Description
We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a generic template for constructing SSL-PRGs that combines the following two ingredients:
(i) noisy‑NC0 PRGs, computable by constant‑depth circuits fed with sparse noise, with
(ii) new local compression schemes for sparse vectors derived from combinatorial batch codes.
Instantiating the template under the sparse Learning‑Parity‑with‑Noise (LPN) assumption yields the first SSL-PRGs with polynomial stretch and constant locality from a subquadratic‑sample search hardness assumption; a mild strengthening of sparse‑LPN gives strong SSL-PRGs of arbitrary polynomial stretch. We further show that for all standard noise distributions, noisy‑local PRGs cannot be emulated by ordinary local PRGs, thereby separating the two notions.
Plugging SSL-PRGs into existing frameworks, we revisit the canonical applications of local PRGs and demonstrate that SSL-PRGs suffice for:
(i) indistinguishability obfuscation,
(ii) constant-overhead secure computation,
(iii) compact homomorphic secret sharing, and
(iv) deriving hardness results for PAC‑learning DNFs from sparse‑LPN.
Our work thus broadens the landscape of low‑depth pseudorandomness and anchors several primitives to a common, well‑motivated assumption.
Joint work with Benny Applebaum, Dung Bui, and Geoffroy Couteau.
Next sessions
-
Cyclotomic Cosets: Hidden Subgroup and Quantum Sieving Algorithm for Prime-Power Moduli
Speaker : Mathias Boucher - Université de Rennes
The Dihedral Coset Problem (DCP), also known as the hidden shift problem, plays a fundamental role in post-quantum public-key cryptography, since the Learning-With-Error problem reduces to DCP. The “Simon meets Kuperberg” quantum algorithm by Bonnetain and Naya-Plasencia solves the DCP in quasi-polynomial time when the modulus is a power of two. We provide a generalization of this algorithm for[…] -
Adelic reduction of module lattices
Speaker : Henry Bambury - DGA-MI et Inria Rennes
We give a strict generalisation of the LLL algorithm over number fields, based on the reduction theory of $GL(n)$ over the adele ring of a number field. Our algorithm is free of heuristics, with rigorous bounds on output quality and complexity. -- based on joint work with Seungki Kim, Changmin Lee and Phong Nguyen ---
Cryptography
-
-
European Cyber Week: atelier cryptographie post-quantique
Dans la continuité des éditions 2021, 2022 et 2024, la DGA — en partenariat avec CREACH LABS et avec le soutien de l'ANSSI, de l'IRISA, de l'IRMAR et du Pôle d'Excellence Cyber — organise la 4e édition de l'atelier consacré à la cryptographie post-quantique dans le cadre de l'European Cyber Week 2026. Attention, il faut s'inscrire (gratuitement) au préalable — s'inscrire à la conférence Les[…] -
Post-quantum day of the cryptography seminar
A scientific day devoted to post-quantum cryptography, held in the wake of the European Cyber Week, with talks more technical than those presented at the ECW. The talks will take place at Amphi E in building 02A. To register for lunch, please do so before oct 30th using this link. -
Chiffrement homomorphe à l'aide des groupes après Nuida
Speaker : Pierre Guillot - Ravel Technologies/Université de strasbourg
Nuida et d'autres ont montré comment on peut obtenir un protocole de chiffrement pleinement homomorphe si l'on sait chiffrer les éléments d'un groupe G convenable, tout en sachant faire l'opération de G "en homomorphe". Les exemples étaient jusqu'à présent limités au chiffrement d'un bit à la fois, avec beaucoup d'opérations à effectuer pour "simuler" les portes logiques usuelles. Je vais[…]-
Cryptography
-
-
TBD
Speaker : Dung Bui - Northwestern University
-
Nouveaux doctorants
Exposés courts des nouveaux doctorants (Elouan, Quentin, Eliot)