# About Me

I am a PhD. candidate at Télécom Paris under the supervision of Pr. Olivier Rioul and Pr. Sylvain Guilley. Mathematics, especially **Probabilities, Information Theory, Side-Channel Analysis and Cryptology** are my main research interests.

I received my engineering degree from Télécom Paris (2022) and my master degree MICAS (Machine Learning, Communications and Security) from Institut Polytechnique de Paris.

Here is my curriculum vitae.

# Publications

### 2024

**“Formal Security Proofs via Doeblin Coefficients: Optimal Side-channel Factorization from Noisy Leakage to Random Probing”**, J.Béguinot, W. Cheng, O. Rioul and S. Guilley (CRYPTO 2024). In this work we highlight that the complementary Doeblin coefficient yields the optimal reduction from noisy leakages to the random probing model. We show how it combines with existing proof in the random probing model or with Prouff and Rivain’s subsequence decomposition. The CDC is defined by: \[ \overline{\mathcal{E}}(X \to Y) = 1 - \int_y \inf_x p_{Y|X}(y|x) = \mathbb{E}_Y \left [ \sup_x \left ( 1 - \frac{p_{X|Y}(x|Y)}{p_X(x)} \right ) \right ] . \] The long version is availbale here.**“What can Information Guess? Guessing Advantage vs. Rényi Entropy for Small Leakages”**J.Béguinot and O. Rioul (ISIT 2024) We leverage the Gibbs inequality and its natural generalization to Rényi entropies to derive closed-form parametric expressions of the optimal lower bounds of \(\rho\)th-order guessing entropy (guessing moment) of a secret. An important outcome is that it decreases as the square root for small leakages. Most notably, the optimal lower bound on \(G(K|Y)\) vs. \(I(K;Y)\) is given by the parametric curve for \(\mu\in(0,+\infty)\): \[ \begin{cases} \frac{M+1}{2}-G(K|Y) = \frac{1}{2} \bigl( M \coth( M \mu) - \coth( \mu ) \bigr) \\ I(K;Y) = \log \frac{ M \sinh \mu}{\sinh(M \mu)} +2\mu (\log e) ( \frac{M+1}{2}-G(K|Y) ). \end{cases} \] The article is available is availbale here.**“Be My Guesses: The interplay between side-channel leakage metrics”**, J. Béguinot, W. Cheng, S. Guilley, and O. Rioul (MICPRO).

### 2023

**“Maximal Leakage of Masked Implementations Using Mrs. Gerber’s Lemma for Min-Entropy”**, J.Béguinot, Y. Liu, O. Rioul, W. Cheng and S. Guilley, ISIT 2023. The main result is a generalized MGL form maximal leakage. Let \(p_i = \exp(\!-\!H_\infty(X_i))\), without loss of generality we assume \(p_0 \leq p_1 \leq \ldots \leq p_d\). Let \(k = \lfloor p_0^{-1} \!\rfloor\), \(r = \max \{ i | p_i \leq \frac{1}{k}\}\). Let \(H_d=H_\infty(X)\), \[ H_d \! \geq \! \begin{cases} \!-\! \log \bigl( \frac{1}{k+1} \!+\! \frac{1}{k+1} \prod \limits_{j=0}^r ((k\!+\!1)p_i \!-\! 1) \bigl) & \hspace{-1em} \text{ if $r$ is even,} \\ \!-\! \log \bigl( \frac{1}{k+1} \!+\! \frac{k}{k+1} \prod \limits_{j=0}^r ((k\!+\!1)p_i \!-\! 1) \bigl) & \hspace{-1em} \text{ if $r$ is odd.} \end{cases} \] The long version is available here.**“Improved alpha-information bounds for higher-order masked cryptographic implementations”**, Y. Liu, J. Béguinot, W. Cheng, S. Guilley, L. Masure, O. Rioul, and F.-X. Standaert, IEEE Information Theory Workshop (ITW 2023), Saint Malo, France, Apr. 23-28, 2023. The main result is that \[ m \geq \frac{d_2(\mathbb{P}_s||\frac{1}{M})}{ \log\left(1 + \prod_{i=0}^d (e^{I_2^R(X_i;L_i)}-1)\right)}. \] The article is available here.**“Removing the field size loss from Duc et al.’s conjectured security bound for masked encodings”**, J. Béguinot, W. Cheng, S. Guilley, Y. Liu, L. Masure, O. Rioul and F.-X. Standaert, in Proc. 14th International Workshop on Constructive Side-Channel Analysis and Secure Design (COSADE 2023), Munich, Germany, Apr. 3-4, 2023. The main result is that for group of order \(M=2^n\), \[ m \geq \frac{d(\mathbb{P}_s||\frac{1}{M})}{ \phi\left( \prod_{i=0}^d \phi^{-1}( I(X_i;L_i))\right)} \] where \(\phi(x)=\log(2)-h(\frac{1-x}{2})\). The article is available here.

