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**2024/1547**

**Title:**

HHL for tensor-decomposable matrices

**Authors:**
Cezary Pilaszewicz, Marian Margraf

**Abstract:**

We use the HHL algorithm to retrieve a quantum state holding the algebraic normal formal of a Boolean function. Unlike the standard HHL applications, we do not describe the cipher as an exponentially big system of equations. Rather, we perform a set of small matrix inversions which corresponds to the Boolean Möbius transform. This creates a superposition holding information about the ANF in the form: \ket{\mathcal{A}_{f}} =\frac{1}{C} \sum_{I=0}^{2^n-1} c_I \ket{I}, where c_I is the coefficient of the ANF and C is a scaling factor. The procedure has a time complexity of \mathcal{O}(n) for a Boolean function with n bit input. We also propose two approaches how some information about the ANF can be extracted from such a state.

**ePrint:**
https://eprint.iacr.org/2024/1547

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