Post Quantum Learning With Errors Problem Based Key Encapsulation Protocols and Matrix Vector Product

Alkım, Erdem; Yazar, Bilge Kağan

doi:10.1109/ubmk.2019.8907201

Cited by 4 publications

(13 citation statements)

References 19 publications

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“…Significant progress has been made to improve the asymptotical and practical efficiency of SVP and lattice reduction algorithms [13][14][15][16][17][18][19] and to better understand their behaviours [20][21][22][23]. Based on the cost models of SVP and lattice reduction, some generic cryptanalysis methodologies were presented with extensive experimental verifications [24][25][26]. Additionally, there are various attacks proposed to specific security models and parameters.…”

Section: Systematic Security Estimatesmentioning

confidence: 99%

“…x; yÞ A, b) is an LWE sample, then 〈u, b〉 = −〈v, s〉 + 〈u, e〉 mod q is closely distributed as a Gaussian of standard deviation ℓ 1 ℓ 2 ffi ffi ffi ffi ffi ffi ffiffi ⋅ q m=d where d = m + n. In the concrete cryptanalysis, the attacker needs about 1/ϵ 2 many such short vectors to get a success probability at least 1/ 2. For more details, we refer [24].…”

Section: �àmentioning

confidence: 99%

“…In kleptographic attacks, attackers can steal information securely and subliminally through a backdoor embedded in the cryptosystems. There have been a few works [24,150,151] discussing kleptographic attacks against lattice-based schemes.…”

Section: Kleptographic Attacksmentioning

confidence: 99%

“…An analysis in ref. [24] showed that BKZ β would recover ( s , e , −1) if β satisfies

\Vert (\mathbf{s},\mathbf{e},-1)\Vert \sqrt{\frac{\beta }{d}}\le {\delta }_{\beta }^{2\beta -d-1}\cdot {q}^{\tfrac{m}{d}}

where

{\delta }_{\beta }={\left(\frac{{(\pi \beta )}^{\tfrac{1}{\beta }}\beta }{2\pi e}\right)}^{\tfrac{1}{2(\beta -1)}}

and d = m + n + 1. This analysis was later verified experimentally in ref.…”

Section: Security Estimatesmentioning

confidence: 99%

“…x ∈ Z mþnþ1 |ðA I n bÞx ¼ 0 mod q � and (s, e, −1) is a short vector of L. An analysis in ref. [24] showed that BKZ β would recover (s, e, −1) if β satisfies kðs; e; −1Þk…”

mentioning

confidence: 99%

See 4 more Smart Citations

Lattice‐based cryptosystems in standardisation processes: A survey

Wang

Xiao

2022

IET Information Security

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The current widely used public‐key cryptosystems are vulnerable to quantum attacks. To prepare for cybersecurity in the quantum era, some projects have been launched to call for post‐quantum alternatives. Due to solid security and desirable performance, lattice‐based cryptosystems are viewed as promising candidates in the upcoming standardisation of post‐quantum cryptography. This study surveys the lattice‐based cryptosystems in the post‐quantum standardisation processes including the NIST Post‐Quantum Cryptography Standardisation and the Chinese Cryptographic Algorithm Design Competition, from both design and security aspects. We present generic design paradigms of lattice‐based schemes and describe several representative proposals and recent progress. We also recap some main cryptanalytic results and methods for estimating the concrete security of lattice‐based schemes.

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Section: Systematic Security Estimatesmentioning

confidence: 99%

Section: �àmentioning

confidence: 99%

Section: Kleptographic Attacksmentioning

confidence: 99%

“…An analysis in ref. [24] showed that BKZ β would recover ( s , e , −1) if β satisfies

\Vert (\mathbf{s},\mathbf{e},-1)\Vert \sqrt{\frac{\beta }{d}}\le {\delta }_{\beta }^{2\beta -d-1}\cdot {q}^{\tfrac{m}{d}}

where

{\delta }_{\beta }={\left(\frac{{(\pi \beta )}^{\tfrac{1}{\beta }}\beta }{2\pi e}\right)}^{\tfrac{1}{2(\beta -1)}}

and d = m + n + 1. This analysis was later verified experimentally in ref.…”

Section: Security Estimatesmentioning

confidence: 99%

mentioning

confidence: 99%

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Lattice‐based cryptosystems in standardisation processes: A survey

Wang

Xiao

2022

IET Information Security

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Improving convergence and practicality of slide-type reductions

Li¹,

Walter²

2023

Information and Computation

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Towards quantum‐secure software defined networks

Nosouhi,

Sood,

Chamola

et al. 2023

IET Quantum Communication

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The evolution of quantum computers is considered a serious threat to public‐key cryptosystems (e.g. RSA, ECDSA, ECDH, etc.). This is indeed a big concern for security of the Internet and other data communication and storage systems. The reason is that public‐key schemes are the basis in the generation of shared symmetric keys that are used to perform data encryption/decryption in communication and data transfer protocols. One possible approach to address this issue is to use Quantum Key Distribution (QKD) (instead of public‐key schemes) for the ultra‐secure generation of symmetric keys. QKD is a physical layer technology that allows two parties (equipped with optical communication interfaces) to generate secure random keys over a quantum channel that is immune to eavesdropping threats. The keys are then used by symmetric encryption schemes (e.g. AES) to encrypt data over classical channels. This allows us to have data encryption/decryption without needing a public‐key scheme. However, due to its inherent characteristics, the implementation of QKD has mostly been considered in particular contexts only (e.g. backhaul networks, point‐to‐point connections, optical networks, etc.). This indeed limits the utility of QKD technology to only some particular applications while it has the potential to be used in a wide range of used cases. Motivated by this (increasing the usability of QKD technology), in this study, the authors propose a model that enables SDN‐based networks to utilise QKD technology and provide QKD security service (i.e., random key generation service) to network applications and security protocols in a practical and efficient way. In the proposed approach, secret keys are generated based on the distribution of quantum entanglement between QKD nodes deployed in the network. The significant characteristic of our proposed model is that it does not rely on quantum repeaters to operate. This also improves the efficiency of the employed QKD mechanisms in terms of the key generation rate.

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Post Quantum Learning With Errors Problem Based Key Encapsulation Protocols and Matrix Vector Product

Cited by 4 publications

References 19 publications

Lattice‐based cryptosystems in standardisation processes: A survey

Lattice‐based cryptosystems in standardisation processes: A survey

Improving convergence and practicality of slide-type reductions

Towards quantum‐secure software defined networks

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