Development of Cryptography since Shannon

This paper presents the development of cryptography since Shannon\u27s seminal paper ``Communication Theory of Secrecy Systems\u27\u27 in 1949

Enhanced fully homomorphic encryption scheme using modified key generation for cloud environment

Fully homomorphic encryption (FHE) is a special class of encryption that allows performing unlimited mathematical operations on encrypted data without decrypting it. There are symmetric and asymmetric FHE schemes. The symmetric schemes suffer from the semantically security property and need more performance improvements. While asymmetric schemes are semantically secure however, they pose two implicit problems. The first problem is related to the size of key and ciphertext and the second problem is the efficiency of the schemes. This study aims to reduce the execution time of the symmetric FHE scheme by enhancing the key generation algorithm using the Pick-Test method. As such, the Binary Learning with Error lattice is used to solve the key and ciphertext size problems of the asymmetric FHE scheme. The combination of enhanced symmetric and asymmetric algorithms is used to construct a multi-party protocol that allows many users to access and manipulate the data in the cloud environment. The Pick-Test method of the Sym-Key algorithm calculates the matrix inverse and determinant in one instance requires only n-1 extra multiplication for the calculation of determinant which takes 0(N3) as a total cost, while the Random method in the standard scheme takes 0(N3) to find matrix inverse and 0(N!) to calculate the determinant which results in 0(N4) as a total cost. Furthermore, the implementation results show that the proposed key generation algorithm based on the pick-test method could be used as an alternative to improve the performance of the standard FHE scheme. The secret key in the Binary-LWE FHE scheme is selected from {0,1}n to obtain a minimal key and ciphertext size, while the public key is based on learning with error problem. As a result, the secret key, public key and tensored ciphertext is enhanced from logq , 0(n2log2q) and ((n+1)n2log2q)2log q to n, (n+1)2log q and (n+1)2log q respectively. The Binary-LWE FHE scheme is a secured but noise-based scheme. Hence, the modulus switching technique is used as a noise management technique to scale down the noise from e and c to e/B and c/B respectively thus, the total cost for noise management is enhanced from 0(n3log2q) to 0(n2log q) . The Multi-party protocol is constructed to support the cloud computing on Sym-Key FHE scheme. The asymmetric Binary-LWE FHE scheme is used as a small part of the protocol to verify the access of users to any resource. Hence, the protocol combines both symmetric and asymmetric FHE schemes which have the advantages of efficiency and security. FHE is a new approach with a bright future in cloud computing

Delegating a Product of Group Exponentiations with Application to Signature Schemes

Many public-key cryptosystems and, more generally, cryptographic protocols, use group exponentiations as important primitive operations. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that a computationally weaker client (i.e., capable of performing a relatively small number of modular multiplications) delegates such primitive operations to a computationally stronger server. Important requirements for such delegation protocols include privacy of the client's input exponent and security of the client's output, in the sense of detecting, except for very small probability, any malicious server's attempt to convince the client of an incorrect exponentiation result. Only recently, ecient protocols for the delegation of a xed-based exponentiation, over cyclic and RSA-type groups with certain properties, have been presented and proved to satisfy both requirements. In this paper we show that a product of many xed-base exponentiations, over a cyclic groups with certain properties, can be privately and securely delegated by keeping the client's online number of modular multiplications only slightly larger than in the delegation of a single exponentiation. We use this result to show the rst delegations of entire cryptographic schemes: the well-known digital signature schemes by El-Gamal, Schnorr and Okamoto, over the q-order subgroup in Zp, for p; q primes, as well as their variants based on elliptic curves. Previous ecient delegation results seem limited to the delegation of single algorithms within cryptographic schemes

Types of lightweight cryptographies in current developments for resource constrained machine type communication devices: challenges and opportunities

Machine-type communication devices have become a vital part of the autonomous industrial internet of things and industry 4.0. These autonomous resource-constrained devices share sensitive data, and are primarily acquired for automation and to operate consistently in remote environments under severe conditions. The requirements to secure the sensitive data shared between these devices consist of a resilient encryption technique with affordable operational costs. Consequently, devices, data, and networks are made secure by adopting a lightweight cryptosystem that should achieve robust security with sufficient computational and communication costs and counter modern security threats. This paper offers in-depth studies on different types and techniques of hardware and software-based lightweight cryptographies for machine-type communication devices in machine-to-machine communication networks

Server-Aided Privacy-Preserving Proximity Testing

Proximity testing is at the core of many Location-Based online Services (LBS) which we use in our daily lives to order taxis, find places of interest nearby, connect with people. Currently, most such services expect a user to submit his location to them and trust the LBS not to abuse this information, and use it only to provide the service. Existing cases of such information being misused (e.g., by the LBS employees or criminals who breached its security) motivates the search for better solutions that would ensure the privacy of user data, and give users control of how their data is being used.In this thesis, we address this problem using cryptographic techniques. We propose three cryptographic protocols that allow two users to perform proximity testing (check if they are close enough to each other) with the help of two servers.In the papers 1 and 2, the servers are introduced in order to allow users not to be online at the same time: one user may submit their location to the servers and go offline, the other user coming online later and finishing proximity testing. The drastically improves the practicality of such protocols, since the mobile devices that users usually run may not always be online. We stress that the servers in these protocols merely aid the users in performing the proximity testing, and none of the servers can independently extract the user data.In the paper 3, we use the servers to offload the users\u27 computation and communication to. The servers here pre-generate correlated random data and send it to users, who can use it to perform a secure proximity testing protocol faster. Paper 3, together with the paper 2, are highly practical: they provide strong security guarantees and are suitable to be executed on resource-constrained mobile devices. In fact, the work of clients in these protocols is close to negligible as most of the work is done by servers

