Society-oriented cryptographic techniques for information protection

Groups play an important role in our modern world. They are more reliable and more trustworthy than individuals. This is the reason why, in an organisation, crucial decisions are left to a group of people rather than to an individual. Cryptography supports group activity by offering a wide range of cryptographic operations which can only be successfully executed if a well-defined group of people agrees to co-operate. This thesis looks at two fundamental cryptographic tools that are useful for the management of secret information. The first part looks in detail at secret sharing schemes. The second part focuses on society-oriented cryptographic systems, which are the application of secret sharing schemes in cryptography. The outline of thesis is as follows

Private membership test protocol with low communication complexity

Ramezanian S, Meskanen T, Naderpour M, Junnila V, Niemi V. Private membership test protocol with low communication complexity. Digital Communications and Networks. 2019 May 13.We introduce a practical method to perform private membership tests. In this method, clients are able to test whether an item is in a set controlled by the server without revealing their query item to the server. After executing the queries, the content of the server's set remains secret. One use case for a private membership test is to check whether a file contains any malware by checking its signature against a database of malware samples in a privacy-preserving way. We apply the Bloom filter and the Cuckoo filter in the membership test procedure. In order to achieve privacy properties, we present a novel protocol based on some homomorphic encryption schemes. In our protocol, we rearrange the data in the set into N-dimensional hypercubes. We have implemented our method in a realistic scenario where a client of an anti-malware company wants to privately check whether a hash value of a given file is in the malware database of the company. The evaluation shows that our method is feasible for real-world applications. We also have tested the performance of our protocol for databases of different sizes and data structures with different dimensions: 2-dimensional, 3-dimensional, and 4-dimensional hypercubes. We present formulas to estimate the cost of computation and communication in our protocol.Peer reviewe

Preimage Selective Trapdoor Function: How to Repair an Easy Problem

Public key cryptosystems are constructed by embedding a trapdoor into a one-way function. So, the one-wayness and the trapdoorness are vital to public key cryptography. In this paper, we propose a novel public key cryptographic primitive called preimage selective trapdoor function. This scenario allows to use exponentially many preimage to hide a plaintext even if the underlying function is not one-way. The compact knapsack problem is used to construct a probabilistic public key cryptosystem, the underlying encryption function of which is proven to be preimage selective trapdoor one-way functions under some linearization attack models. The constructive method can guarantee the noninjectivity of the underlying encryption function and the unique decipherability for ciphertexts simultaneously. It is heuristically argued that the security of the proposal cannot be compromised by a polynomial-time adversary even if the compact knapsack is easy to solve. We failed to provide any provable security results about the proposal; however, heuristic illustrations show that the proposal is secure against some known attacks including brute force attacks, linearization attacks, and key-recovery attacks. The proposal turns out to have acceptable key sizes and performs efficiently and hence is practical

Private membership test protocol with low communication complexity

We introduce a practical method to perform private membership tests. In this method, clients are able to test whether an item is in a set controlled by the server without revealing their query item to the server. After executing the queries, the content of the server's set remains secret. One use case for a private membership test is to check whether a file contains any malware by checking its signature against a database of malware samples in a privacy preserving way. We apply the Bloom filter and the Cuckoo filter in the membership test procedure. In order to achieve privacy properties, we present a novel protocol based on some homomorphic encryption schemes. In our protocol, we rearrange the data in the set into N -dimensional hypercubes. We have implemented our method in a realistic scenario where a client of an anti-malware company wants to privately check whether a hash value of a given file is in the malware database of the company. The evaluation shows that our method is feasible for real-world applications. We also have tested the performance of our protocol for databases of different sizes and data structures with different dimensions: 2-dimensional, 3-dimensional and 4-dimensional hypercubes. We present formulas to estimate the cost of computation and communication in our protocol.</p

