Abstract
A fault injection framework for the decryption algorithm of the Niederreiter public-key cryptosystem using binary irreducible Goppa codes and classical decoding techniques is described. In particular, we obtain low-degree polynomial equations in parts of the secret key. For the resulting system of polynomial equations, we present an efficient solving strategy and show how to extend certain solutions to alternative secret keys. We also provide estimates for the expected number of required fault injections, apply the framework to state-of-the-art security levels, and propose countermeasures against this type of fault attack.
Highlights
Many established public-key cryptosystems rely on the hardness of the factorization problem or the discrete logarithm problem
For the resulting system of polynomial equations, we present an efficient solving strategy and show how to extend certain solutions to alternative secret keys
We provide estimates for the expected number of required fault injections, apply the framework to state-of-the-art security levels, and propose countermeasures against this type of fault attack
Summary
Many established public-key cryptosystems rely on the hardness of the factorization problem or the discrete logarithm problem Their long-term security is not guaranteed, because they can be broken in polynomial time using sufficiently large quantum-computers [22]. Key words and phrases: Niederreiter cryptosystem, binary Goppa code, side-channel analysis, fault attack. For carrying out the actual fault injections, we need to hit the register holding a certain 10-13 bit wide coefficient at a specified point in time Using modern equipment, this is a mild requirement (see for instance [12] and [5]). Looking through the NIST Post-Quantum Standardization candidates, there are three original submissions based on Goppa codes: “BIG Quake” which is vulnerable to our attack, “Classic McEliece”, and “NTS-KEM”
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