Gröbner basis attack on stark-friendly symmetric-key primitives: jarvis, mimc and gmimcerf

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2021-2-11

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Kara, Gizem

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A number of arithmetization-oriented ciphers emerge for use in advanced cryptographic protocols such as secure multi-party computation (MPC), fully homomorphic encryption (FHE) and zero-knowledge proofs (ZK) in recent years. The standard block ciphers like AES and the hash functions SHA2/SHA3 are proved to be efficient in software and hardware but not optimal to use in this field, for this reason, new kind of cryptographic primitives proposed. However, unlike traditional ones, there is no standard approach to design and analyze such block ciphers and the hash functions, therefore their security analysis needs to be done carefully. In 2018, StarkWare launched a public STARK-Friendly Hash (SFH) Challenge to select an efficient and secure hash function to be used within ZK-STARKs, transparent and post-quantum secure proof systems. The block cipher JARVIS is one of the first ciphers designed for STARK applications but, shortly after its publication, the cipher has been shown vulnerable to Gröbner basis attack. This master thesis aims to describe a Gröbner basis attack on new block ciphers, MiMC, GMiMCerf (SFH candidates) and the variants of JARVIS. We present the complexity of Gröbner basis attack on JARVIS-like ciphers, results from our experiments for the attack on reduced-round MiMC and a structure we found in the Gröbner basis for GMiMCerf.

Subject Keywords

Gröbner basis, Jarvis, MiMC, GMiMC, Secure multi-party computation (MPC), ZK-STARKs

URI

https://hdl.handle.net/11511/89612

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

G. Kara, “Gröbner basis attack on stark-friendly symmetric-key primitives: jarvis, mimc and gmimcerf,” M.S. - Master of Science, Middle East Technical University, 2021.