# An Algebraic Interpretation of AES-128

@inproceedings{Toli2004AnAI, title={An Algebraic Interpretation of AES-128}, author={Ilia Toli and Alberto Zanoni}, booktitle={AES Conference}, year={2004} }

We analyze an algebraic representation of $\mathcal{AES}$128 as an embedding in $\mathcal{BES}$, due to Murphy and Robshaw. We present two systems of equations S⋆ and K⋆ concerning encryption and key generation processes. After some simple but rather cumbersome substitutions, we should obtain two new systems ${\mathcal{C}}_{1}$ and ${\mathcal{C}}_{2}$. ${\mathcal{C}}_{1}$ has 16 very dense equations of degree up to 255 in each of its 16 variables. With a single pair (p,c), with p a cleartext…

## 10 Citations

Efficient Multiplication in Finite Fields of Characteristic 3 and 5 for Pairing Based Cryptography

- Computer Science, Mathematics
- 2008

A new equation system for AES is proposed that results in new algebraic attack on reduced AES up to 5 rounds, and even by worst method like guessing the unknowns is faster than the brute force attack.

Algebraic aspects of the advanced encryption standard

- Computer Science, Mathematics
- 2006

This work will examine some algebraic aspects of the AES and consider a number of algebraic techniques that could be used in the analysis of the cipher, and focus on the large, though surprisingly simple, systems of multivariate quadratic equations derived from the encryption operation.

The Interaction between Propositional Satisfiability and Applications in Cryptography and Ramsey Problems

- Computer Science, Mathematics
- 2010

An investigation into general methods for representing small boolean functions is the main presentation, used to translate the small components of the AES, and an upper bound is given on the size of the decision-tree and hitting clause-set representations, which are used at intermediate stages of such translations.

On algebraic and statistical properties of AES-like ciphers

- Computer Science, Mathematics
- 2009

A mixed algebraic-statistical attack is developed using the internal algebraic structure of any AES-like cipher to build an algebraic setting where a related-key (statistical) distinguishing attack can be mounted.

On Some Weak Extensions of AES and BES

- Mathematics, Computer ScienceICICS
- 2004

It is shown that the AES and BES can be embedded in their extensions by restricting these extensions on a given subset, and that these natural extensions are trivially weak by describing a cryptanalysis of them despite it leads to no consequence about the security of AES or BES.

On the internal structure of the advanced encryption standard and two AES-based cryptographic constructions

- Computer Science, Mathematics
- 2012

A five-round algebraic property of the AES cipher is proposed which shows that if one carries out four extra exclusive or operations on four fixed-position bytes in some round, five consecutive rounds of such operations will cancel out all changes made to the intermediate results and the final output of the encryption will not be affected by these changes.

PolyBoRi: A framework for Gröbner-basis computations with Boolean polynomials

- Computer Science, MathematicsJ. Symb. Comput.
- 2009

Obtaining and Solving Systems of Equations in Key Variables Only for the Small Variants of AES

- Computer Science, MathematicsMath. Comput. Sci.
- 2008

This work investigates a system of equations that naturally arises in the AES, and introduces an elimination of all the intermediate variables via normal form reductions, and solves the resulting system in key variables only.

A possible intrinsic weakness of AES and other cryptosystems

- Computer Science, MathematicsArXiv
- 2010

This paper uses the algebraic structure of AES-like cipher to construct a cipher embedding where the ciphers may lose their non-linearity, and shows some examples.

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