Implementing Conjunction Obfuscation Under Entropic Ring LWE

Abstract

Abstract-We address the practicality challenges of secure program obfuscation by implementing, optimizing, and experimentally assessing an approach to securely obfuscate conjunction programs proposed in [1]. Conjunction programs evaluate functions f (x1, . . . , xL) = i∈I yi, where yi is either xi or ¬xi and I ⊆ [L], and can be used as classifiers. Our obfuscation approach satisfies distributional Virtual Black Box (VBB) security based on reasonable hardness assumptions, namely an entropic variant of the Ring Learning with Errors (Ring-LWE) assumption. Prior implementations of secure program obfuscation techniques support either trivial programs like point functions, or support the obfuscation of more general but less efficient branching programs to satisfy Indistinguishability Obfuscation (IO), a weaker security model. Further, the more general implemented techniques, rather than relying on standard assumptions, base their security on conjectures that have been shown to be theoretically vulnerable.Our work is the first implementation of non-trivial program obfuscation based on polynomial rings. Our contributions include multiple design and implementation advances resulting in reduced program size, obfuscation runtime, and evaluation runtime by many orders of magnitude. We implement our design in software and experimentally assess performance in a commercially available multi-core computing environment. Our implementation achieves runtimes of 6.7 hours to securely obfuscate a 64-bit conjunction program and 2.5 seconds to evaluate this program over an arbitrary input. We are also able to obfuscate a 32-bit conjunction program with 53 bits of security in 7 minutes and evaluate the obfuscated program in 43 milliseconds on a commodity desktop computer, which implies that 32-bit conjunction obfuscation is already practical. Our graph-induced (directed) encoding implementation runs up to 25 levels, which is higher than previously reported in the literature for this encoding. Our design and implementation advances are applicable to obfuscating more general compute-and-compare programs and can also be used for many cryptographic schemes based on lattice trapdoors.

Implementation and Performance Evaluation of RNS Variants of the BFV Homomorphic Encryption Scheme

“…We remark that our best GPU results, namely the homomorphic multiplication runtime of 51 ms for n = 2 16 and log 2 q = 1, 770 and 18.7 ms for n = 2 16 and log 2 q = 1, 020, are more than two orders of magnitude faster than best previously reported runtimes for other implementations of the BFV scheme. For instance, the FPGAbased implementation HEPCloud in [18] of the textbook BFV scheme computed a homomorphic multiplication for n = 2 15 and log 2 q = 1, 228 in 26.67 seconds (with 3.36 seconds spent on the computation and the rest on the off-chip memory access).…”

“…We provide below an example showing an estimate for the average number of cores used over all kernels for V100. We profiled the implementation for running the five HPS primitives (KeyGen, Enc, Dec, EvalAdd and EvalMul) under the settings (n, log q, t) = (2 16 , 1770, 2 16 + 1). The average achieved occupancy was found to be 0.628, i.e., 40.192 active warps per a SM (since the maximum active warps for V100 is 64).…”

“…Other implementations of the BFV scheme can be found in PALISADE [12], an open source C++ lattice cryptography library that includes the implementations of multiple HE and proxy re-encryption schemes [13]; digital signature, identity-based encryption, and attribute-based encryption constructions [14], [15]; and conjunction obfuscation scheme [16]. Starting with v1.1, PALISADE provides an implementation of the HPS variant.…”

Homomorphic signcryption with public plaintext‐result checkability

“…Although the initial results required significant amounts of time to implement programme obfuscation [11,12,14], there are some recent advances that are very promising. More precisely, Cousins et al [16] implemented obfuscation for conjunction programme satisfying distributional virtual black box (VBB) security. The obfuscation for a 64-bit conjunction programme takes 6.7 h and the evaluation takes only 3.5 s. Except software-only-based approaches to implement programme obfuscation, there are also some significant advances in hardware-based approaches.…”

“…Due to the building blocks that our constructions are based on, it is inevitable to discuss the practicality of obfuscation and function encryption. As far as we know, there are several articles [11–16] investigating the practicality of programme obfuscation focussing on implementing and evaluating the performance of the obfuscators. Although the initial results required significant amounts of time to implement programme obfuscation [11, 12, 14], there are some recent advances that are very promising.…”