A suite of quantum algorithms for the shortestvector problem

Crytography has come to be an essential part of the cybersecurity infrastructure that provides a safe environment for communications in an increasingly connected world. The advent of quantum computing poses a threat to the foundations of the current widely-used cryptographic model, due to the breaking of most of the cryptographic algorithms used to provide confidentiality, authenticity, and more. Consequently a new set of cryptographic protocols have been designed to be secure against quantum computers, and are collectively known as post-quantum cryptography (PQC). A forerunner among PQC is lattice-based cryptography, whose security relies upon the hardness of a number of closely related mathematical problems, one of which is known as the shortest vector problem (SVP). In this thesis I describe a suite of quantum algorithms that utilize the energy minimization principle to attack the shortest vector problem. The algorithms outlined span the gate-model and continuous time quantum computing, and explore methods of parameter optimization via variational methods, which are thought to be effective on near-term quantum computers. The performance of the algorithms are analyzed numerically, analytically, and on quantum hardware where possible. I explain how the results obtained in the pursuit of solving SVP apply more broadly to quantum algorithms seeking to solve general real-world problems; minimize the effect of noise on imperfect hardware; and improve efficiency of parameter optimization.Open Acces

Public keys quality

Dissertação de mestrado em Matemática e ComputaçãoThe RSA cryptosystem, invented by Ron Rivest, Adi Shamir and Len Adleman ([Rivest et al., 1978]) is the most commonly used cryptosystem for providing privacy and ensuring authenticity of digital data. RSA is usually used in contexts where security of digital data is priority. RSA is used worldwide by web servers and browsers to secure web traffic, to ensure privacy and authenticity of e-mail, to secure remote login sessions and to provide secure electronic creditcard payment systems. Given its importance in the protection of digital data, vulnerabilities of RSA have been analysed by many researchers. The researches made so far led to a number of fascinating attacks. Although the attacks helped to improve the security of this cryptosystem, showing that securely implementing RSA is a nontrivial task, none of them was devastating. This master thesis discusses the RSA cryptosystem and some of its vulnerabilities as well as the description of some attacks, both recent and old, together with the description of the underlying mathematical tools they use. Although many types of attacks exist, in this master thesis only a few examples were analysed. The ultimate attack, based in the batch-GCD algorithm, was implemented and tested in the RSA keys produced by a certificated Hardware Security Modules Luna SA and the results were commented. The random and pseudorandom numbers are fundamental to many cryptographic applications, including the RSA cryptosystems. In fact, the produced keys must be generated in a specific random way. The National Institute of Standards and Technology, responsible entity for specifying safety standards, provides a package named "A Statistical Test Suit for Random and Pseudorandom Number Generators for Cryptography Applications" which was used in this work to test the randomness of the Luna SA generated numbers. All the statistical tests were tested in different bit sizes number and the results commented. The main purpose of this thesis is to study the previous subjects and create an applications capable to test the Luna SA generated numbers randomness, a well as evaluate the security of the RSA. This work was developed in partnership with University of Minho and Multicert.O RSA, criado por Ron Rivest, Adi Shamir e Len Adleman ([Rivest et al., 1978]) é o sistema criptográfico mais utilizado para providenciar segurança e assegurar a autenticação de dados utilizados no mundo digital. O RSA é usualmente usado em contextos onde a segurança é a grande prioridade. Hoje em dia, este sistema criptográfico é utilizado mundialmente por servidores web e por browsers, por forma a assegurar um tráfego seguro através da Internet. É o sistema criptográfico mais utilizado na autenticação de e-mails, nos inícios de sessões remotos, na utilização de pagamentos através de cartões multibanco, garantindo segurança na utilização destes serviços. Dada a importância que este sistema assume na proteção da informação digital, as suas vulnerabilidades têm sido alvo de várias investigações. Estas investigações resultaram em vários ataques ao RSA. Embora nenhum destes ataques seja efetivamente eficaz, todos contribuíram para um aumento da segurança do RSA, uma vez que as implementações de referência deste algoritmo passaram a precaver-se contra os ataques descobertos. Esta tese de mestrado aborda o sistema criptográfico RSA, discutindo algumas das suas vulnerabilidades, assim como alguns ataques efetuados a este sistema, estudando todos os métodos matemáticos por estes usados. Embora existam diversos ataques, apenas alguns serão abordados nesta tese de mestrado. O último ataque, baseado no algoritmo batch-GCD foi implementado e foram feitos testes em chaves RSA produzidas por um Hardware Security Module Luna SA certificado e os resultados obtidos foram discutidos. Os números aleatórios e pseudoaleatórios são fundamentais a todas as aplicações criptográficas, incluindo, portanto, o sistema criptográfico RSA. De facto, as chaves produzidas deverão ser geradas com alguma aleatoriedade intrínseca ao sistema. O Instituto Nacional de Standards e Tecnologia, entidade responsável pela especificação dos standards de segurança, disponibiliza um pacote de testes estatísticos, denominado por "A Statistical Test Suit for Random and Pseudorandom Number Generators for Cryptography Applications". Estes testes estatísticos foram aplicados a números gerados pelo Luna SA e os resultados foram, também, comentados. O objetivo desta tese de mestrado é desenvolver capacidade de compreensão sobre os assuntos descritos anteriormente e criar uma aplicação capaz de testar a aleatoriedade dos números gerados pelo Luna SA, assim como avaliar a segurança do sistema criptográfico RSA. Este foi um trabalho desenvolvido em parceria com a Universidade do Minho e com a Multicert

