On the Usage of Fully Homomorphic Encryption Libraries

Ivan Chizhov, Alexandra Garazha, Ilya Gerasimov, Maxim Nikolaev

Abstract


Fully homomorphic encryption allows computation to be performed on encrypted data without knowing or learning the decryption key. Therefore this technology can be extremely useful for storing and processing personal data. Due to the great interest in this technology, many software tools and libraries are now known to support fully homomorphic encryption. However, this field of cryptography is still relatively young. Standards and guidelines for using fully homomorphic encryption schemes are still under development. Thus, when using these libraries, it is necessary to pay attention to the cryptographic strength of the used schemes to avoid significant information security risks. We consider the issues of the practical application of fully homomorphic encryption schemes, including the choice of suitable libraries and their initialization parameters to ensure a sufficient security level.

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References


Rivest R L, Adleman L, Dertouzos M L. On data banks and pri- vacy homomorphisms // FoundationsHAHA of Secure Computation, Academia Press. –– 1978. –– P. 169–179.

Rivest R. L., Shamir A., Adleman L. A method for obtaining digital signatures and public-key cryptosystems // Commun. ACM. –– 1978. –– Vol. 21, no. 2. –– P. 120–126. –– URL: https://doi.org/10.1145/359340. 359342.

El Gamal Taher. A public key cryptosystem and a signature scheme based on discrete logarithms // Proceedings of CRYPTO 84 on Ad- vances in Cryptology. –– Berlin, Heidelberg : Springer-Verlag, 1985. –– P. 10–18.

Paillier Pascal. Public-key cryptosystems based on composite degree residuosity classes // Advances in Cryptology — EUROCRYPT ’99 / Ed. by Jacques Stern. –– Berlin, Heidelberg : Springer Berlin Heidel- berg, 1999. –– P. 223–238.

Boneh Dan, Goh Eu-Jin, Nissim Kobbi. Evaluating 2-dnf formulas on ciphertexts // Theory of Cryptography / Ed. by Joe Kilian. –– Berlin, Heidelberg : Springer Berlin Heidelberg, 2005. –– P. 325–341.

Gentry Craig. A Fully Homomorphic Encryption Scheme : Ph.D. thesis / Craig Gentry. –– Stanford, CA, USA : Stanford University, 2009.

Halevi Shai. Homomorphic Encryption // Tutorials on the Foun- dations of Cryptography: Dedicated to Oded Goldreich / Ed. by Yehuda Lindell. –– Cham : Springer International Publishing, 2017. –– P. 219–276. –– ISBN: 978-3-319-57048-8. –– URL: https://doi.org/10. 1007/978- 3- 319- 57048- 8_5.

Halevi Shai, Shoup Victor. Bootstrapping for helib.–– Cryptology ePrint Archive, Report 2014/873. –– 2014. –– https://eprint.iacr.org/ 2014/873.

Gentry Craig, Sahai Amit, Waters Brent. Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster,

Helib. –– https://github.com/shaih/HElib.

Brakerski Zvika, Gentry Craig, Vaikuntanathan Vinod. Fully ho-

momorphic encryption without bootstrapping. –– Cryptology ePrint

Archive, Report 2011/277. –– 2011. –– https://eprint.iacr.org/2011/277.

Cheon Jung Hee, Kim Andrey, Kim Miran, Song Yongsoo. Homomor- phic encryption for arithmetic of approximate numbers. –– Cryptology ePrint Archive, Report 2016/421. –– 2016. –– https://eprint.iacr.org/

/421.

Microsoft SEAL (release 3.5).–– https://github.com/Microsoft/

SEAL. –– 2020. –– apr. –– Microsoft Research, Redmond, WA.

Brakerski Zvika. Fully homomorphic encryption without modulus switching from classical gapsvp. –– Cryptology ePrint Archive, Report 2012/078. –– 2012. –– https://eprint.iacr.org/2012/078.

Fan Junfeng, Vercauteren Frederik. Somewhat practical fully homo- morphic encryption. –– Cryptology ePrint Archive, Report 2012/144. –– 2012. –– https://eprint.iacr.org/2012/144.

PALISADE Lattice Cryptography Library (release 1.9.2). –– https:// palisade-crypto.org/. –– 2020. –– April.

