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Additively Homomorphic Encryption with d-Operand Multiplications [chapter]

Carlos Aguilar Melchor, Philippe Gaborit, Javier Herranz
2010 Lecture Notes in Computer Science  
Chained encryption schemes are generically constructed by concatenating cryptosystems with the appropriate homomorphic properties; such schemes are common in lattice-based cryptography.  ...  In this work we define a theoretical object, chained encryption schemes, which allow an efficient evaluation of polynomials of degree d over encrypted data.  ...  Finding a non-trivial (i.e. for d > 1) d-multiplicative fully homomorphic encryption scheme has also been a long standing open problem.  ... 
doi:10.1007/978-3-642-14623-7_8 fatcat:6bcz3p22ybdq3authmbdufs4gu

Study of MA protection based on homomorphic encryption and composite function technology

Jiehong Wu, Hang Yin, Po Zhang, Xiangbin Shi
2012 Proceedings of 2012 UKACC International Conference on Control  
Homomorphic encryption is a technique in which the encrypted mobile codes can be executed directly on different platforms without decryption.  ...  This paper presents a protection scheme of mobile agent (AMHCFES) in network management application, which combining protect method of homomorphic encryption and composite function technology.  ...  Take away the operands dependance problem aroused by addition-multiplication homomorphic encryption scheme(take away encrypted data by addition-multiplication homomorphic) Three address codes operating  ... 
doi:10.1109/control.2012.6334735 fatcat:pnzyelfanncpnk2a4zskpkatk4

How Practical is Homomorphically Encrypted Program Execution? An Implementation and Performance Evaluation

Michael Brenner, Henning Perl, Matthew Smith
2012 2012 IEEE 11th International Conference on Trust, Security and Privacy in Computing and Communications  
In previous work we showed how homomorphic encryption can be used to execute arbitrary programs in encrypted space, showing that at least in theory real world problems can be computed protected by homomorphic  ...  For this we present the implementation of a method to compute non-linear secret programs on an untrusted resource using encrypted circuits embedded in an encrypted virtual machine.  ...  As an optimization in line 4 we can check wether d is zero and then use either c i or encrypt(0). This saves an additional multiplication and provides a cleaner ciphertext matrix to start with.  ... 
doi:10.1109/trustcom.2012.174 dblp:conf/trustcom/BrennerPS12 fatcat:4wm2mo4iizbv7i4exp22t33ize

The use of encrypted functions for mobile agent security

Hyungjick Lee, J. Alves-Foss, S. Harrison
2004 37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the  
no homomorphic encryption schemes are found for their approach.  ...  Our approach provides a practical idea for implementing mobile cryptography by suggesting a hybrid method that mixes a function composition technique and a homomorphic encryption scheme that we have found  ...  • Step 2 The operand dependency problem (data encrypted by HES should not be encrypted again) caused by the additive-multiplicative homomorphic encryption scheme is removed.  ... 
doi:10.1109/hicss.2004.1265700 dblp:conf/hicss/LeeAH04 fatcat:sx4csdrninfpfpxrlqevwlhua4

Database Secure Manipulation based on Paillier's Homomorphic Encryption (DSM-PHE)

Somchai Prakancharoen
2019 International Journal of Interactive Mobile Technologies  
Unfortunately, Paillier's Homomorphic encryption is normally coverage only addition and multiplication mathematical data operation.  ...  User's data is manipulated or processed on many times such as addition, subtraction, multiplication and division.  ...  For example, RSA encryption is covered just a multiplication homomorphic property. While, Paillier's encryption algorithm has multiplication and addition Homomorphic property.  ... 
doi:10.3991/ijim.v13i12.11396 fatcat:vluic5ezirahjp5d2uji4gwjty

Cryptoleq: A Heterogeneous Abstract Machine for Encrypted and Unencrypted Computation

Oleg Mazonka, Nektarios Georgios Tsoutsos, Michail Maniatakos
2016 IEEE Transactions on Information Forensics and Security  
The program operands are protected using the Paillier partially homomorphic cryptosystem, which supports addition on the encrypted domain.  ...  Full homomorphism over addition and multiplication, which is necessary for enabling general-purpose computation, is achieved by inventing a heuristically obfuscated software re-encryption module written  ...  D.  ... 
doi:10.1109/tifs.2016.2569062 fatcat:n2jztvxbfneaxac73enzkmrqgy

Performance of Hierarchical Transforms in Homomorphic Encryption: A case study on Logistic Regression inference [article]

Pedro Geraldo M. R. Alves, Jheyne N. Ortiz, Diego F. Aranha
2022 IACR Cryptology ePrint Archive  
Recent works challenged the Number-Theoretic Transform (NTT) as the most efficient method for polynomial multiplication in GPU implementations of Fully Homomorphic Encryption schemes such as CKKS and BFV  ...  multiplication.  ...  Instead, the operands' transposition enables its replacement by a sequence of homomorphic multiplications and additions, as seen in Algorithm 8.  ... 
dblp:journals/iacr/AlvesOA22 fatcat:2mdv2u5kifbifa3dgnm2q6xuai

Quantum-Resistant Network for Classical Client Compatibility

Te-Yuan Lin, Chiou-Shann Fuh
2021 Information Technology and Control  
Quantumkey distribution fundamentally solves the problem of eavesdropping; nevertheless, it requires quantumpreparatory work and quantum-network infrastructure, and these remain unrealistic with classical  ...  National Taiwan University-IBM Q Hub, who sponsored the state-of-the-art quantum computers and application interfaces to contribute this research as a great testing platform for simulating the factorization with  ...  version scheme comes in and is classified as Somewhat Homomorphic Encryption (SHE) since f can operate both addition and multiplication with limited rounds.  ... 
doi:10.5755/j01.itc.50.2.27570 fatcat:o54oxyae75cydoiuyf6kf2esua