### 2022

**“Side-Channel Expectation-Maximization Attacks”**, Julien Béguinot, Wei Cheng, Sylvain Guilley and Olivier Rioul in IACR Transactions on Cryptographic Hardware and Embedded Systems (TCHES 2022),Leuven, Belgium. Article is here and the slides here.**“Side-channel information leakage of code-based masked implementations”**, W. Cheng, O. Rioul, Y. Liu, J. Béguinot, and S. Guilley, 17th Canadian Workshop on Information Theory (CWIT 2022), Ottawa, Ontario, Canada, June 5-8, 2022. Article here.**“La véritable (et méconnue) théorie de l’information de Shannon”**, O. Rioul, J. Béguinot, V. Rabiet et A. Souloumiac, in Proc. 28e Colloque GRETSI’22, Nancy, France, 6-9 Sept. 2022. Article here.**“Be my guess: Guessing entropy vs. success rate for evaluating side-channel attacks of secure chips”**, J. Béguinot, W. Cheng, S. Guilley, and O. Rioul, in Proc. 25th Euromicro Conference on Digital System Design (DSD 2022), Maspalomas, Gran Canaria, Spain, Aug. 31–Sep. 2nd, 2022. Article here.

# Presentations & Posters

**Information Theoretic Security Bound of Boolean Masking**, SSH Seminar, Mai 16th, Palaiseau, France**Information Theoretic Security Bound of Boolean Masking**, ComNum Seminar, April 20th, Palaiseau, France**Side-Channel Security. How Much Are you Secure ?**, IMT Risques et Cyber 2023, April 13th, Palaiseau, France. Poster PDF**“Unprofiled expectation-maximization attack”**, 18th International Workshop on Cryptographic Architectures Embedded in Logic Devices (CryptArchi 2022) J. Béguinot, W. Cheng, S. Guilley, and O. Rioul,Porquerolles, France, May 29-June 1st, 2022. Slides PDF**“Robust Ring Oscilator PUFs”**, Junior Conference on Wireless and Optical Communication (JWOC 2022), Julien Béguinot, France, 6 October 2022

# Sublimaths

I coorganize a mathematical club for middle school students on the week-end called Sublimath. For more information you can take a look at our dedicated webpage.

# Teaching

In 2023-2024, I am teaching assistant at Télécom Paris.

**Probability:**measure theory, conditional expectation, martingale (MACS 201)**Algebra:**group theory, finite fields (ACCQ 201)**Information Theory**(ACCQ 202)**Coding Theory**(ACCQ 204)**Statistical Learning**(SI 221/ MICAS 911)**Cryptography**(MICAS 931)**Physical Layer Security**(MICAS 932)

For 2022-2023 I am a teaching assistant for LIX (Ecole polytechnique).

**INF442 Algorithms for Data Analysis in C++.**This covers efficient implementation of learning algorithms in C++ for 2nd years Polytechnicians.**CSE103 Introduction to Algorithms.**This covers the basics of algorithmics for bachelor students (sorting algorithms, divide and conquer, dynamic programming and complexity).

I created this website using Quarto https://quarto.org/docs/websites.