Cryptanalysis of a Homomorphic Encryption Scheme

Homomorphic encryption allows to make specific operations on private data which stays encrypted. While applications such as cloud computing require to have a practical solution, the encryption scheme must be secure. In this article, we detail and analyze in-depth the homomorphic encryption scheme proposed by Zhou and Wornell in~\cite{zhou}. From the analysis of the encryption scheme, we are able to mount three attacks. The first attack enables to recover a secret plaintext message broadcasted to multiple users. The second attack performs a chosen ciphertext key recovery attack and it was implemented and verified. The last attack is a related chosen plaintext decryption attack

A fast single server private information retrieval protocol with low communication cost

Existing single server Private Information Retrieval (PIR) protocols are far from practical. To be practical, a single server PIR protocol has to be both communicationally and computationally efficient. In this paper, we present a single server PIR protocol that has low communication cost and is much faster than existing protocols. A major building block of the PIR protocol in this paper is a tree-based compression scheme, which we call folding/unfolding. This compression scheme enables us to lower the communication complexity to O(loglogn). The other major building block is the BGV fully homomorphic encryption scheme. We show how we design the protocol to exploit the internal parallelism of the BGV scheme. This significantly reduces the server side computational overhead and makes our protocol much faster than the existing protocols. Our protocol can be further accelerated by utilising hardware parallelism. We have built a prototype of the protocol. We report on the performance of our protocol based on the prototype and compare it with the current most efficient protocols

REISCH: incorporating lightweight and reliable algorithms into healthcare applications of WSNs

Healthcare institutions require advanced technology to collect patients' data accurately and continuously. The tradition technologies still suffer from two problems: performance and security efficiency. The existing research has serious drawbacks when using public-key mechanisms such as digital signature algorithms. In this paper, we propose Reliable and Efficient Integrity Scheme for Data Collection in HWSN (REISCH) to alleviate these problems by using secure and lightweight signature algorithms. The results of the performance analysis indicate that our scheme provides high efficiency in data integration between sensors and server (saves more than 24% of alive sensors compared to traditional algorithms). Additionally, we use Automated Validation of Internet Security Protocols and Applications (AVISPA) to validate the security procedures in our scheme. Security analysis results confirm that REISCH is safe against some well-known attacks

Practical Homomorphic Encryption Over the Integers for Secure Computation in the Cloud

We present novel homomorphic encryption schemes for integer arithmetic, intended primarily for use in secure single-party computation in the cloud. These schemes are capable of securely computing arbitrary degree polynomials homomorphically. In practice, ciphertext size and running times limit the polynomial degree, but this appears sufficient for most practical applications. We present four schemes, with increasing levels of security, but increasing computational overhead. Two of the schemes provide strong security for high-entropy data. The remaining two schemes provide strong security regardless of this assumption. These four algorithms form the first two levels of a hierarchy of schemes which require linearly decreasing entropy. We have evaluated these four algorithms by computing low-degree polynomials. The timings of these computations are extremely favourable by comparison with even the best of existing methods, and dramatically out-perform running times of directly comparable schemes by a factor of up to 1000, and considerably more than that for fully homomorphic schemes, used in the same context. The results clearly demonstrate the practical applicability of our schemes

LPN in Cryptography:an Algorithmic Study

The security of public-key cryptography relies on well-studied hard problems, problems for which we do not have efficient algorithms. Factorization and discrete logarithm are the two most known and used hard problems. Unfortunately, they can be easily solved on a quantum computer by Shor's algorithm. Also, the research area of cryptography demands for crypto-diversity which says that we should offer a range of hard problems for public-key cryptography. If one hard problem proves to be easy, we should be able to provide alternative solutions. Some of the candidates for post-quantum hard problems, i.e. problems which are believed to be hard even on a quantum computer, are the Learning Parity with Noise (LPN), the Learning with Errors (LWE) and the Shortest Vector Problem (SVP). A thorough study of these problems is needed in order to assess their hardness. In this thesis we focus on the algorithmic study of LPN. LPN is a hard problem that is attractive, as it is believed to be post-quantum resistant and suitable for lightweight devices. In practice, it has been employed in several encryption schemes and authentication protocols. At the beginning of this thesis, we take a look at the existing LPN solving algorithms. We provide the theoretical analysis that assesses their complexity. We compare the theoretical results with practice by implementing these algorithms. We study the efficiency of all LPN solving algorithms which allow us to provide secure parameters that can be used in practice. We push further the state of the art by improving the existing algorithms with the help of two new frameworks. In the first framework, we split an LPN solving algorithm into atomic steps. We study their complexity, how they impact the other steps and we construct an algorithm that optimises their use. Given an LPN instance that is characterized by the noise level and the secret size, our algorithm provides the steps to follow in order to solve the instance with optimal complexity. In this way, we can assess if an LPN instance provides the security we require and we show what are the secure instances for the applications that rely on LPN. The second framework handles problems that can be decomposed into steps of equal complexity. Here, we assume that we have an adversary that has access to a finite or infinite number of instances of the same problem. The goal of the adversary is to succeed in just one instance as soon as possible. Our framework provides the strategy that achieves this. We characterize an LPN solving algorithm in this framework and show that we can improve its complexity in the scenario where the adversary is restricted. We show that other problems, like password guessing, can be modeled in the same framework

Cryptanalysis of a homomorphic encryption scheme from ISIT 2008

International audienceAt ISIT 2008, Aguilar Melchor, Castagnos and Gaborit presented a lattice-based homomorphic encryption scheme (abbreviated as MCG). Its security is based on the Computational Knapsack Vector Problem. In this paper, we explore a secret linear relationship between the public keys and the secret keys, which can be used to construct a reduced-dimension lattice, and then we obtain a group of equivalent private keys by solving the Closest Vector Problem of the lattice. Moreover, our attack is practical on all the three settings of recommended parameters, and the running time to recover the equivalent private keys is only several hours on a single PC