EVA Improved: Compiler and Extension Library for CKKS [article]

Sangeeta Chowdhary, Wei Dai, Kim Laine, Olli Saarikivi
2021 IACR Cryptology ePrint Archive  
Homomorphic encryption (HE), especially the CKKS scheme, can be extremely challenging to use. The EVA language and compiler (Dathathri et al., PLDI 2020) was an attempt at addressing this challenge.  ...  EVA allows a developer to express their encrypted computation in a simple form with a Python-integrated language called PyEVA.  ...  Encrypted Computing The CKKS scheme supports encrypted element-wise vector addition, negation, multiplication, and complex conjugation, as well as cyclic vector rotation (in either direction); for addition  ... 
dblp:journals/iacr/ChowdharyDLS21 fatcat:6u5s5456tbd2ffmo7df3aewosm

Fully Homomorphic Encryption Based On the Parallel Computing

2018 KSII Transactions on Internet and Information Systems  
Fully homomorphic encryption(FHE) scheme may be the best method to solve the privacy leakage problem in the untrusted servers because of its ciphertext calculability.  ...  Experimental results show that the time overhead of the homomorphic operations in new FHE scheme will be reduced manyfold with the increasing of processing units number.  ...  At present, only the homomorphic addition and multiplication of GSW scheme is in accordance with the operational rule of common arithmetic operations, and the other homomorphic operations need to redefine  ... 
doi:10.3837/tiis.2018.01.024 fatcat:h4ai4ywtmbfj5aehlfjmt7v35i

Automatic Protocol Selection in Secure Two-Party Computations [chapter]

Florian Kerschbaum, Thomas Schneider, Axel Schröpfer
2014 Lecture Notes in Computer Science  
In this paper we propose automatic protocol selection which selects a protocol for each operation resulting in a mix with the best performance so far.  ...  Then the additive homomorphism can be expressed as D X (E X (x) · E X (y)) = x+y. Multiplication with a constant c can easily be derived as D X (E X (x) c ) = cx.  ...  Homomorphic Encryption Secure computation can also be implemented based on additively homomorphic encryption.  ... 
doi:10.1007/978-3-319-07536-5_33 fatcat:4bawobygpjel7dlqprgdx4m554

Why and How zk-SNARK Works [article]

Maksym Petkus
2019 arXiv   pre-print
Despite the existence of multiple great resources on zk-SNARK construction, from original papers to explainers, due to the sheer number of moving parts the subject remains a black box for many.  ...  Hence the focus of this work is to shed light onto the topic with a straightforward and clean approach based on examples and answering many whys along the way so that more individuals can appreciate the  ...  All the homomorphic properties of the scheme are preserved in the modular realm: encryption : 5 3 = 6 (mod 7) multiplication : 6 2 = (5 3 ) 2 = 5 6 = 1 (mod 7) addition : 5 3 · 5 2 = 5 5 = 3 (mod 7) Note  ... 
arXiv:1906.07221v1 fatcat:4c2rwnwbvrftbg3wgdpbxuydwe

Utilizing Homomorphic Encryption to Implement Secure and Private Medical Cloud Computing

Ovunc Kocabas, Tolga Soyata
2015 2015 IEEE 8th International Conference on Cloud Computing  
We present an approach that eliminates data privacy concerns in the public cloud scenario, by utilizing an emerging encryption technique called Fully Homomorphic Encryption (FHE).  ...  With a large number of commercially-available noninvasive health monitoring sensors today, remote health monitoring of patients in their homes is becoming widespread.  ...  BGV uses polynomial rings in the form of GF (p d ) to represent plaintexts, therefore homomorphic addition (+ h ) and homomorphic multiplication (× h ) correspond to addition and multiplication of plaintexts  ... 
doi:10.1109/cloud.2015.78 dblp:conf/IEEEcloud/KocabasS15 fatcat:bfkwlknevndptmzmsaoh5f3cdi

AUTOCRYPT

Shruti Tople, Shweta Shinde, Zhaofeng Chen, Prateek Saxena
2013 Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security - CCS '13  
We show that x86 code transformed with AUTOCRYPT achieves performance that is significantly better than its alternatives (downloading to a trusted client, or using fully-homomorphic encryption).  ...  Key to achieving this expressiveness over encrypted data, is our scheme to combine and convert between partially-homomorphic encryption (PHE) schemes using a small TCB in the trusted cloud hypervisor.  ...  Similarly, homomorphic schemes with respect to addition / subtraction (e.g. Paillier [48] ), multiplication (e.g. Elgamal [24] ) allow respective computations on the data.  ... 
doi:10.1145/2508859.2516666 dblp:conf/ccs/TopleSCS13 fatcat:t24o7u54sjgjhdxwwm53gnio3u

A Secure Cloud Computing Architecture Using Homomorphic Encryption

Kamal Benzekki, Abdeslam El, Abdelbaki El
2016 International Journal of Advanced Computer Science and Applications  
Many conventional encryption schemes possess either multiplicative or additive homomorphic property and are currently in use for respective applications.  ...  The Purpose of homomorphic encryption is to ensure privacy of data in communication, storage or in use by processes with mechanisms similar to conventional cryptography, but with added capabilities of  ...  The additive homomorphic encryption (addition of the raw data) is the Pailler [4] and Goldwasser-Micalli [5] cryptosystems and the multiplicative homomorphic encryption (only products on raw data)  ... 
doi:10.14569/ijacsa.2016.070241 fatcat:7jju5k7hzrfazp6brbh7jk2yb4
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