@inproceedings {27709,
	title = {Boolean Polynomials, BDDs and CRHS Equations {\textendash} Connecting the Dots with CryptaPath},
	journal = {Selected Areas in Cryptography},
	volume = {12804},
	year = {2021},
	month = {07/2021},
	pages = {229-251},
	publisher = { Springer},
	address = {Cham},
	abstract = {When new symmetric-key ciphers and hash functions are proposed they are expected to document resilience against a number of known attacks. Good, easy to use tools may help designers in this process and give improved cryptanalysis. In this paper we introduce CryptaPath, a tool for doing algebraic cryptanalysis which utilizes Compressed Right-Hand Side (CRHS) equations to attack SPN ciphers and sponge constructions. It requires no previous knowledge of CRHS equations to be used, only a reference implementation of a primitive.
The connections between CRHS equations, binary decision diagrams and Boolean polynomials have not been described earlier in literature. A comprehensive treatment of these relationships is made before we explain how CryptaPath works. We then describe the process of solving CRHS equation systems while introducing a new operation, dropping variables.},
	keywords = {algebraic cryptanalysis, binary decision diagram, block cipher, equation system, Open Source, tool},
	isbn = {978-3-030-81651-3},
	doi = {https://doi.org/10.1007/978-3-030-81652-0_9},
	url = {https://link.springer.com/chapter/10.1007/978-3-030-81652-0_9},
	author = {John Petter {Indr{\o}y} and Costes, Nicolas and Raddum, H{\r a}vard},
	editor = {O., Dunkelman and Jr. M.J. {Jacobson} and C., O{\textquoteright}Flynn}
}
@inproceedings {27705,
	title = {Graphs and Self-dual additive codes over GF(4)},
	journal = {The Eleventh International Workshop on Coding and Cryptography},
	year = {2019},
	abstract = {We initiate the study of self-dual codes over GF(4) whose corresponding graphs have fixed rankwidth. We show that by combining the structural properties of rankwidth 1 graphs, the classification of corresponding codes becomes significantly faster.
We give a new algorithm for computing weight enumerators using Binary Decision Diagrams (BDD), which has similar complexity to brute force O(2^k) but has the benefit that we automatically get complexity O(2^min{k,n-k}) (for k > n/2) without needing to consider the dual code.
We show that the minimum distance of a code is at least 3 if and only if the corresponding graph does not contain any pendant vertex or any twin-pairs. We also give an algorithm for computing an approximate minimum distance in codes corresponding to general graphs.},
	keywords = {binary decision diagram, Minimum Distance, Rankwidth, Self-dual, Stabilizer Code},
	author = {Kumar, Mithilesh and Varadharajan, Srimathi and Raddum, H{\r a}vard}
}
@inproceedings {23484,
	title = {Algebraic Attacks Using Binary Decision Diagrams},
	journal = {BalkanCryptSec 2014},
	volume = {9024},
	year = {2015},
	month = {07/2015},
	pages = {40 - 54},
	publisher = {Lecture Notes in Computer Science, Springer.Verlag},
	abstract = {Algebraic attacks have been developed against symmetric primitives during the last decade. In this paper we represent equation systems using binary decision diagrams, and explain techniques for solving them. Next, we do experiments with systems describing reduced versions of DES and AES, as well as systems for the problem of determining EA-equivalence. We compare our results against Gröbner basis and CryptoMiniSat.},
	keywords = {algebraic attack, binary decision diagram, block cipher, symmetric primitives},
	isbn = {978-3-319-21356-9},
	issn = {0302-9743},
	doi = {10.1007/978-3-319-21356-9_4},
	url = {http://link.springer.com/chapter/10.1007/978-3-319-21356-9_4},
	author = {Raddum, H{\r a}vard and Kazymyrov, Oleksandr}
}
@article {23486,
	title = {Influence of addition modulo 2^n on algebraic attacks},
	journal = {Cryptography and Communications},
	volume = {8},
	year = {2015},
	month = {05/2015},
	pages = {277-289},
	publisher = {Springer Verlag},
	abstract = {Many modern ciphers have a substitution-permutation (SP) network as a main component. This design is well researched in relation to Advanced Encryption Standard (AES). One of the ways to improve the security of cryptographic primitives is the use of additional nonlinear layers. However, this replacement may not have any effect against particular cryptanalytic attacks. In this paper we use algebraic attacks to analyze an SP network with addition modulo 2^n as the key mixing layer. In particular, we show how to reduce the number of intermediate variables in round functions based on SP networks. We also apply the proposed method to the GOST 28147-89 block cipher that allows us to break reduced 8- and 14-round versions with complexity at most 2^{155} and 2^{215.4}, respectively.},
	keywords = {Addition modulo 2^n, algebraic attack, binary decision diagram, block cipher},
	issn = {1936-2455},
	doi = {10.1007/s12095-015-0136-7},
	url = {http://link.springer.com/article/10.1007/s12095-015-0136-7},
	author = {Kazymyrov, Oleksandr and Oliynykov, Roman and Raddum, H{\r a}vard}
}
