Information Set Decoding in the Lee Metric with Applications to Cryptography
This work addresses key size reduction in post-quantum cryptography, offering a domain-specific improvement for cryptographic applications.
The authors adapted Stern's information set decoding algorithm to the Lee metric over the ring Z/4Z, establishing a framework for McEliece and Niederreiter cryptosystems that reduces key sizes compared to Hamming metric codes.
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 $\mathbb{Z}/p^s\mathbb{Z}$.