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Improved Fully Homomorphic Encryption over the Integers with Shorter Public Keys

Can Xiang, Chun-ming Tang
2014 International Journal of Security and Its Applications  
Furthermore, we prove the security of our schemes based on difficulties of the approximate greatest common divisor (AGCD) problem and the sparse subset sum problem. 366 Copyright ⓒ 2014 SERSC perform arithmetic  ...  Fully homomorphic encryption (FHE) is a "holy grail" of cryptography. However, it is not yet adopted in practice because no known scheme is efficient.  ...  Somewhat Homomorphic Encryption Scheme In this section, we first recall the SWHE in the DGHV scheme over the integers [3] , the scheme is based on the AGCD problem.  ... 
doi:10.14257/ijsia.2014.8.6.31 fatcat:bdtckdmtebahnc4ihj5t4l32vm

Leveled Fully Homomorphic Encryption Schemes with Hensel Codes [article]

David William Honorio Araujo da Silva, Luke Harmon, Gaetan Delavignette, Carlos Paz de Araujo
2021 IACR Cryptology ePrint Archive  
The efficiency and security (under an AGCD variant) of the public-key scheme are discussed in detail.  ...  Further, our results can be seen as a natural unification of error-free computation (computation free of rounding errors over rational numbers) and homomorphic encryption.  ...  In Table 1 we display runtime results for the key generation, encryption, and decryption algorithms, and the homomorphic evaluation of the dot product of two 3D vectors. y), then |x| ≤ N and |y| ≤ 2N  ... 
dblp:journals/iacr/SilvaHDA21 fatcat:wyyv6mfgv5g6bc3tesw327vkpi

Efficient GSW-Style Fully Homomorphic Encryption over the Integers

Jianan Zhao, Ruwei Huang, Bo Yang, Angel M. Del Rey
2021 Security and Communication Networks  
Moreover, the computational efficiency in the homomorphic evaluation can be improved by hybrid homomorphic operations between integers and vectors.  ...  We propose a GSW-style fully homomorphic encryption scheme over the integers (FHE-OI) that is more efficient than the prior work by Benarroch et al. (PKC 2017).  ...  Moreover, the computational efficiency in homomorphic evaluation can be improved by hybrid homomorphic operations between integers and vectors.  ... 
doi:10.1155/2021/8823787 fatcat:f76x6j7dkjhbvbeflk52vsi3qm

FHE over the Integers: Decomposed and Batched in the Post-Quantum Regime [chapter]

Daniel Benarroch, Zvika Brakerski, Tancrède Lepoint
2017 Lecture Notes in Computer Science  
Fully homomorphic encryption over the integers (FHE-OI) is currently the only alternative to lattice-based FHE.  ...  ., we do require circular security for our scheme, even for bounded homomorphism.  ...  Rivest, Adleman and Dertouzos [28] proposed the notion of fully homomorphic encryption (FHE) where the scheme is homomorphic w.r.t any efficiently computable f .  ... 
doi:10.1007/978-3-662-54388-7_10 fatcat:bi27v6ouy5hwbdhtlg6fz3i7cu

Development of Cryptography since Shannon [article]

Funda Özdemir, Çetin Kaya Koç
2022 IACR Cryptology ePrint Archive  
The aim is to construct a leveled HE scheme for approximate arithmetic. Let the integer L be the depth of the arithmetic circuit to be evaluated homomorphically and p > 0 be a base.  ...  The security of this fully homomorphic DGHV scheme is based on the "approximate gcd (AGCD) problem" and "sparse subset sum problem (SSSP)".  ... 
dblp:journals/iacr/OzdemirK22 fatcat:wzia5wptezdt3guwsic2a4oo6m

On the IND-CCA1 Security of FHE Schemes

Prastudy Fauzi, Martha Norberg Hovd, Håvard Raddum
2022 Cryptography  
There are numerous FHE schemes, all of which are expanded from somewhat homomorphic encryption (SHE) schemes, and some of which are considered viable in practice.  ...  Fully homomorphic encryption (FHE) is a powerful tool in cryptography that allows one to perform arbitrary computations on encrypted material without having to decrypt it first.  ...  We note that the scheme is designed so that the matrix and vector encryption and decryption use the same secret key material and that the scheme only allows for matrix-matrix and vector-matrix multiplications  ... 
doi:10.3390/cryptography6010013 fatcat:5adm5jv6erbxfcmgmtafyxfpwm

