Cryptography and Residue Arithmetic

Neueste Paper

• Quotient Tree Arithmetic: Deferred-Division Computation with Bounded Symbolic Depth and Cross-Subtree Cancellation

  Gregory Magarshak · 28. Juli 2026

  We introduce Quotient Tree Arithmetic (QTA), a computational substrate in which values are represented as deferred quotient pairs (N, D) whose ratio is evaluated lazily at a designated materialization boundary. The framework applies to any domain: IEEE 754 doubles used as exact integer containers gi…

• Machines Learn Number Fields, But How? The Case of Galois Groups

  Kyu-Hwan Lee, Seewoo Lee · 19. Mai 2026

  By applying interpretable machine learning methods such as decision trees, we study how simple models can classify the Galois groups of Galois extensions over $\mathbb{Q}$ of degrees 4, 6, 8, 9, and 10, using Dedekind zeta coefficients. Our interpretation of the machine learning results allows us to…

• Enabling AI ASICs for Zero Knowledge Proof

  Jianming Tong, Jingtian Dang, Simon Langowski, Tianhao Huang, Asra Ali, Jeremy Kun, Jevin Jiang, Srinivas Devadas, Tushar Krishna · 21. April 2026

  Zero-knowledge proof (ZKP) provers remain costly because multi-scalar multiplication (MSM) and number-theoretic transforms (NTTs) dominate runtime as they need significant computation. AI ASICs such as TPUs provide massive matrix throughput and SotA energy efficiency. We present MORPH, the first fra…

• Inhibitor Transformers and Gated RNNs for Torus Efficient Fully Homomorphic Encryption

  Rickard Br\"annvall, Tony Zhang, Henrik Forsgren, Andrei Stoian, Fredrik Sandin, Marcus Liwicki · 24. März 2026

  This paper introduces efficient modifications to neural network-based sequence processing approaches, laying new grounds for scalable privacy-preserving machine learning under Fully Homomorphic Encryption (FHE). Transformers are now ubiquitous in AI applications and have largely supplanted Gated Rec…

• MXNorm: Reusing MXFP block scales for efficient tensor normalisation

  Callum McLean, Luke Y. Prince, Alexandre Payot, Paul Balan\c{c}a, Carlo Luschi · 16. März 2026

  Matrix multiplication performance has long been the major bottleneck to scaling deep learning workloads, which has stimulated the design of new accelerators that use increasingly low-precision number formats. However, improvements in matrix multiplication performance have far outstripped improvement…

• Accelerating Post-Quantum Cryptography via LLM-Driven Hardware-Software Co-Design

  Yuchao Liao, Tosiron Adegbija, Roman Lysecky · 11. Februar 2026

  Post-quantum cryptography (PQC) is crucial for securing data against emerging quantum threats. However, its algorithms are computationally complex and difficult to implement efficiently on hardware. In this paper, we explore the potential of Large Language Models (LLMs) to accelerate the hardware-so…

• Mage: Cracking Elliptic Curve Cryptography with Cross-Axis Transformers

  Lily Erickson · 16. Dezember 2025

  With the advent of machine learning and quantum computing, the 21st century has gone from a place of relative algorithmic security, to one of speculative unease and possibly, cyber catastrophe. Modern algorithms like Elliptic Curve Cryptography (ECC) are the bastion of current cryptographic securi…