Study of Fully Homomorphic Encryption over Integers

Fully homomorphic encryption has long been regarded as an open problem of cryptography. The method of constructing first fully homomorphic encryption scheme by Gentry is complicate so that it has been considered difficult to understand. This paper explains the idea of constructing fully homomorphic encryption and presents a general framework from various scheme of fully homomorphic encryption. Specially, this general framework can show some possible ways to construct fully homomorphic encryption. We then analyze the procedure how to obtaining fully homomorphic encryption over the integers. The analysis of recrypt procedure show the growth of noise, and the bound of noise in recrypt procedure is given. Finally, we describe the steps of implementation.

Quantum Fully Homomorphic Encryption With Verification

Fully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerous applications of classical FHE (zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is reasonable to hope that quantum FHE (or QFHE) will lead to many new results in the quantum setting. However, a crucial ingredient in almost all applications of FHE is circuit verification. Classically, verification is performed by checking a transcript of the homomorphic computation. Quantumly, this strategy is impossible due to no-cloning. This leads to an important open question: can quantum computations be delegated and verified in a non-interactive manner? In this work, we answer this question in the affirmative, by constructing a scheme for QFHE with verification (vQFHE). Our scheme provides authenticated encryption, and enables arbitrary polynomial-time quantum computations without the need of interaction between client and server. Verification is almost entirely classical; for computations that start and end with classical states, it is completely classical. As a first application, we show how to construct quantum one-time programs from classical one-time programs and vQFHE.Comment: 30 page

Experimental Demonstration of Quantum Fully Homomorphic Encryption with Application in a Two-Party Secure Protocol

A fully homomorphic encryption system hides data from unauthorized parties while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of cryptographic functionalities. Designing such a scheme remained an open problem until 2009, decades after the idea was first conceived, and the past few years have seen the generalization of this functionality to the world of quantum machines. Quantum schemes prior to the one implemented here were able to replicate some features in particular use cases often associated with homomorphic encryption but lacked other crucial properties, for example, relying on continual interaction to perform a computation or leaking information about the encrypted data. We present the first experimental realization of a quantum fully homomorphic encryption scheme. To demonstrate the versatility of a a quantum fully homomorphic encryption scheme, we further present a toy two-party secure computation task enabled by our scheme

On Fully Homomorphic Encryption

Täielikult homomorfne krüpteerimine on krüptosüsteem, mille puhul üks osapool saab enda valdusesse krüpteeritud andmed ning saab nende andmetega tõhusalt sooritada erinevaid operatsioone. Operatsioone saab teha hoolimata sellest, et andmed jäävad krüpteerituks ning seega ei ole ka vajalik teada dekrüpteerimisvõtit. Selline süsteem oleks äärmiselt kasulik, näiteks tagades andmete privaatsuse, mis on saadetud kolmanda osapoole teenusele. Täielikult homomorfne krüpteerimine on vastandiks krüptosüsteemidele nagu Paillier, kus ei ole võimalik teostada krüpteeritud andmete peal korrutamist ilma neid enne dekrüpteerimata, või ElGamal, kus ei saa sooritada krüpteeritud andmete liitmist enne andmete dekrüpteerimist. Täielikult homomorfne krüpteerimine on väga uus uurimisala: esimese taolise süsteemi lõi Gentry aastal 2009. Gentry läbimurdest alates on olnud palju tema tööst inspireeritud edasiminekuid. Kõik viimased täielikult homomorfsed krüptosüsteemid kasutavad avaliku võtmega krüptograafiat ja põhinevad võredel. Võre-põhine krüptograafia äratab üha enam huvi oma turvalisuse püsimisega kvantarvutites ning oma halvima juhu turvagarantiidega. Siiski jääb püsima peamine probleem: süsteemidel ei ole veel tõhusat teostust, mis säilitaks adekvaatsed turvalisuse nõuded. Selles valguses vaadatuna, viimased edasiminekud täielikult homomorfses krüpteerimises kas täiendavad eelnevate süsteemide tõhusust või pakuvad välja uue parema efektiivsusega skeemi. Antud uurimus on ülevaade hiljutistest täielikult homomorfsetest krüptosüsteemidest. Õpime tundma mõningaid viimaseid täielikult homomorfseid krüptosüsteeme, analüüsime ning võrdleme neid. Neil süsteemidel on teatud ühised elemendid: 1. Tõhus võre-põhine krüptosüsteem turvalisusega, mis põhineb üldteada võreprobleemide keerulisusel. 2. Arvutusfunktsioon definitsioonidega homomorfsele liitmisele ja korrutamisele müra kasvu piiramiseks. 3. Meetodid, et muuta süsteem täielikult homomorfseks selle arvutusfunktsiooniga. Niipea kui võimalik, kirjutame nende süsteemide peamised tulemused ümber detailsemas ja loetavamas vormis. Kõik skeemid, mida me arutame, välja arvatud Gentry, on väga uued. Kõige varasem arutletav töö avaldati oktoobris aastal 2011 ning mõningad tööd on veel kättesaadavad ainult elektroonilisel kujul. Loodame, et käesolev töö aitab lugejail olla kursis täielikult homomorfse krüpteerimisega, rajades teed edasistele arengutele selles vallas

