Top Mathematics discussions
NishMath - #cryptography
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@martinescardo.github.io
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ellipticnews.wordpress.com
The mathematics community is buzzing with activity, including upcoming online events and ongoing discussions about research methodologies. A significant event to watch for is the online celebration marking the 40th anniversary of Elliptic Curve Cryptography (ECC) on August 11, 2025. This event will commemorate the foundational work of Victor Miller and Neal Koblitz in 1985. It is anticipated to be a very important event for those in the cryptography community and to those who work with elliptic curves.
The ECC celebration will feature personal reflections from Miller and Koblitz, alongside lectures by Dan Boneh and Kristin Lauter, who will explore ECC's broad impact on cryptography and its unforeseen applications. The history of ECC is used as a good example of how fundamental research can lead to unexpected and practical outcomes. This serves as a good way to promote blue skies research. In other news, mathematicians are actively discussing the use of formal methods in their research. One Mathstodon user described using LaTeX and Agda in TypeTopology for writing papers and formalizing mathematical remarks. They found that formalizing remarks in a paper could reveal errors in thinking and improve results, even in meta-mathematical methodology. This shows how computational tools are increasingly being used to verify and explore mathematical ideas, highlighting the practical utility of pure math skills in applied contexts. Recommended read:
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@www.microsoft.com
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References:
medium.com
, www.microsoft.com
Microsoft is undertaking a significant modernization effort of its SymCrypt cryptographic library by rewriting key components in the Rust programming language. This strategic move aims to bolster memory safety and provide enhanced defenses against sophisticated side-channel attacks. The decision to use Rust is driven by its ability to enable formal verification, ensuring that cryptographic implementations behave as intended and remain secure against potential vulnerabilities, an essential component of robust security. This modernization also ensures the library can maintain backward compatibility through a Rust-to-C compiler.
This initiative is particularly focused on the implementation of elliptic curve cryptography (ECC), a vital cryptographic algorithm used to secure Web3 applications and other sensitive systems. ECC offers a modern approach to asymmetric key cryptography, providing comparable security to older methods like RSA but with significantly smaller key sizes. This efficiency is crucial for resource-constrained devices such as mobile phones and IoT devices, enabling faster encryption and decryption processes while maintaining high levels of security against cryptanalytic attacks, providing a strong foundation for secure digital interactions. The project involves incorporating formal verification methods using tools like Aeneas, developed by Microsoft Azure Research and Inria, allowing the mathematical verification of program properties. This process confirms that code will always satisfy given properties, regardless of input, thereby preventing attacks stemming from flawed implementations. Furthermore, the team plans to analyze compiled code to detect side-channel leaks caused by timing or hardware-level behavior, ensuring a comprehensive defense against a wide range of threats, solidifying Microsoft's commitment to providing cutting-edge security solutions. Recommended read:
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@medium.com
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Medium is currently hosting a series of articles that delve into the core concepts and practical applications of cryptography. These articles aim to demystify complex topics such as symmetric key cryptography, also known as secret key or private key cryptography, where a single shared key is used for both encryption and decryption. This method is highlighted for its speed and efficiency, making it suitable for bulk data encryption, though it primarily provides confidentiality and requires secure key distribution. The resources available are designed to cater to individuals with varying levels of expertise, offering accessible guides to enhance their understanding of secure communication and cryptographic systems.
The published materials offer detailed explorations of cryptographic techniques, including AES-256 encryption and decryption. AES-256, which stands for Advanced Encryption Standard with a 256-bit key size, is a symmetric encryption algorithm renowned for its high level of security. Articles break down the internal mechanics of AES-256, explaining the rounds of transformation and key expansion involved in the encryption process. These explanations are presented in both technical terms for those with a deeper understanding and in layman's terms to make the concepts accessible to a broader audience. In addition to theoretical explanations, the Medium articles also showcase the practical applications of cryptography. One example provided is the combination of OSINT (Open Source Intelligence), web, crypto, and forensics techniques in CTF (Capture The Flag) challenges. These challenges offer hands-on experience in applying cryptographic principles to real-world scenarios, such as identifying the final resting place of historical figures through OSINT techniques. The series underscores the importance of mastering cryptography in the evolving landscape of cybersecurity, equipping readers with the knowledge to secure digital communications and protect sensitive information. Recommended read:
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@www.iansresearch.com
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The increasing capabilities of quantum computers are posing a significant threat to current encryption methods, potentially jeopardizing the security of digital assets and the Internet of Things. Researchers at Google Quantum AI are urging software developers and encryption experts to accelerate the implementation of next-generation cryptography, anticipating that quantum computers will soon be able to break widely used encryption standards like RSA. This urgency is fueled by new estimates suggesting that breaking RSA encryption may be far easier than previously believed, with a quantum computer containing approximately 1 million qubits potentially capable of cracking it. Experts recommend that vulnerable systems should be deprecated after 2030 and disallowed after 2035.
