Vie privée en pratique : que changent les réseaux euclidiens
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1 Vie privée en pratique : que changent les réseau euclidiens Bringing PETs to life : what ideal lattices change in practice Marc-Olivier KILLIJIAN UQAM 10/2017
2 Who am I? 2 Directeur de Recherche CNRS Affecté officiellement au CRM Prof. Visiteur du LATECE pour 2 ans LAAS : CS, Robotics, Micro-electronics, etc. TSF team : reliability, safety, security and Privacy and applied crypto geo-privacy: inference, mobility models, sanitization geo-crypto: location proofs PETS, applied-crypto DuckDuckGo me for publications
3 Ideal lattices what? Private Information Retrieval - PIR among other PETs impractical, e.g. [Sion & Carbunar - NDSS 07] «On the Computational Practicality of Private Information Retrieval» : (PIR) rather reflect an inherent limitation with respect to modern hardware, likely the result of a communication-cost centric protocol design. We argue that this is likely to hold on non-specialized traditional hardware in the foreseeable future. inefficient, ~100s Mbps [Trostle&Parrish - ISC 10] Lack of efficient homomorphic encryption schemes 3
4 Bringing PETs to life what ideal lattices change in practice EPFL 03/2016
5 Bringing PETs to life what ideal lattices change in practice NFLLib : NTT-based Fast Lattices Library [CT-RSA 16] + github.nfllib EPFL 03/2016
6 Homomorphic Encryption (Not Homomorphic) Encryption D k (C k (m)) = m D k (C k (m 1 )+C k (m 2 )) = noise Homomorphic Encryption D k (C k (m)) = m D k (C k (m 1 ) C k (m 2 )) = m 1 + m 2 D k (C k (m 1 ) C k (m 2 )) = m 1. m 2 Somewhat Fully vs. Fully (SFHE/FHE) bounded number of homomorphic ops vs. unbounded Cloud computing on private data, searchable encryption, etc.
7 NFLlib is a C++ library (efficient) Polynomial calculus Specialized, i.e. not-generic targeting ideal lattices in R p =Z p []/( n +1) fied degree polynomials (n power of 2) fied size coefficients (>p) for modular operations (but several instances can co-eist and interact) Available on github Described in Aguilar et al.@ct-rsa 16 7
8 NFLlib Performance Illustrated Number of key echange per second (RSA15360) RSA & ECDH with openssl 1.0.1f [Linder & Peckert] Ring LWE scheme with NFLLib more clients with 10 less CPU and 2 security
9 9 Ease of use
10 What makes it different? Number-theoretic Transform (NTT) representation NTT and NTT -1 optimized algorithms Chinese Reminder Theorem (CRT) representation for big moduli e.g bits polynomials -> bits Specific (static) moduli enabling optimized NTT & lazy modular ops Efficient noise generation (~1cpu-cycle/bit) Recent architectures optimizations (SSE, AVX2) 10
11 NTT polynomials representation? Impacts polynomials product classical function form p()=a 0 +a 1.++a n-1. n-1 p()=p 1 ().p 2 () O(n 2 ) n distinct values p()=(p( 0 ),,p( n-1 )) p()=p 1 ().p 2 () O(n) Polynomial evaluation and interpolation to switch between these representations can ease products but switching has a cost 11
12 Contet: Poly. Interpolation/Evaluation Lagrange O(n 2 ) NTT: a discrete Fourier Transform 12 O(n.log n ) NTT : evaluation NTT -1 : interpolation
13 NFLlib for SFHE [Fan & Verboten] SFHE scheme n = 4096, T=uint128, p =124bits NFLlib vs flint general purpose Achieving this level of performance clearly changes the perspectives on using HE for building PETs 13
14 Bringing PETs to life what ideal lattices change in practice EPFL 03/2016
15 Bringing PETs to life what ideal lattices change in practice XPIR : Private Information Retrieval for Everyone [PETS 16] + github.xpir EPFL 03/2016
16 Private Information Retrieval 101 Informally A protocol allowing a user to retrieve an element from a database, without revealing which one {Private Information} Retrieval? No! The information retrieved is a priori public Private {Information Retrieval} Element retrieved is unknown 16