Trend of Bootstrapping from 2009 to 2016

Paulin Boale Bomolo, Eugene Mbuyi Mukendi, Simon Ntumba Badibanga
2021 International Journal of Advanced Computer Science and Applications  
The pedestal of fully homomorphic encryption is bootstrapping which allows unlimited processing on encrypted data. This technique is a bottleneck in the practicability of homomorphic encryption.  ...  From 2009 to 2016, the execution time of bootstrapping decreased from several hours to a few thousandths of a second for processing a logic gate on two encrypted bits.  ...  Encrypted messages are square matrices, addition and homomorphic multiplication is addition and multiplication matrix respectively.  ... 
doi:10.14569/ijacsa.2021.0121212 fatcat:x44iblyiuzc5bfbdq23qt6f564

CUDA-Accelerated RNS Multiplication in Word-Wise Homomorphic Encryption Schemes [article]

Shiyu Shen, Hao Yang, Yu Liu, Zhe Liu, Yunlei Zhao
2022 IACR Cryptology ePrint Archive  
trade-offs between resource and efficiency, yielding a solution suitable for accelerating RNS homomorphic multiplication on both high-performance and embedded GPUs.  ...  Homomorphic encryption (HE), which allows computation over encrypted data, has often been used to preserve privacy.  ...  For different fully homomorphic encryption schemes, especially those based on RLWE, the low-level operations have low arithmetic density and share similar constructions.  ... 
dblp:journals/iacr/ShenYLLZ22 fatcat:dn5rmr3rvjdabnggeb5uvwez2a

Privacy-Preserving Oriented Floating-Point Number Fully Homomorphic Encryption Scheme

Shuangjie Bai, Geng Yang, Jingqi Shi, Guoxiu Liu, Zhaoe Min
2018 Security and Communication Networks  
Homomorphic encryption can be operated directly on the ciphertext; this encryption provides a new method for privacy-preserving.  ...  We encrypt a matrix of plaintext bits as a single ciphertext to reduce the ciphertext expansion ratio and reduce the public key size by encrypting with a quadratic form in three types of public key elements  ...  ), and Postdoctoral Science Foundation Project of China (2016M601859).  ... 
doi:10.1155/2018/2363928 fatcat:dnf4nm7fbfebvfconueifmidr4

Verifiable Encodings for Secure Homomorphic Analytics [article]

Sylvain Chatel, Christian Knabenhans, Apostolos Pyrgelis, Jean-Pierre Hubaux
2022 arXiv   pre-print
Homomorphic encryption, which enables the execution of arithmetic operations directly on ciphertexts, is a promising solution for protecting privacy of cloud-delegated computations on sensitive data.  ...  Our authenticators operate on top of trending ring learning with errors based fully homomorphic encryption schemes over the integers.  ...  [77] propose a homomorphic authenticated-encryption based on the error-free approximate greatest common divisor (AGCD) problem, and Goldwasser et al.  ... 
arXiv:2207.14071v1 fatcat:zxo6estt5bfezguldfg37elitq

Tile-based modular architecture for accelerating homomorphic function evaluation on FPGA

Mustafa Khairallah, Maged Ghoneima
2016 2016 IEEE 59th International Midwest Symposium on Circuits and Systems (MWSCAS)  
In this paper, a new architecture for accelerating homomorphic function evaluation on FPGA is proposed. A parallel cached NTT algorithm with an overall time complexity O( √ N log √ N ) is presented.  ...  The architecture has been evaluated by computing a block of each of the AES and SIMON-64/128 on the LTV and YASHE schemes.  ...  The LTV scheme (Lopez-Tromer-Vaikuntanathan Leveled Fully Homomorphic Encryption Scheme) [9] was introduced in 2012 as the first fully-fledged FHE scheme based on NTRU.  ... 
doi:10.1109/mwscas.2016.7870149 dblp:conf/mwscas/KhairallahG16 fatcat:tbmbcwl7ifamnpl73ferfnuxjy