<p>One of the main candidates for post-quantum cryptography is code-based cryptography (as opposed to lattice-based). The Niederreiter cryptosystem based on Goppa codes is shown to be resistant to hidden subgroup attacks.  <strong>Do we have any similar result for other code-based systems using codes other than Goppa?</strong> There are many code-based systems coming up (being proposed) regularly and I don't see if such resistance will be trivially adapted by such variants.</p>

CC BY-SA 4.0
2019-07-26T08:06:42.463Z
What's the exact difference between McEliece and Niderreiter cryptosystems?
kodlu
CC BY-SA 4.0
2019-07-26T08:16:49.340Z
@kodlu Basic difference is that McEliece encryption is with Generator matrix of the code while for Niederreiter its the parity check matrix. This causes requirement for some slight modification in the system such as space of possible plaintexts and corresponding error decoding along the code. On the security point of view, Niederreiter systems have a signature scheme and I am not aware of any such progress with McEliece.
Root
<quantum-computing><cr.crypto-security><coding-theory><security>
Quantum security of cryptosystems: Are any non-Goppa code-based systems resistant to hidden subgroup attacks?
Root
# Quantum security of cryptosystems: Are any non-Goppa code-based systems resistant to hidden subgroup attacks?

(Asked by: username_0 on 2019-07-25)

One of the main candidates for post-quantum cryptography is code-based cryptography (as opposed to lattice-based). The Niederreiter cryptosystem based on Goppa codes is shown to be resistant to hidden subgroup attacks. **Do we have any similar result for other code-based systems using codes other than Goppa?** There are many code-based systems coming up (being proposed) regularly and I don't see if such resistance will be trivially adapted by such variants.

**Tags:** quantum-computing, cr.crypto-security, coding-theory, security

> **Comments:**
> **username_1**: What's the exact difference between McEliece and Niderreiter cryptosystems?  
> **username_0**: @username_1 Basic difference is that McEliece encryption is with Generator matrix of the code while for Niederreiter its the parity check matrix. This causes requirement for some slight modification in the system such as space of possible plaintexts and corresponding error decoding along the code. On the security point of view, Niederreiter systems have a signature scheme and I am not aware of any such progress with McEliece.  

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