Ducas Léo, Micciancio Daniele. Fhew: Bootstrapping homomorphic encryption in less than a second. –– Cryptology ePrint Archive, Report 2014/816. –– 2014. –– https://eprint.iacr.org/2014/816.

Chillotti Ilaria, Gama Nicolas, Georgieva Mariya, Izabachène Malika. Faster fully homomorphic encryption: Bootstrapping in less than 0.1 seconds. –– Cryptology ePrint Archive, Report 2016/870. –– 2016. –– https://eprint.iacr.org/2016/870.

Tfhe. –– https://github.com/tfhe/tfhe.

Heaan. –– https://github.com/snucrypto/HEAAN.

Lol. –– https://github.com/cpeikert/Lol.

Lattigo 1.3.1. –– Online: http://github.com/ldsec/lattigo. –– 2020. –– feb. –– EPFL-LDS.

Halevi Shai, Shoup Victor. Algorithms in helib. –– Cryptology ePrint

Archive, Report 2014/106. –– 2014. –– https://eprint.iacr.org/2014/106.

node-seal. –– https://github.com/morfix- io/node- seal.

libscarab. –– https://github.com/hcrypt- project/libScarab.

Fhew. –– https://github.com/lducas/FHEW.

Krypto. –– https://github.com/kryptnostic/krypto/tree/develop.

Fv-nfllib. –– https://github.com/CryptoExperts/FV- NFLlib.

cuhe: Homomorphic and fast. –– https://github.com/vernamlab/cuHE. [30] cufhe. –– https://github.com/vernamlab/cuFHE.

cuyashe. –– https://github.com/cuyashe- library/cuyashe.

A gpu implementation of fully homomorphic encryption on torus. ––

https://github.com/nucypher/nufhe.

Costache Anamaria, Smart Nigel P. Which ring based somewhat ho-

momorphic encryption scheme is best? –– Cryptology ePrint Archive,

Report 2015/889. –– 2015. –– https://eprint.iacr.org/2015/889.

Costache Anamaria, Laine Kim, Player Rachel. Evaluating the effec- tiveness of heuristic worst-case noise analysis in fhe. –– Cryptology ePrint Archive, Report 2019/493. –– 2019. –– https://eprint.iacr.org/

/493.

Albrecht Martin, Chase Melissa, Chen Hao et al. Homomorphic

encryption standard. –– Cryptology ePrint Archive, Report 2019/939. ––

–– https://eprint.iacr.org/2019/939.

Albrecht Martin R., Player Rachel, Scott Sam. On the concrete

hardness of learning with errors. –– Cryptology ePrint Archive, Report

/046. –– 2015. –– https://eprint.iacr.org/2015/046.

Lwe-estimator. –– https://bitbucket.org/malb/lwe-estimator.

Arora Sanjeev, Ge Rong. New algorithms for learning in presence

of errors // Proceedings of the 38th International Colloquim Con- ference on Automata, Languages and Programming - Volume Part I. –– ICALP’11. –– Berlin, Heidelberg : Springer-Verlag, 2011. –– P. 403–415.

Schnorr Claus, Euchner M. Lattice basis reduction: Improved practical algorithms and solving subset sum problems // Mathematical Program- ming. –– 1994. –– 08. –– Vol. 66. –– P. 181–199.

Schnorr Claus Peter. Lattice reduction by random sampling and birth- day methods // STACS 2003 / Ed. by Helmut Alt, Michel Habib. –– Berlin, Heidelberg : Springer Berlin Heidelberg, 2003. –– P. 145–156.

Babai László. On lovász’ lattice reduction and the nearest lattice point problem (shortened version) // Proceedings of the 2nd Symposium of Theoretical Aspects of Computer Science. –– STACS ’85. –– Berlin, Heidelberg : Springer-Verlag, 1985. –– P. 13–20.

Lindner Richard, Peikert Chris. Better key sizes (and attacks) for lwe- based encryption // Proceedings of the 11th International Conference on Topics in Cryptology: CT-RSA 2011. –– CT-RSA’11. –– Berlin, Heidelberg : Springer-Verlag, 2011. –– P. 319–339.

attribute-based. –– Cryptology ePrint Archive,

Report 2013/340. –– 2013. –– https://eprint.iacr.org/2013/340.

