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Polynomial-time plaintext recovery attacks on the IKKR code-based cryptosystems

  • * Corresponding author: T. S. C. Lau

    * Corresponding author: T. S. C. Lau 
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  • Recently, Ivanov et al. proposed a new approach to construct code-based cryptosystems, namely the $ {\sf IKKR} $ public-key encryptions (PKE) in the International Workshop on Code-Based Cryptography (CBCrypto 2020) [9]. Unlike the usual construction in code-based encryption schemes which has restrictions on the Hamming weight of the error introduced into the ciphertext, the $ {\sf IKKR} $ approach allows error vectors of arbitrary weight being introduced into the ciphertext. Using this new approach, Ivanov et al. constructed two cryptosystems, namely the modified and the upgraded $ {\sf IKKR} $-PKE. This paper aims to discuss the practical security of the $ {\sf IKKR} $-PKE. In particular, we describe the weaknesses in the design of the public key used in the $ {\sf IKKR} $-PKE. We exploit such weaknesses and propose two attacks to recover the plaintext in the $ {\sf IKKR} $-PKE. The approach of our first attack is similar to the LCKN attack [12], whilst our second attack is more efficient than the LCKN attack. Our experimental results show that we can recover the plaintext from a given ciphertext in less than 176 milliseconds for schemes based on random Goppa codes and BCH codes.

    Mathematics Subject Classification: 14G50, 94A60, 11T71.

    Citation:

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  • Table 1.  Differences between the modified and the upgraded $ {\sf IKKR} $-PKE

    PKE $ {\sf MDF} $.$ {\sf IKKR} $ $ {\sf UGD} $.$ {\sf IKKR} $
    $ \mathcal{C} $ must be decodable any random code
    $ E_{\sf pub} $ $ WD[UG+P]M $ $ Q[UG + T]M $
    $ \text{rk} (E_{\sf pub}) $ $ =t< n-k $ $ =n-k $
    ${\sf Decrypt} (\mathit{\boldsymbol{m}}) $ requires decoding does not require decoding
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    Table 2.  Parameters proposed for the $ {\sf MDF} $.$ {\sf IKKR} $-PKE and the $ {\sf UGD} $.$ {\sf IKKR} $-PKE

    Instance Code $ (q,n,k,t) $ $ {\sf pk} $ size Security
    $ {\sf MDF} $.$ {\sf IKKR} $-Goppa Goppa $ (2,256,128,16) $ 12,288 KB 80-bit
    $ {\sf UGD} $.$ {\sf IKKR} $-BCH BCH $ (2,121,71,9) $ 2,513 KB 56-bit
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    Table 3.  Simulation results of our plaintext recovery attacks

    Instance Security Plaintext Recovery Attack $ t_{\sf PRA} $
    $ {\sf MDF} $.$ {\sf IKKR} $-Goppa 80-bit Algorithm 2 176 ms
    Algorithm 3 103 ms
    $ {\sf UGD} $.$ {\sf IKKR} $-BCH 56-bit Algorithm 2 120 ms
    Algorithm 3 77 ms
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