential while maintaining transparency and integrity of execution. Other applications: Secure outsourcing of data analytics Encrypted database queries Privacy-preserving searches Efficient multi-party computation for digital signatures And more --- Project Status and Collaboration This textbook is an open project hosted at: https://fhetextbook.github.io Collaboration is welcomed from FHE experts to help expand the draft. --- Accessing the Paper PDF: Download PDF TeX Source available Other formats available via arXiv --- Additional Resources on arXiv Bibliographic and citation tools such as Bibliographic Explorer, Connected Papers, Litmaps, and scite.ai Smart Citations Code, data, and associated media linked via services including alphaXiv, CatalyzeX, DagsHub, Gotit.pub, Hugging Face, Papers with Code, ScienceCast Demos integration via Replicate, Hugging Face Spaces, TXYZ.AI Related papers and recommender tools like Influence Flower and CORE Recommender --- Contact and Support Contact arXiv: Support & Contact arXiv is supported by the Simons Foundation and member institutions. Donations to support arXiv are welcomed. --- This textbook offers a comprehensive beginner's guide to Fully Homomorphic Encryption, promising valuable insights for researchers, practitioners, and students interested in privacy-preserving cryptographic protocols and secure computing.