Last week, Craig Gidney from Google Quantum AI published research that significantly lowers the estimated quantum resources needed to break RSA-2048. Where previous estimates projected that cracking RSA-2048 would require around 20 million qubits and 8 hours of computation, the new analysis reveals that it could be done in under a week using fewer than 1 million noisy qubits. This more than 95% reduction in hardware requirements is a seismic shift in the projected timeline for "Q-Day," the hypothetical moment when quantum computers can break modern encryption. RSA encryption, used in secure web browsing, email encryption, VPNs, and blockchain systems, relies on the difficulty of factoring large numbers into their prime components. Quantum computers, leveraging Shor's algorithm, can exponentially accelerate this process. Recent innovations, including Approximate Residue Arithmetic, Magic State Cultivation, Optimized Period Finding with Ekerå-Håstad Algorithms, and Yoked Surface Codes & Sparse Lookups, have collectively reduced the physical qubit requirement to under 1 million and allow the algorithm to complete in less than 7 days. Recommended read:
References :
@medium.com
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Google Quantum AI has published a study that dramatically lowers the estimated quantum resources needed to break RSA-2048, one of the most widely used encryption standards. The study, authored by Craig Gidney, indicates that RSA cracking may be possible with fewer qubits than previously estimated, potentially impacting digital security protocols used in secure web browsing, email encryption, VPNs, and blockchain systems. This breakthrough could significantly accelerate the timeline for "Q-Day," the point at which quantum computers can break modern encryption.
Previous estimates, including Gidney's 2019 study, suggested that cracking RSA-2048 would require around 20 million qubits and 8 hours of computation. However, the new analysis reveals it could be done in under a week using fewer than 1 million noisy qubits. This reduction in hardware requirements is attributed to several technical innovations, including approximate residue arithmetic, magic state cultivation, optimized period finding with Ekerå-Håstad algorithms, and yoked surface codes & sparse lookups. These improvements minimize the overhead in fault-tolerant quantum circuits, enabling better scaling. Google's researchers have discovered that, thanks to new error correction tricks and smarter algorithms, the encryption could be broken with under 1 million qubits and in less than a week, given favorable assumptions like a 0.1% gate error rate and a 1-microsecond gate time. This significantly faster encryption breaking capability, potentially 20x faster than previously anticipated, raises concerns about the security of Bitcoin wallets and other financial systems that rely on RSA encryption. The findings could potentially make Bitcoin wallets and financial systems vulnerable much sooner than expected. Recommended read:
References :
@medium.com
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The Post-Quantum Cryptography Coalition (PQCC) has recently published a comprehensive roadmap designed to assist organizations in transitioning from traditional cryptographic systems to quantum-resistant alternatives. This strategic initiative comes as quantum computing capabilities rapidly advance, posing a significant threat to existing data security measures. The roadmap emphasizes the importance of proactive planning to mitigate long-term risks associated with cryptographically relevant quantum computers. It is structured into four key implementation categories: Preparation, Baseline Understanding, Planning and Execution, and Monitoring and Evaluation.
The roadmap offers detailed steps for organizations to customize their adoption strategies, regardless of size or sector. Activities include inventorying cryptographic assets, assigning migration leads, prioritizing systems for upgrades, and aligning stakeholders across technical and operational domains. Furthermore, it underscores the urgency of Post-Quantum Cryptography (PQC) adoption, particularly for entities managing long-lived or sensitive data vulnerable to "harvest now, decrypt later" attacks. Guidance is also provided on vendor engagement, creating a cryptographic bill of materials (CBOM), and integrating cryptographic agility into procurement and system updates. In related advancements, research is focusing on enhancing the efficiency of post-quantum cryptographic algorithms through hardware implementations. A new study proposes a Modular Tiled Toeplitz Matrix-Vector Polynomial Multiplication (MT-TMVP) method for lattice-based PQC algorithms, specifically designed for Field Programmable Gate Arrays (FPGAs). This innovative approach significantly reduces resource utilization and improves the Area-Delay Product (ADP) compared to existing polynomial multipliers. By leveraging Block RAM (BRAM), the architecture also offers enhanced robustness against timing-based Side-Channel Attacks (SCAs), making it a modular and scalable solution for varying polynomial degrees. This combined with hybrid cryptographic models is a practical guide to implementing post quantum cryptography using hybrid models for TLS, PKI, and identity infrastructure. Recommended read:
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@quantumcomputingreport.com
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The rapid advancement of quantum computing poses a significant threat to current encryption methods, particularly RSA, which secures much of today's internet communication. Google's recent breakthroughs have redefined the landscape of cryptographic security, with researchers like Craig Gidney significantly lowering the estimated quantum resources needed to break RSA-2048. A new study indicates that RSA-2048 could be cracked in under a week using fewer than 1 million noisy qubits, a dramatic reduction from previous estimates of around 20 million qubits and eight hours of computation. This shift accelerates the timeline for "Q-Day," the hypothetical moment when quantum computers can break modern encryption, impacting everything from email to financial transactions.
This vulnerability stems from the ability of quantum computers to utilize Shor's algorithm for factoring large numbers, a task prohibitively difficult for classical computers. Google's innovation involves several technical advancements, including approximate residue arithmetic, magic state cultivation, optimized period finding with Ekerå-Håstad algorithms, and yoked surface codes with sparse lookups. These improvements streamline modular arithmetic, reduce the depth of quantum circuits, and minimize overhead in fault-tolerant quantum circuits, collectively reducing the physical qubit requirement to under 1 million while maintaining a relatively short computation time. In response to this threat, post-quantum cryptography (PQC) is gaining momentum. PQC refers to cryptographic algorithms designed to be secure against both classical and quantum attacks. NIST has already announced the first set of quantum-safe algorithms for standardization, including FrodoKEM, a key encapsulation protocol offering a simple design and strong security guarantees. The urgency of transitioning to quantum-resistant cryptographic systems is underscored by ongoing advances in quantum computing. While the digital world relies on encryption, the evolution to AI and quantum computing is challenging the security. Professionals who understand both cybersecurity and artificial intelligence will be the leaders in adapting to these challenges. Recommended read:
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