Unified Program Generation and Verification: A Case Study on Number-Theoretic Transform

• Published in: Functional and Logic Programming Vol. 13215; pp. 133 - 151
• Main Authors: Masuda, Masahiro, Kameyama, Yukiyoshi
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 01.01.2022; Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 3030994600; 9783030994600
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-99461-7_8

Giving correctness assurance to the generated code in the context of generative programming is a poorly explored problem. Such assurance is particularly desired for applications where correctness of the optimized code is far from obvious, such as cryptography. This work presents a unified approach to program generation and verification, and applies it to an implementation of Number-Theoretic Transform, a key building block in lattice-based cryptography. Our strategy for verification is based on problem decomposition: While we found that an attempt to prove functional correctness of the whole program all at once is intractable, low-level components in the optimized program and its high-level algorithm structure can be separately verified using procedures of appropriate levels of abstraction. We demonstrate that such a decomposition and subsequent verification of each component are naturally realized in a program-generation approach based on the tagless-final style, leading to an end-to-end functional correctness verification of a highly optimized program.