NishMath - #general

The UK's National Cyber Security Centre (NCSC) has released a roadmap for transitioning to post-quantum cryptography (PQC), establishing key dates for organizations to assess risks, define strategies, and fully transition by 2035. This initiative aims to mitigate the future threat of quantum computers, which could potentially break today's widely used encryption methods. The NCSC’s guidance recognizes that PQC migration is a complex and lengthy process requiring significant planning and investment.

By 2028, organizations are expected to complete a discovery phase, identifying systems and services reliant on cryptography that need upgrades, and draft a migration plan. High-priority migration activities should be completed by 2031, with infrastructure prepared for a full transition. The NCSC emphasizes that these steps are essential for addressing quantum threats and improving overall cyber resilience. Ali El Kaafarani, CEO of PQShield, noted that these timelines give clear instructions to protect the UK’s digital future.

Researchers have also introduced ZKPyTorch, a compiler that integrates ML frameworks with ZKP engines to simplify the development of zero-knowledge machine learning (ZKML). ZKPyTorch automates the translation of ML operations into optimized ZKP circuits and improves proof generation efficiency. Through case studies, ZKPyTorch successfully converted VGG-16 and Llama-3 models into ZKP-compatible circuits.


References :

• The Quantum Insider: UK Sets Timeline, Road Map for Post-Quantum Cryptography Migration
• The Register - Security: The post-quantum cryptography apocalypse will be televised in 10 years, says UK's NCSC
• Dhole Moments: Post-Quantum Cryptography Is About The Keys You Don’t Play
• IACR News: ePrint Report: An Optimized Instantiation of Post-Quantum MQTT protocol on 8-bit AVR Sensor Nodes YoungBeom Kim, Seog Chung Seo Since the selection of the National Institute of Standards and Technology (NIST) Post-Quantum Cryptography (PQC) standardization algorithms, research on integrating PQC into security protocols such as TLS/SSL, IPSec, and DNSSEC has been actively pursued. However, PQC migration for Internet of Things (IoT) communication protocols remains largely unexplored. Embedded devices in IoT environments have limited computational power and memory, making it crucial to optimize PQC algorithms for efficient computation and minimal memory usage when deploying them on low-spec IoT devices. In this paper, we introduce KEM-MQTT, a lightweight and efficient Key Encapsulation Mechanism (KEM) for the Message Queuing Telemetry Transport (MQTT) protocol, widely used in IoT environments. Our approach applies the NIST KEM algorithm Crystals-Kyber (Kyber) while leveraging MQTT’s characteristics and sensor node constraints. To enhance efficiency, we address certificate verification issues and adopt KEMTLS to eliminate the need for Post-Quantum Digital Signatures Algorithm (PQC-DSA) in mutual authentication. As a result, KEM-MQTT retains its lightweight properties while maintaining the security guarantees of TLS 1.3. We identify inefficiencies in existing Kyber implementations on 8-bit AVR microcontrollers (MCUs), which are highly resource-constrained. To address this, we propose novel implementation techniques that optimize Kyber for AVR, focusing on high-speed execution, reduced memory consumption, and secure implementation, including Signed LookUp-Table (LUT) Reduction. Our optimized Kyber achieves performance gains of 81%,75%, and 85% in the KeyGen, Encaps, and DeCaps processes, respectively, compared to the reference implementation. With approximately 3 KB of stack usage, our Kyber implementation surpasses all state-of-the-art Elliptic Curve Diffie-Hellman (ECDH) implementations. Finally, in KEM-MQTT using Kyber-512, an 8-bit AVR device completes the handshake preparation process in 4.32 seconds, excluding the physical transmission and reception times.

Classification:

• HashTags: #PostQuantum #Cryptography #ZeroKnowledgeProofs
• Company: Cryptography
• Target: Security
• Product: Cryptography
• Feature: ZeroKnowledge
• Type: Crypto
• Severity: Major

Terence Tao has recently uploaded a paper to the arXiv titled "Decomposing a factorial into large factors." The paper explores a mathematical quantity, denoted as t(N), which represents the largest value such that N! can be factorized into t(N) factors, with each factor being at least N. This concept, initially introduced by Erdös, delves into how equitably a factorial can be split into its constituent factors.

Erdös initially conjectured that an upper bound on t(N) was asymptotically sharp, implying that factorials could be split into factors of nearly uniform size for large N. However, a purported proof by Erdös, Selfridge, and Straus was lost, leading to the assertion becoming a conjecture. The paper establishes bounds on t(N), recovering a previously lost result. Further conjectures were made by Guy and Selfridge, exploring whether relationships held true for all values of N.

On March 30th, mathematical enthusiasts celebrated facts related to the number 89. Eighty-nine is a Fibonacci prime, and patterns emerge when finding it's reciprocal. Also, the number 89 can be obtained by a summation of the first 5 integers to the power of the first 5 Fibonacci numbers. 89 is also related to Armstrong numbers, which are numbers that are the sum of their digits raised to the number of digits in the number.


References :

• beuke.org: Your browser does not support the audio element. Profunctor optics are a modern, category-theoretic generalization of optics – bidirectional data accessors used to focus on and update parts of a data structure.
• What's new: I;ve just uploaded to the arXiv the paper “Decomposing a factorial into large factors“. This paper studies the quantity , defined as the largest quantity such that it is possible to factorize into factors , each of which is at least .

Classification:

• HashTags: #Mathematics #Research #FunFacts
• Target: Knowledge
• Product: General
• Feature: Insights
• Type: Research
• Severity: Informative

The London Mathematical Society has awarded Polina Vytnova a Research in Pairs grant, dated February 14th. The grant will enable Vytnova to host Victor Kleptsyn, a CNRS Researcher from the University of Rennes, at the University of Surrey. Together, they will collaborate on a joint research project focusing on the "Arithmetic of Cantor sets."

Also, Terry Tao has announced a collaboration with Grant Sanderson of 3blue1brown, along with Tanya Klowden, to produce a two-part video about the history of the cosmic distance ladder. This project builds upon a previous public lecture by Tao and is related to their forthcoming book. The first part of the video is already available, with Sanderson currently editing the second part.


References :

• blogs.surrey.ac.uk: Polina Vytnova has been awarded a Research in Pairs grant (Award date 14 February) by the London Mathematical Society.
• : “Think about the knife tip. That is where you are. Now feel with it, very gently. You’re looking for a gap so small you could never see it with your eyes, but the knife tip will find it, if you put your mind there. Feel along the air till you sense the smallest little gap […]
• What's new: Grant Sanderson (who creates the website and Youtube channel 3blue1brown) has been collaborating with myself and others (including my coauthor Tanya Klowden) on producing a two-part video giving an account of some of the history of the cosmic distance ladder, building upon a previous public lecture I gave on this topic, and also relating to […]

Classification:

• HashTags: #Mathematics #Books #Research
• Company: WordPress
• Target: Knowledge
• Product: General
• Feature: Research
• Type: News
• Severity: Informative