Crafting certified elliptic curve cryptography implementations in Coq
Name
1015202268-MIT.pdf
Description
Full printable version
Size
379.08 KB
Format
Adobe PDF
Checksum (MD5)
5fef5ed6ce67f74c06c2d8a352823e29
Author(s)
Erbsen, Andres
Advisor(s)
Adam Chlipala.
Date Issued
2017
Publisher
Massachusetts Institute of Technology
Abstract
Elliptic curve cryptography has become a de-facto standard for protecting the privacy and integrity of internet communications. To minimize the operational cost and enable near-universal adoption, increasingly sophisticated implementation techniques have been developed. While the complete specification of an elliptic curve cryptosystem (in terms of middle school mathematics) fits on the back of a napkin, the fast implementations span thousands of lines of low-level code and are only intelligible to a small group of experts. However, the complexity of the code makes it prone to bugs, which have rendered well-designed security systems completely ineffective. I describe a principled approach for writing crypto code simultaneously with machine-checkable functional correctness proofs that compose into an end-to-end certificate tying highly optimized C code to the simplest specification used for verification so far. Despite using template-based synthesis for creating low-level code, this workflow offers good control over performance: I was able to match the fastest C implementation of X25519 to within 1% of arithmetic instructions per inner loop and 7% of overall execution time. While the development method itself relies heavily on a proof assistant such as Coq and most techniques are explained through code snippets, every Coq feature is introduced and motivated when it is first used to accommodate a non-Coq-savvy reader.
Description
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 103-106).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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