On the Design of Cryptographic Primitives

The main objective of this work is twofold. On the one hand, it gives a brief overview of the area of two-party cryptographic protocols. On the other hand, it proposes new schemes and guidelines for improving the practice of robust protocol design. In order to achieve such a double goal, a tour through the descriptions of the two main cryptographic primitives is carried out. Within this survey, some of the most representative algorithms based on the Theory of Finite Fields are provided and new general schemes and specific algorithms based on Graph Theory are proposed

A Private Interactive Test of a Boolean Predicate and Minimum-Knowledge Public-Key Cryptosystems

We introduce a new two-party protocol with the following properties: 1. The protocol gives a proof of the value, 0 or 1, of a particular Boolean predicate which is (assumed to be) hard to compute. This extends the 'interactive proof systems' of (7), which are only used to prove that a certain predicate has value 1. 2. The protocol is provably minimum-knowledge ill the sense that it communicates no additional knowledge (besides the value of the predicate) that might be used, for example, to compromise the private key of a user of a public-key cryptosystem. 3. The protocol is result-indistinguishable: an eavesdropper, overhearing an execution of the protocol, does not know the value of the predicate that was proved. This bit is cryptographically secure. The protocol achieves this without the use of encryption functions, all messages being sent in the clear. These properties enable us to define a minimum-knowledge cryptosystem, in which each user receives exactly the knowledge he is supposed to receive and nothing more. In particular, the system is provably secure against both chosen-message and chosen-ciphertext attack. Moreover, extending the Diffie-Hellman model, it allows a user to encode messages to other users with his own public key. This enables a symmetric use of public-key encryption

A Survey on Homomorphic Encryption Schemes: Theory and Implementation

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the survey that is being submitted to ACM CSUR and has been uploaded to arXiv for feedback from stakeholder

Security Analysis of ElGamal Implementations

International audienceThe ElGamal encryption scheme is not only the most extensively used alternative to RSA, but is also almost exclusively used in voting systems as an effective homomorphic encryption scheme. Being easily adaptable to a wide range of cryptographic groups, the ElGamal encryption scheme enjoys homomorphic properties while remaining semantically secure. This is subject to the upholding of the Decisional Diffie-Hellman (DDH) assumption on the chosen group. We analyze 26 libraries that implement the ElGamal encryption scheme and discover that 20 of them are semantically insecure as they do not respect the Decisional Diffie-Hellman (DDH) assumption. From the five libraries that do satisfy the DDH assumption, we identify and compare four different message encoding and decoding techniques

PRIVACY-PRESERVING QUERY PROCESSING ON OUTSOURCED DATABASES IN CLOUD COMPUTING

Database-as-a-Service (DBaaS) is a category of cloud computing services that enables IT providers to deliver database functionality as a service. In this model, a third party service provider known as a cloud server hosts a database and provides the associated software and hardware supports. Database outsourcing reduces the workload of the data owner in answering queries by delegating the tasks to powerful third-party servers with large computational and network resources. Despite the economic and technical benefits, privacy is the primary challenge posed by this category of services. By using these services, the data owners will lose the control of their databases. Moreover, the privacy of clients may be compromised since a curious cloud operator can follow the queries of a client and infer what the client is after. The challenge is to fulfill the main privacy goals of both the data owner and the clients without undermining the ability of the cloud server to return the correct query results. This thesis considers the design of protocols that protect the privacy of the clients and the data owners in the DBaaS model. Such protocols must protect the privacy of the clients so that the data owner and the cloud server cannot infer the constants contained in the query predicate as well as the query result. Moreover, the data owner privacy should be preserved by ensuring that the sensitive information in the database is not leaked to the cloud server and nothing beyond the query result is revealed to the clients. The results of the complexity and performance analysis indicates that the proposed protocols incur reasonable communication and computation overhead on the client and the data owner, considering the added advantage of being able to perform the symmetrically-private database search

О нестойкости двух симметричных гомоморфных криптосистем, основанных на системе остаточных классов

Одной из наиболее актуальных задач, связанных с защитой облачных вычислений, является анализ криптостойкости гомоморфных шифров. Данная статья посвящена изучению вопроса о защищенности двух недавно предложенных гомоморфных криптосистем, которые, в связи с их высокой вычислительной эффективностью, могут быть использованы для шифрования данных на облачных серверах. Обе криптосистемы основаны на системах остаточных классов, что позволяет рассмотреть их с единых позиций. Именно использование систем остаточных классов делает применение этих криптосистем в реальных приложениях заманчивым с точки зрения эффективности по сравнению с другими гомоморфными шифрами, так как появляется возможность легко распараллелить вычисления. Однако их криптостойкость не была в достаточной мере изучена в литературе и нуждается в анализе. Отметим, что ранее предшественниками была рассмотрена криптосистема похожая на один из шифров, криптостойкость которого исследуется. Была предложена идея адаптивной атаки по выбранным открытым текстам на эту конструкцию и дана оценка необходимого для раскрытия ключа количества пар >. Здесь проводится анализ этой атаки и показываем, что иногда она может работать некорректно. Также описывается более общий алгоритм атаки с известными открытыми текстами. Приводятся теоретические оценки вероятности успешного раскрытия секретного ключа с его помощью и практические оценки этой вероятности, полученные в ходе вычислительного эксперимента. Защищенность второй криптосистемы не была исследована ранее в литературе. Изучена её стойкость к атаке с известными открытыми текстами. Проанализирована зависимость необходимого для взлома количества пар > от параметров криптосистемы и даны рекомендации, которые могут помочь улучшить криптостойкость. Итог проведенного анализа заключается в том, что обе криптосистемы являются уязвимыми к атаке с известными открытыми текстами. Поэтому использовать их для шифрования конфиденциальных данных может быть небезопасно. Основным алгоритмом, используемым в предложенных атаках на криптосистемы, является алгоритм поиска наибольшего общего делителя. Как следствие, время, необходимое для реализации атак, является полиномиальным от размера входных данных