17 Classic non-private retrieval i 1 2 i n send the inde i receive the ith element 17
18 Trivial PIR request n n 18 send request receive the complete database read the ith element too much communication overhead
19 Typical cpir i Query Gener ator q1 q2 1 2 i Reply Etrac tor qn i n generate a query for the ith element the server computes a reply using the query and the full DB decode the reply and obtain the ith element 19
20 Typical HE cpir i Query Gener ator q1 q2 1 2 i Reply Etrac tor qn i n 20 generate a query for the ith element cyphers of 0 ecept for the ith which is a cypher of 1 the server computes a reply using the query and the full DB mul each element to its subquery and sums the products decode the sum of products (0+0++i+0++0)
21 d dimensions «recursive» cpir q2,1 q2,n Query i,j Gener q1,1 ator q1,2 1,1 1,2 n,1 n,2 i,j Reply Etrac tor q1,n 1,n i,j n,n view the db as a matri(2, 3, or d dimensions) produce a sub-request per dimension which selects the appropriate slice in each dimension 21
22 PIR historical performances (1) Communication cost Main parameter: d, nb of dimensions to represent the database [Paillier99,DJ03] with n <= query < 1 MB i Query Gener ator q1 q2 1 2 reply epansion factor < 6 Computational cost i Reply Etrac tor qn i n Limiting factor: reply generation Cost: > 2048b mod-op/database bit High-end CPU : T = 1 Mbits/s Perceived throughput: T/n Slower than sending the whole database 22 henceforth [Sion&Carbunar]
23 PIR performances (2) 23 [Paillier99,DJ03] : 1 Mbits/s More recent (but broken) schemes [Aguilar08] : 100Mbits/s (100) [Trostel&Parrish10] : 100Mbits/s Lessons learnt Standard noise distribution (was constant) Take into account dual-lattice attacks use RLWE and NTT instead of LWE XPIR - PIR inspired from [Stern 98] + RLWE insp. from [BV11] T=15Gbits/s (15000 wrt. Paillier) Self parameterized, RLWE, 256b security, no weird assumptions
24 XPIR contributions 24 Invalidates [Sion&Carbunar] cpir can be practical Provides an open-source PIR library in 2 flavours ready-to-use and self parameterized for non eperts make-your-own-scheme NTT+CRT representations for polynomials polynomials product O(n 2.log 2 p) -> O(n.log p) Newton quotient pre-computation of modulus in RLWE 128b division is done only once for each modulus then 6464 mod-ops can be done on 64b only (vs 128)
25 XPIR usecases (1) Tput on static data Netfli-like : private streaming of HD movies 25 Static data : preprocessing occurs only once Tput for 1 core (1 user) on a commodity CPU 9000 HD movies (X100 trivial PIR)
26 XPIR usecases (2) Tput on dynamic data IPTV-like : private streaming of TV broadcasts 26 Dynamic data has to be preprocessed on the fly Tput for 1 core (but for 1 user) commodity CPU 2000 HD channels
27 XPIR usecases (3) Latency Latency main limitation is upload speed 27 Impact of recursive PIR on request size d=1 : O(n) d=2 : O( n)
28 Wrap-up Progress in ideal lattices crypto. allows new HE performance NFLlib for encoding your favorite crypto system Provides a few schemes as showcase Allows PIR to become usable in real applications XPIR for using a PIR DB handled at 15/5 Gbps (static/dynamic data) a choice of underlying cryptosystems (Paillier, NTRU, BV, FV) depending on network/client/server and on latency/rtt/tput XPIR-as-a-lib to build your own (released very soon) 28
29 What s net 29 Currently working on Bloom filters, Secure Scalar Products Private Set Intersection - (n=2 15 ) Paillier-based [DeCristofaro-FC10]: 3 hours / 16 MB OT-based [Pinkas-UseniSec14]: 1458 ms / 8MB NFLlib: 110ms / 128ko PSI Private searching ORAM, Anonymous direct downloads, name your favorite PET, etc.?
30 Vie privée en pratique : que changent les réseau euclidiens Bringing PETs to life : what ideal lattices change in practice Merci! UQAM 10/2017
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