Secure Strassen-Winograd Matrix Multiplication with MapReduce

Radu Ciucanu (1, 2, 3) , Matthieu Giraud (4, 5) , Pascal Lafourcade (4, 5) , Lihua Ye (6)

1 INSA CVL - Institut National des Sciences Appliquées - Centre Val de Loire
2 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans
3 SDS - Sécurité des Données et des Systèmes
4 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
5 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]
6 HIT - Harbin Institute of Technology

Matrix multiplication is a mathematical brick for solving many real life problems. We consider the Strassen-Winograd algorithm (SW), one of the most efficient matrix multiplication algorithms. Our first contribution is to redesign SW with the MapReduce programming model that allows to process big data sets in parallel on a cluster. Moreover, our main contribution is to address the inherent security and privacy concerns that occur when outsourcing data to a public cloud. We propose a secure approach of SW with MapReduce called S2M3, for Secure Strassen-Winograd Matrix Multiplication with MapReduce. We prove the security of our protocol in a standard security model and provide a proof-of-concept empirical evaluation suggesting its efficiency.

Mots clés: Security; Intersection; Database; Privacy; MapReduce

Domaines: Cryptographie et sécurité [cs.CR]

Radu Ciucanu, Matthieu Giraud, Pascal Lafourcade, Lihua Ye. Secure Strassen-Winograd Matrix Multiplication with MapReduce. International Conference on Security and Cryptography (SECRYPT), Jul 2019, Prague, Czech Republic. pp.220-227. ⟨hal-02129149⟩