@inproceedings {43122,
	title = {From Farfalle to Megafono via Ciminion: The PRF Hydra for MPC Applications},
	journal = {Advances in Cryptology {\textendash} EUROCRYPT 2023},
	year = {2023},
	author = {Grassi, Lorenzo and {\O}ygarden, Morten and Schofnegger, Markus and Walch, Roman}
}
@inproceedings {43123,
	title = {A New Algebraic Approach to the Regular Syndrome Decoding Problem and Implications for PCG Constructions},
	journal = {Advances in Cryptology {\textendash} EUROCRYPT 2023},
	year = {2023},
	author = {Briaud, Pierre and {\O}ygarden, Morten}
}
@phdthesis {28344,
	title = {Algebraic Cryptanalysis of Cryptographic Schemes with Extension Field Structure},
	year = {2021},
	url = {https://bora.uib.no/bora-xmlui/handle/11250/2771891},
	author = {{\O}ygarden, Morten}
}
@inproceedings {28252,
	title = {Analysis of Multivariate Encryption Schemes: Application to Dob},
	journal = {Public-Key Cryptography (PKC 2021)},
	volume = {LNCS, vol 12710},
	year = {2021},
	month = {05/2021},
	pages = {155 - 183},
	publisher = {Springer International Publishing},
	address = {Cham},
	abstract = {In this paper, we study the effect of two modifications to multivariate public key encryption schemes: internal perturbation (ip), and Q_+. Focusing on the Dob encryption scheme, a construction utilising these modifications, we accurately predict the number of degree fall polynomials produced in a Gr{\"o}bner basis attack, up to and including degree five. The predictions remain accurate even when fixing variables. Based on this new theory we design a novel attack on the Dob encryption scheme, which breaks Dob using the parameters suggested by its designers. While our work primarily focuses on the Dob encryption scheme, we also believe that the presented techniques will be of particular interest to the analysis of other big{\textendash}field schemes},
	isbn = {978-3-030-75244-6},
	issn = {0302-9743},
	doi = {10.1007/978-3-030-75245-310.1007/978-3-030-75245-3_7},
	url = {https://link.springer.com/10.1007/978-3-030-75245-3},
	author = {{\O}ygarden, Morten and Felke, Patrick and Raddum, H{\r a}vard},
	editor = {Juan A. {Garay}}
}
@inproceedings {28343,
	title = {On the Effect of Projection on Rank Attacks in Multivariate Cryptography},
	journal = {The 12th International Conference on Post-Quantum Cryptography (PQCRYPTO 2021)},
	volume = {LNCS, vol 12841},
	year = {2021},
	pages = {98-113},
	publisher = {Springer},
	address = {Cham},
	abstract = {The multivariate scheme HFEv- used to be considered a promising candidate for a post-quantum signature system. First suggested in the early 2000s, a version of the scheme made it to the third round of the ongoing NIST post-quantum standardization process. In late 2020, the system suffered from an efficient rank attack due to Tao, Petzoldt, and Ding. In this paper, we inspect how this recent rank attack is affected by the projection modification. This modification was introduced to secure the signature scheme PFLASH against its predecessor{\textquoteright}s attacks. We prove upper bounds for the rank of projected HFEv- (pHFEv-) and PFLASH under the new attack, which are tight for the experiments we have performed. We conclude that projection could be a useful tool in protecting against this recent cryptanalysis.},
	author = {{\O}ygarden, Morten and Smith-Tone, Daniel and Verbel, Javier}
}
@inproceedings {27643,
	title = {An Algebraic Attack on Ciphers with Low-Degree Round Functions: Application to Full MiMC},
	journal = {Advances in Cryptology {\textendash} ASIACRYPT 2020},
	year = {2020},
	pages = {477-506},
	publisher = {Springer},
	author = {Eichlseder, Maria and Grassi, Lorenzo and L{\"u}ftenegger, Reinhard and {\O}ygarden, Morten and Rechberger, Christian and Schofnegger, Markus and Wang, Qingju}
}
@inproceedings {27134,
	title = {Cryptanalysis of the Multivariate Encryption Scheme EFLASH},
	journal = {RSA Conference Cryptographers{\textquoteright} Track 2020},
	volume = {12006},
	year = {2020},
	month = {02/2020},
	pages = {85-105},
	publisher = { Springer},
	address = {Lecture Notes in Computer Science},
	abstract = {EFLASH is a multivariate public-key encryption scheme proposed by Cartor and Smith-Tone at SAC 2018. In this paper we investigate the hardness of solving the particular equation systems arising from EFLASH, and show that the solving degree for these types of systems is much lower than estimated by the authors. We show that a Gr{\"o}bner basis algorithm will produce degree fall polynomials at a low degree for EFLASH systems. In particular we are able to accurately predict the number of these polynomials occurring at step degrees 3 and 4 in our attacks. We performed several experiments using the computer algebra system MAGMA, which indicate that the solving degree is at most one higher than the one where degree fall polynomials occur; moreover, our experiments show that whenever the predicted number of degree fall polynomials is positive, it is exact. Our conclusion is that EFLASH does not offer the level of security claimed by the designers. In particular, we estimate that the EFLASH version with 80-bit security parameters offers at most 69 bits of security.},
	isbn = {978-3-030-40186-3},
	author = {{\O}ygarden, Morten and Felke, Patrick and Raddum, H{\r a}vard and Cid, Carlos}
}
