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Practical Secure Delegated Linear Algebra with Trapdoored Matrices

  • 2026
  • OriginalPaper
  • Chapter
Published in:
Authors
Mark Braverman
Stephen Newman
Published in
Theory of Cryptography
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the realm of secure delegated linear algebra, focusing on the efficient and secure computation of matrix-vector and matrix-matrix multiplications. The authors introduce two novel cryptographic primitives: trapdoored matrices and targeted trapdoored matrices. These primitives are designed to mask operands before requesting their product from a server, thereby enhancing both security and computational efficiency. The chapter provides detailed constructions of these primitives under a standard Learning Parity with Noise (LPN) hardness assumption, ensuring robust security. The authors also implement and benchmark their protocol, demonstrating its practicality and efficiency. The protocol achieves both theoretically and practically small complexity blowup over computation in the clear, significantly reducing client computation. The chapter concludes with a discussion on the potential for further improvements and broader applications of these techniques in secure linear algebra.
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previous chapter Efficient Garbled Pseudorandom Functions and Lookup Tables from Minimal Assumption
next chapter On Achieving “Best-in-the-Multiverse” MPC
Title
Practical Secure Delegated Linear Algebra with Trapdoored Matrices
Authors
Mark Braverman
Stephen Newman
Copyright Year
2026
Book
Theory of Cryptography

Print ISBN: 978-3-032-12286-5

Electronic ISBN: 978-3-032-12287-2

Copyright Year: 2026

DOI
https://doi.org/10.1007/978-3-032-12287-2_4
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