Error analysis of weak Poly-LWE instances

Chen, Yao; Case, Benjamin M.; Gao, Shuhong; Gong, Guang

doi:10.1007/s12095-018-0301-x

Cited by 2 publications

(3 citation statements)

References 10 publications

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“…An explicit method of calculating the probability distribution of e(α) given the distribution of the polynomial coefficients of e is presented in [4]. Theorem 3.8.…”

Section: The Distribution Of E(α)mentioning

confidence: 99%

“…Theorem 3.8. [4] Suppose e 0 , e 1 , ..., e n−1 are independent random variables in Z q with the same probability distribution (c 0 , c 1 , ..., c q−1 ). Let c(x) = i∈Zq c i x i .…”

Section: The Distribution Of E(α)mentioning

confidence: 99%

“…We can compute the discrete Gaussian distribution over Z q = Z/qZ as in [4]. The parameter used is σ = β √ 2π * q.…”

Section: The Distribution Of E(α)mentioning

confidence: 99%

See 2 more Smart Citations

The Polynomial Learning With Errors Problem and the Smearing Condition

Babinkostova¹,

Chin²,

Kirtland³

et al. 2020

Preprint

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As quantum computing advances rapidly, guaranteeing the security of cryptographic protocols resistant to quantum attacks is paramount. Some leading candidate cryptosystems use the Learning with Errors (LWE) problem, attractive for its simplicity and hardness guaranteed by reductions from hard computational lattice problems. Its algebraic variants, Ring-Learning with Errors (RLWE) and Polynomial Learning with Errors (PLWE), gain in efficiency over standard LWE, but their security remains to be thoroughly investigated. In this work, we consider the "smearing" condition, a condition for attacks on PLWE and RLWE introduced in [6]. We expand upon some questions about smearing posed by Elias et al. in [6] and show how smearing is related to the Coupon Collector's Problem. Furthermore, we develop some practical algorithms for calculating probabilities related to smearing. Finally, we present a smearing-based attack on PLWE, and demonstrate its effectiveness.

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“…An explicit method of calculating the probability distribution of e(α) given the distribution of the polynomial coefficients of e is presented in [4]. Theorem 3.8.…”

Section: The Distribution Of E(α)mentioning

confidence: 99%

“…Theorem 3.8. [4] Suppose e 0 , e 1 , ..., e n−1 are independent random variables in Z q with the same probability distribution (c 0 , c 1 , ..., c q−1 ). Let c(x) = i∈Zq c i x i .…”

Section: The Distribution Of E(α)mentioning

confidence: 99%

See 1 more Smart Citation

The Polynomial Learning With Errors Problem and the Smearing Condition

Babinkostova¹,

Chin²,

Kirtland³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

The polynomial learning with errors problem and the smearing condition

Babinkostova

Chin

Kirtland

et al. 2022

Journal of Mathematical Cryptology

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As quantum computing advances rapidly, guaranteeing the security of cryptographic protocols resistant to quantum attacks is paramount. Some leading candidate cryptosystems use the learning with errors (LWE) problem, attractive for its simplicity and hardness guaranteed by reductions from hard computational lattice problems. Its algebraic variants, ring-learning with errors (RLWE) and polynomial learning with errors (PLWE), gain efficiency over standard LWE, but their security remains to be thoroughly investigated. In this work, we consider the “smearing” condition, a condition for attacks on PLWE and RLWE introduced in Elias et al. We expand upon some questions about smearing posed by Elias et al. and show how smearing is related to the coupon collector’s problem. Furthermore, we develop an algorithm for computing probabilities related to smearing. Finally, we present a smearing-based algorithm for solving the PLWE problem.

show abstract

Error analysis of weak Poly-LWE instances

Cited by 2 publications

References 10 publications

The Polynomial Learning With Errors Problem and the Smearing Condition

The Polynomial Learning With Errors Problem and the Smearing Condition

The polynomial learning with errors problem and the smearing condition

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