Albrecht Martin R. On dual lattice attacks against small-secret lwe and parameter choices in helib and seal. –– Cryptology ePrint Archive, Report 2017/047. –– 2017. –– https://eprint.iacr.org/2017/047.

Albrecht Martin R., Fitzpatrick Robert, öpfert Florian G. On the effi- cacy of solving lwe by reduction to unique-svp. –– Cryptology ePrint Archive, Report 2013/602. –– 2013. –– https://eprint.iacr.org/2013/602.

Micciancio Daniele, Regev Oded. Lattice-based Cryptography // Post- Quantum Cryptography / Ed. by Daniel J. Bernstein, Johannes Buch- mann, Erik Dahmen.–– Berlin, Heidelberg : Springer Berlin Hei- delberg, 2009. –– P. 147–191. –– ISBN: 978-3-540-88702-7. –– URL: https://doi.org/10.1007/978- 3- 540- 88702- 7_5.

Archer David, Chen Lily, Cheon Jung et al. Applications of homo- morphic encryption. –– 2017. –– 07.

Assessment of cloud-based health monitoring using homomorphic encryption / Ovunc Kocabas, Tolga Soyata, Jean-Philippe Couderc et al. –– 2013. –– 10.

Secure large-scale genome-wide association studies using homomor- phic encryption / Marcelo Blatt, Alexander Gusev, Yuriy Polyakov, Shafi Goldwasser // Proceedings of the National Academy of Sci- ences. –– 2020. –– Vol. 117, no. 21. –– P. 11608–11613.

Masters Oliver, Hunt Hamish, Steffinlongo Enrico et al. Towards a homomorphic machine learning big data pipeline for the financial services sector. –– Cryptology ePrint Archive, Report 2019/1113. –– 2019. –– https://eprint.iacr.org/2019/1113.

Troncoso-Pastoriza Juan Ramón, González-Jiménez Daniel, Pérez- González Fernando. Fully private noninteractive face verification // IEEE Transactions on Information Forensics and Security. –– 2013. –– Vol. 8, no. 7. –– P. 1101–1114.

Engelsma Joshua J, Jain Anil K, Boddeti Vishnu Naresh. Hers: Homomorphically encrypted representation search // arXiv preprint arXiv:2003.12197. –– 2020.

Gong Sixue, Boddeti Vishnu Naresh, Jain Anil K. On the intrinsic dimensionality of image representations // Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. –– 2019. –– P. 3987–3996.

Abadi Martín, Agarwal Ashish, Barham Paul et al. TensorFlow: Large- scale machine learning on heterogeneous systems. –– 2015. –– Software available from tensorflow.org. URL: https://www.tensorflow.org/.

Boddeti Vishnu Naresh. Secure face matching using fully homo- morphic encryption // 2018 IEEE 9th International Conference on Biometrics Theory, Applications and Systems (BTAS) / IEEE.–– 2018. –– P. 1–10.

Maalouf Maher. Logistic regression in data analysis: An overview // International Journal of Data Analysis Techniques and Strategies. –– 2011. –– 07. –– Vol. 3. –– P. 281–299.

Machine learning techniques and chi-square feature selection for cancer classification using sage gene expression profiles / Xin Jin, Anbang Xu, Rongfang Bie, Ping Guo. –– Vol. 3916. –– 2006. –– 04. –– P. 106–115.

The alexnet moment for homomorphic encryption: Hcnn, the first homomorphic cnn on encrypted data with gpus / Ahmad Al Badawi, Jin Chao, Jie Lin et al. // arXiv preprint arXiv:1811.00778. –– 2018.

High-performance fv somewhat homomorphic encryption on gpus: An implementation using cuda / Ahmad Al Badawi, Bharadwaj Veeravalli, Chan Fook Mun, Khin Mi Mi Aung // IACR Transactions on Crypto- graphic Hardware and Embedded Systems. –– 2018. –– P. 70–95.

Lopez-Alt Adriana, Tromer Eran, Vaikuntanathan Vinod. On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. –– Cryptology ePrint Archive, Report 2013/094. –– 2013. –– https://eprint.iacr.org/2013/094.

Sharma Tannishk. E-voting using homomorphic encryption scheme // International Journal of Computer Applications. –– 2016. –– 05. –– Vol. 141. –– P. 14–16.

Helios. –– https://github.com/benadida/helios-server.


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