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Patrick Karl

@pkarlx.bsky.social

Doctoral candidate at TU Munich, working on Post-Quantum Cryptography, Hardware- and Software Implementations

20 Followers  |  47 Following  |  1 Posts  |  Joined: 02.03.2025  |  1.3166

Latest posts by pkarlx.bsky.social on Bluesky

Abstract. A significant effort in designing and engineering post-quantum cryptosystems is currently ongoing, also as a result of the National Institute of Standards and Technology (NIST) Post-quantum Cryptography (PQC) standardization process that started in 2016 and recently completed selecting two Key Encapsulation Mechanisms (KEMs), CRYSTALS-Kyber and HQC, and three digital signatures CRYSTALS-Dilithium, Falcon, and SPHINCS+ for standardization. In 2022, NIST launched another standardization effort for additional post-quantum digital signatures, preferably not based on the security assumptions of structured lattices, and with performance better than or equal to that of already standardized schemes (e.g., SPHINCS+ ). This initiative has narrowed down the initial 40 candidates to 14 in October 2024, eliciting public scrutiny of their algorithms and technical evaluation of their performance figures. Among the schemes admitted to the second round of evaluation, the code-based CROSS signature scheme was praised for its speed and the noticeably smaller signature sizes over the standardized version of SPHINCS+ . In this work, we present the first RTL hardware design of CROSS tailored for FPGA devices, delineating efficient implementation strategies for the critical components of the cryptographic scheme. Depending on the chosen security level, our design generates a key pair in 9 to 152 µs, signs a message in 404 µs to 5.89 ms, and verifies a signature in 322 µs to 4.38 ms on the NIST reference FPGA, a Xilinx Artix-7 device, proving competitive when compared with other candidates in the on-ramp standardization effort, namely LESS, MEDS, MAYO, Raccoon and SDitH, and comparable to current standard-selected ML-DSA, FN-DSA, and SLH-DSA in terms of efficiency.

Abstract. A significant effort in designing and engineering post-quantum cryptosystems is currently ongoing, also as a result of the National Institute of Standards and Technology (NIST) Post-quantum Cryptography (PQC) standardization process that started in 2016 and recently completed selecting two Key Encapsulation Mechanisms (KEMs), CRYSTALS-Kyber and HQC, and three digital signatures CRYSTALS-Dilithium, Falcon, and SPHINCS+ for standardization. In 2022, NIST launched another standardization effort for additional post-quantum digital signatures, preferably not based on the security assumptions of structured lattices, and with performance better than or equal to that of already standardized schemes (e.g., SPHINCS+ ). This initiative has narrowed down the initial 40 candidates to 14 in October 2024, eliciting public scrutiny of their algorithms and technical evaluation of their performance figures. Among the schemes admitted to the second round of evaluation, the code-based CROSS signature scheme was praised for its speed and the noticeably smaller signature sizes over the standardized version of SPHINCS+ . In this work, we present the first RTL hardware design of CROSS tailored for FPGA devices, delineating efficient implementation strategies for the critical components of the cryptographic scheme. Depending on the chosen security level, our design generates a key pair in 9 to 152 µs, signs a message in 404 µs to 5.89 ms, and verifies a signature in 322 µs to 4.38 ms on the NIST reference FPGA, a Xilinx Artix-7 device, proving competitive when compared with other candidates in the on-ramp standardization effort, namely LESS, MEDS, MAYO, Raccoon and SDitH, and comparable to current standard-selected ML-DSA, FN-DSA, and SLH-DSA in terms of efficiency.

Image showing part 2 of abstract.

Image showing part 2 of abstract.

High-Performance FPGA Accelerator for the Post-quantum Signature Scheme CROSS (Patrick Karl, Francesco Antognazza, Alessandro Barenghi, Gerardo Pelosi, Georg Sigl) ia.cr/2025/1161

20.06.2025 21:10 — 👍 0    🔁 1    💬 0    📌 0
Abstract. The Unbalanced Oil and Vinegar construction (UOV) has been the backbone of multivariate cryptography since the fall of HFE-based schemes. In fact, 7 UOV-based schemes have been submitted to the NIST additional call for signatures, and 4 of these made it to the second round. For efficiency considerations, most of these schemes are defined over a field of characteristic 2. This has as a side effect that the polar forms of the UOV public maps are not only symmetric, but also alternating.

In this work, we propose a new key-recovery attack on UOV in characteristic 2 that makes use of this property. We consider the polar forms of the UOV public maps as elements of the exterior algebra. We show that these are contained in a certain subspace of the second exterior power that is dependent on the oil space. This allows us to define relations between the polar forms and the image of the dual of the oil space under the Plücker embedding. With this, we can recover the secret oil space using sparse linear algebra.

This new attack has an improved complexity over previous methods and reduces the security by 4, 11, and 20 bits for uov-Ip, uov-III, and uov-V, respectively. Furthermore, the attack is applicable to MAYO₂ and improves on the best attack by 28 bits.

Abstract. The Unbalanced Oil and Vinegar construction (UOV) has been the backbone of multivariate cryptography since the fall of HFE-based schemes. In fact, 7 UOV-based schemes have been submitted to the NIST additional call for signatures, and 4 of these made it to the second round. For efficiency considerations, most of these schemes are defined over a field of characteristic 2. This has as a side effect that the polar forms of the UOV public maps are not only symmetric, but also alternating. In this work, we propose a new key-recovery attack on UOV in characteristic 2 that makes use of this property. We consider the polar forms of the UOV public maps as elements of the exterior algebra. We show that these are contained in a certain subspace of the second exterior power that is dependent on the oil space. This allows us to define relations between the polar forms and the image of the dual of the oil space under the Plücker embedding. With this, we can recover the secret oil space using sparse linear algebra. This new attack has an improved complexity over previous methods and reduces the security by 4, 11, and 20 bits for uov-Ip, uov-III, and uov-V, respectively. Furthermore, the attack is applicable to MAYO₂ and improves on the best attack by 28 bits.

Image showing part 2 of abstract.

Image showing part 2 of abstract.

Wedges, oil, and vinegar – An analysis of UOV in characteristic 2 (Lars Ran) ia.cr/2025/1143

19.06.2025 00:26 — 👍 6    🔁 4    💬 0    📌 1
Preview
FrodoKEM: Bolstering cryptography for a quantum future The recent advances in quantum computing offer many advantages—but also challenge current cryptographic strategies. Learn how FrodoKEM could help strengthen security, even in a future with powerful qu...

Nice post explaining FrodoKEM:

www.microsoft.com/en-us/resear...

28.05.2025 04:52 — 👍 1    🔁 0    💬 0    📌 0
Preview
CHES 2025 contact information Cryptographic Hardware and Embedded Systems

🔊 Call for Tutorials – CHES 2025!
We invite proposals for tutorials on cryptographic hardware, side channels, and secure designs at CHES!
📍 Kuala Lumpur, Malaysia
Details: ches.iacr.org/2025/callfor...
#CHES2025 #Crypto #HardwareSecurity

11.04.2025 08:03 — 👍 0    🔁 1    💬 0    📌 0

As part of the round-2 NIST submission, we developed a complete proof of security of SQIsign!

04.03.2025 09:05 — 👍 11    🔁 5    💬 1    📌 0

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