A Study of Privacy Preserving Queries with Bloom Filters

This thesis focuses on the private membership test (PMT) problem and presents three single server protocols to resolve this problem. In the presented solutions, a client can perform an inclusion test for some record x in a server's database, without revealing his record. Moreover after executing the protocols, the contents of server's database remain secret. In each of these solutions, a different cryptographic protocol is utilized to construct a privacy preserving variant of Bloom filter. The three suggested solutions are slightly different from each other, from privacy perspective and also from complexity point of view. Therefore, their use cases are different and it is impossible to choose one that is clearly the best between all three. We present the software developments of the three protocols by utilizing various pseudocodes. The performance of our implementation is measured based on a real case scenario. This thesis is a spin-off from the Academy of Finland research project "Cloud Security Services".Siirretty Doriast

The Theory and Applications of Homomorphic Cryptography

Homomorphic cryptography provides a third party with the ability to perform simple computations on encrypted data without revealing any information about the data itself. Typically, a third party can calculate one of the encrypted sum or the encrypted product of two encrypted messages. This is possible due to the fact that the encryption function is a group homomorphism, and thus preserves group operations. This makes homomorphic cryptosystems useful in a wide variety of privacy preserving protocols. A comprehensive survey of known homomorphic cryptosystems is provided, including formal definitions, security assumptions, and outlines of security proofs for each cryptosystem presented. Threshold variants of several homomorphic cryptosystems are also considered, with the first construction of a threshold Boneh-Goh-Nissim cryptosystem given, along with a complete proof of security under the threshold semantic security game of Fouque, Poupard, and Stern. This approach is based on Shoup's approach to threshold RSA signatures, which has been previously applied to the Paillier and Damg\aa rd-Jurik cryptosystems. The question of whether or not this approach is suitable for other homomorphic cryptosystems is investigated, with results suggesting that a different approach is required when decryption requires a reduction modulo a secret value. The wide variety of protocols utilizing homomorphic cryptography makes it difficult to provide a comprehensive survey, and while an overview of applications is given, it is limited in scope and intended to provide an introduction to the various ways in which homomorphic cryptography is used beyond simple addition or multiplication of encrypted messages. In the case of strong conditional oblivious tranfser, a new protocol implementing the greater than predicate is presented, utilizing some special properties of the Boneh-Goh-Nissim cryptosystem to achieve security against a malicious receiver

Cryptographically Secure Information Flow Control on Key-Value Stores

We present Clio, an information flow control (IFC) system that transparently incorporates cryptography to enforce confidentiality and integrity policies on untrusted storage. Clio insulates developers from explicitly manipulating keys and cryptographic primitives by leveraging the policy language of the IFC system to automatically use the appropriate keys and correct cryptographic operations. We prove that Clio is secure with a novel proof technique that is based on a proof style from cryptography together with standard programming languages results. We present a prototype Clio implementation and a case study that demonstrates Clio's practicality.Comment: Full version of conference paper appearing in CCS 201