Fully homomorphic SIMD operations

By Nigel P. Smart, Frederik Vercauteren. Designs, Codes and Cryptography, 2012

812 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3cfc0b1e3c19ffb422f0c98754c382a9d8fbbc0b

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Citations in the corpus

Efficient Multi-Key Homomorphic Encryption with Packed Ciphertexts with Application to Oblivious Neural Network Inference (2019, methodology): “For example, one can encrypt multiple plaintext values into a single packed ciphertext, and use the single instruction multiple data (SIMD) techniques to perform operations on these values in parallel [26, 48].”
Design and Implementation of a Homomorphic-Encryption Library (2012, methodology): “Just as in [2, 4, 10] each factor corresponds to a “plaintext slot”.”
Oblivious Neural Network Predictions via MiniONN Transformations (2017, methodology): “One way to alleviate this issue is to encode several messages into a single plaintext and use the single instruction multiple data (SIMD) [54] technique to process these encrypted messages in batch without introducing any extra cost.”
Algorithms in HElib (2014, background): “Smart and Vercauteren observed [19] that (for a prime p) an element in this native plaintext space can be used to encode a vector of values from a finite field Fpd , for some integer d that depends on F and p, and that homomorphic operations then induce the corresponding entry-wise operation on the ”
Secure Outsourced Matrix Computation and Application to Neural Networks (2018, unknown): “After Smart and Vercauteren [45] first introduced a packing technique based on polynomial-CRT, it has been one of the most important features of HE systems.”
Bandwidth Efficient PIR from NTRU (2014, methodology): “Batching was introduced by Smart and Vercauteren [8, 9].”
Accelerating NTRU based homomorphic encryption using GPUs (2014, methodology): “For instance, techniques for eliminating the need for expensive bootstrapping evaluations [12] and techniques for batching multiple bits together for more effective parallel processing [13]–[15] have been developed.”
Modular Hardware Architecture for Somewhat Homomorphic Function Evaluation (2015, methodology): “However, we put no restriction on f ( x ), which allows us to deal with any cyclotomic polynomial Φ d ( x ) and thus to utilize single instruction multiple data (SIMD) operations [36,37].”
Improved Security for a Ring-Based Fully Homomorphic Encryption Scheme (2013, methodology): “This approach is different than the ones introduced in [22] and [7], since in contrast to these schemes, we do not use the CRT to pack information into different plain text slots of a single ciphertext.”
Multiparty Computation from Somewhat Homomorphic Encryption (2012, methodology): “Thus SHE suffices, we do not need bootstrapping, and we can use the SHE SIMD approach of [28] to handle many values in parallel in a single ciphertext.”
Secure Face Matching Using Fully Homomorphic Encryption (2018, methodology): “[41] proposed techniques for homomorphic encryption and decryption over an array of numbers instead of a single number at a time.”
CrypTFlow2: Practical 2-Party Secure Inference (2020, unknown): “optimization [46, 61] that enables operation on plaintext vectors over the field Zn , where n is a prime plaintext modulus of the form 7The protocol of (k 1 ) -OTl [44] incurs a communication cost of λ + kl .”
Cheetah: Optimizing and Accelerating Homomorphic Encryption for Private Inference (2020, methodology): “Packing signiﬁcantly improves HE performance; n is typically on the order of thousands and the beneﬁts of packing are proportional [60].”