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Information set decoding in the Lee metric with applications to cryptography

  • * Corresponding author: Violetta Weger

    * Corresponding author: Violetta Weger
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  • 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 substantially 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} $.

    Mathematics Subject Classification: Primary: 11T71; Secondary: 68P30.


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  • Table 1.  Key sizes and security levels (both in bits) for GV-codes over $ \mathbb Z_4 $ with $ n = 150 $ and $ d = 81 $

    $ k_1 $ 1 2 3 $ \dots$ 18 19 $ \dots$ 24 25 26
    best $ \ell $ 0 0 0 $ \dots$ 0 0 $ \dots$ 0 1 2
    best $ v $ 4 4 4 $ \dots$ 3 3 $ \dots$ 2 2 2
    key size 5198 5296 5390 $ \dots$ 6110 6160 $ \dots$ 6440 6446 6448
    security level 31 31 31 $ \dots$ 27 27 $ \dots$ 28 28 28
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