Reusable garbled gates for new fully homomorphic encryption service

In this paper, we propose a novel way to provide a fully homomorphic encryption service, namely by using garbled circuits. From a high level perspective, garbled circuits and fully homomorphic encryption, both aim at implementing complex computation on ciphertexts. We define a new cryptographic primitive named reusable garbled gate, which comes from the area of garbled circuits, then based on this new primitive we show that it is very easy to construct a fully homomorphic encryption. However, the instantiation of reusable garbled gates is rather difficult, in fact, we can only instantiate this new primitive based on indistinguishable obfuscation. Furthermore, reusable garbled gates can be a core component for constructing the reusable garbled circuits, which can reduce the communication complexity of them from O(n) to O(1). We believe that reusable garbled gates promise a new way to provide fully homomorphic encryption and reusable garbled circuits service fast.Peer ReviewedPostprint (author's final draft

Symmetric Ciphers for Fully Homomorphic Encryption

Fully homomorphic encryption is the latest addition to the world of cryptography. It is a type of encryption that allows operations to be done on ciphertexts, which is not possible with traditional encryption. The field has gained a lot of traction since it was first theoretically proved possible in 2009. This thesis goes through how fully homomorphic encryption works, from making a somewhat homomorphic encryption scheme, into a fully homomorphic scheme. We also explain in detail the different aspects required, such as bootstrapping and noise. Since 2009 several schemes and libraries to optimize homomorphic encryption have been suggested, so that it one day may be feasible to implement it in regular modern-day applications. Some libraries target regular developers without an extensive cryptographic background, so they may still be able to use homomorphic encryption in applications, while others aim for researchers to implement and discover the possibilities that come with fully homomorphic encryption. With a focus on the use for fully homomorphic encryption within cloud computing, this thesis focuses on how symmetric ciphers can make fully homomorphic encryption possible, also for use with small IoT devices. We look at several such ciphers that have been suggested and focus on the family of stream ciphers called Rasta. We have implemented one variant of the Rasta cipher using the software library HElib and timed its performance.Masteroppgave i informatikkINF399MAMN-INFMAMN-PRO

Integer-based fully homomorphic encryption

The concept of fully homomorphic encryption has been considered the holy grail of cryptography since the discovery of secure public key cryptography in the 1970s. Fully homomorphic encryption allows arbitrary computation on encrypted data to be performed securely. Craig Gentry\u27s new method of bootstrapping introduced in 2009 provides a technique for constructing fully homomorphic cryptosystems. In this paper we explore one such bootstrappable system based on simple integer arithmetic in a manner that someone without a high level of experience in homomorphic encryption can readily understand. Further, we present an implementation of the system as well as a lattice- based attack. We present performance results of our implementation under various parameter choices and the resistance of the system to the lattice-based attack under those parameters. Unfortunately, while the system is very interesting from a theoretical point of view, the results show that it is still not feasible for use