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Information Set Decoding in the Lee Metric with Applications to Cryptography
Cryptography and Security · Submitted 18 Mar 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that using Lee metric codes can drastically decrease the key size, compared to Hamming metric codes.
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The abstract, sentence by sentence
We convert Stern's information set decoding (ISD) algorithm to the ring $\mathbb{Z}/4 \mathbb{Z}$ equipped with the Lee metric. Moreover, we set up the general framework for a McEliece and a Niederreiter cryptosystem over this ring. The complexity of the ISD algorithm determines the minimum key size in these cryptosystems for a given security level. We show that using Lee metric codes can drastically decrease the key size, compared to Hamming metric codes. In the end we explain how our results can be generalized to other Galois rings $\mathbb{Z}/p^s\mathbb{Z}$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We convert Stern's information set decoding (ISD) algorithm to the ring $\mathbb{Z}/4 \mathbb{Z}$ equipped with the Lee metric. | contribution 0.90 | 0.95 | 0.08 | asserted 1.00 |
| s1 | Moreover, we set up the general framework for a McEliece and a Niederreiter cryptosystem over this ring. | contribution 0.99 | 0.94 | 0.07 | asserted 1.00 |
| s2 | The complexity of the ISD algorithm determines the minimum key size in these cryptosystems for a given security level. | background 0.67 | 0.18 | 0.09 | asserted 1.00 |
| s3 | We show that using Lee metric codes can drastically decrease the key size, compared to Hamming metric codes. | result 0.94 | 0.88 | 0.74 | asserted 0.99 |
| s4 | In the end we explain how our results can be generalized to other Galois rings $\mathbb{Z}/p^s\mathbb{Z}$. | future work 0.87 | 0.81 | 0.08 | asserted 0.82 |
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The paper
Original abstract
We convert Stern's information set decoding (ISD) algorithm to the ring $\mathbb{Z}/4 \mathbb{Z}$ equipped with the Lee metric. Moreover, we set up the general framework for a McEliece and a Niederreiter cryptosystem over this ring. The complexity of the ISD algorithm determines the minimum key size in these cryptosystems for a given security level. We show that using Lee metric codes can drastically decrease the key size, compared to Hamming metric codes. In the end we explain how our results can be generalized to other Galois rings $\mathbb{Z}/p^s\mathbb{Z}$.
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2 arXiv papers cite this in 3 sentences
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Cites it as background 1 paper
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New families of error correcting codes endowed with the Lee metric together with an iterative decoding algorithm were proposed [ref] while information set decoding (ISD) in the Lee metric has been analyzed [ref] .
On the Properties of Error Patterns in the Constant Lee Weight Channel · Introduction · 0.89
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