Communication--Computation Trade-offs in PIR

We study the computation and communication costs and their possible trade-offs in various constructions for private information retrieval (PIR), including schemes based on homomorphic encryption and the Gentry--Ramzan PIR (ICALP\u2705). We improve over the construction of SealPIR (S&P\u2718) using compression techniques and a new oblivious expansion, which reduce the communication bandwidth by 60% while preserving essentially the same computation cost. We then present MulPIR, a PIR protocol leveraging multiplicative homomorphism to implement the recursion steps in PIR. This eliminates the exponential dependence of PIR communication on the recursion depth due to the ciphertext expansion, at the cost of an increased computational cost for the server. Additionally, MulPIR outputs a regular homomorphic encryption ciphertext, which can be homomorphically post-processed. As a side result, we describe how to do conjunctive and disjunctive PIR queries. On the other end of the communication--computation spectrum, we take a closer look at Gentry--Ramzan PIR, a scheme with asymptotically optimal communication rate. Here, the bottleneck is the server\u27s computation, which we manage to reduce significantly. Our optimizations enable a tunable trade-off between communication and computation, which allows us to reduce server computation by as much as 85%, at the cost of an increased query size. We further show how to efficiently construct PIR for sparse databases. Our constructions support batched queries, as well as symmetric PIR. We implement all of our PIR constructions, and compare their communication and computation overheads with respect to each other for several application scenarios

Arbitrary Univariate Function Evaluation and Re-Encryption Protocols over Lifted-ElGamal Type Ciphertexts

Homomorphic encryption (HE) is one of the main tools in secure multiparty computation (MPC), and the (elliptic-curve) lifted-ElGamal cryptosystem is certainly the most efficient among the existing HE schemes. However, the combination of MPC with this most efficient HE has rarely appeared in the literature. This is mainly because the major known techniques for (additively) HE-based MPC are not available for this scheme due to its typical restriction that only a plaintext in a small range can be efficiently decrypted. In this paper, we resolve this problem. By our technique, a Server having a lifted-ElGamal ciphertext $[[m]]$ with unknown small plaintext $m$ can obtain a ciphertext $[[ \varphi(m) ]]$ for an arbitrary function $\varphi$ by just one-round communication with a semi-honest Client (and also two-rounds with a malicious Client) having a decryption key, where $m$ is kept secret for both parties. This property enlarges much the variations of MPC based on the most efficient lifted-ElGamal cryptosystem. As an application, we implemented MPC for exact edit distance between two encrypted strings; our experiment for strings of length $1024$ shows that the protocol takes only $45$ seconds in LAN environments and about $3$ minutes even in WAN environments. Moreover, our technique is also available with other lifted-ElGamal type HE schemes and admits different keys/schemes for the original and the resulting ciphertexts. For example, we can securely convert a level-2 (i.e., after multiplication) ciphertext for some two-level HE schemes into a level-1 (i.e., before multiplication) ciphertext, and securely apply arbitrary functions $\varphi(m)$ to encrypted plaintexts for some attribute-based HE schemes. This is the first result (even by using communication) on realizing these two functionalities

There Is Always a Way Out! Destruction-Resistant Key Management: Formal Definition and Practical Instantiation

A central advantage of deploying cryptosystems is that the security of large high-sensitive data sets can be reduced to the security of a very small key. The most popular way to manage keys is to use a $(t,n)-$threshold secret sharing scheme: a user splits her/his key into $n$ shares, distributes them among $n$ key servers, and can recover the key with the aid of any $t$ of them. However, it is vulnerable to device destruction: if all key servers and user\u27s devices break down, the key will be permanently lost. We propose a $\mathrm{\underline{D}}$estruction-$\mathrm{\underline{R}}$esistant $\mathrm{\underline{K}}$ey $\mathrm{\underline{M}}$anagement scheme, dubbed DRKM, which ensures the key availability even if destruction occurs. In DRKM, a user utilizes her/his $n^{*}$ personal identification factors (PIFs) to derive a cryptographic key but can retrieve the key using any $t^{*}$ of the $n^{*}$ PIFs. As most PIFs can be retrieved by the user $\textit{per se}$ without requiring $\textit{stateful}$ devices, destruction resistance is achieved. With the integration of a $(t,n)-$threshold secret sharing scheme, DRKM also provides $\textit{portable}$ key access for the user (with the aid of any $t$ of $n$ key servers) before destruction occurs. DRKM can be utilized to construct a destruction-resistant cryptosystem (DRC) in tandem with any backup system. We formally prove the security of DRKM, implement a DRKM prototype, and conduct a comprehensive performance evaluation to demonstrate its high efficiency. We further utilize Cramer\u27s Rule to reduce the required buffer to retrieve a key from 25 MB to 40 KB (for 256-bit security)