Practical Public Key Cryptosystem Research Articles

An alternative practical public-key cryptosystems based on the Dependent RSA Discrete Logarithm Problems

In this paper, an alternative public-key cryptosystems (PKCs) are proposed based on the new algebraic problems namely “Dependent RSA Discrete Logarithm Problems” derived from the RSA and Discrete Logarithm (DLog) assumptions together. These PKCs are provably secure for the notions of security: indistinguishable encryptions under chosen-plaintext attacks (IND-CPA), and adaptive chosen-ciphertext attacks (IND-CCA2). Initially, a new algebraic “Computational-Dependent RSA Discrete Logarithm Problem” is presented. Then, its variant named “Decisional-Dependent RSA Discrete Logarithm Problem” is presented. Thereafter, a specific discussion has been done about their hardness and their relations to each other. Also, some arguments are given to validate the cryptographic purpose of these problems. Next, using this decisional variant an efficient PKC: “Dependent RSA Discrete Logarithm” (DRDL) cryptosystem that has indistinguishable encryptions under chosen-plaintext attacks, in the standard model is presented. Further, a PKC variant: DRDL-1 cryptosystem with improved security properties that has indistinguishable encryptions under adaptive chosen-ciphertext attacks using this decisional variant in the random oracle model, with a low computational cost is presented. These new algebraic problems constructed by using the apparent hardness of RSA and Discrete Logarithm (DLog) problems are helpful in combining both efficiency and security. Hence, it becomes more efficient than all the cryptosystems specially designed for the ElGamal cryptosystem to make it indistinguishable encryptions under adaptive chosen-ciphertext attacks.

Design and Implementation of a Low-Latency Modular Multiplication Algorithm

Modular multiplication is one of the most compute-intensive arithmetic operations. Most public-key cryptosystems utilize modular multiplication of integers of various lengths, depending on security requirements. Efficient algorithms and implementations are required to realize a practical public-key cryptosystem. Different parameters, such as area, power and time, can be optimized for different implementation requirements. Low latency was not as important as high throughput requirement for modular multiplication implementations before. However, with recent work on Verifiable Delay Functions (VDFs), a necessity for the lowest possible latency for modular multiplication implementations emerged. VDFs are designed to take a prescribed time to realize the underlying computation that can be publicly verified. VDF constructions utilize inherently sequential arithmetic operations. Efficient VDF constructions have been proposed recently, based on time-lock puzzles constructed by Rivest, Shamir, and Wagner. An exponentiation operation in an RSA group needs to be realized for these VDF constructions. In this paper, a modular multiplication algorithm suitable for low-latency circuit implementations is proposed and an FPGA-optimized variant of this algorithm is presented.

Practical $$\mathsf {MP} \text{- }\mathsf {LWE} $$-based encryption balancing security-risk versus efficiency

Middle-product learning with errors ( $$\mathsf {MP} \text{- }\mathsf {LWE} $$ ) is a variant of the $$\mathsf {LWE}$$ problem introduced at CRYPTO 2017 by Rosca et al. (Advances in cryptology—CRYPTO, Springer, Berlin, 2017). Asymptotically, the theoretical results of Rosca et al. (2017) suggest that $$\mathsf {MP} \text{- }\mathsf {LWE} $$ gives lattice-based public-key cryptosystems offering a ‘security-risk vs. efficiency’ trade-off: higher performance than cryptosystems based on unstructured lattices ( $$\mathsf {LWE}$$ problem) and lower risk than cryptosystems based on structured lattices (Polynomial/Ring $$\mathsf {LWE}$$ problem). However, although promising in theory, Rosca et al. (2017) left the practical implications of $$\mathsf {MP} \text{- }\mathsf {LWE} $$ for lattice-based cryptography unclear. In this paper, we show how to build practical public-key cryptosystems with strong security guarantees based on $$\mathsf {MP} \text{- }\mathsf {LWE} $$ . On the implementation side, we present optimised fast algorithms for computing the middle-product operation over polynomial rings $${\mathbb {Z}}_q[x]$$ , the dominant computation for $$\mathsf {MP} \text{- }\mathsf {LWE} $$ -based cryptosystems. On the security side, we show how to obtain a nearly tight security proof for $$\mathsf {MP} \text{- }\mathsf {LWE} $$ from the hardest Polynomial LWE problem over a large family of rings, improving on the loose reduction of Rosca et al. (2017). We also show and analyze an optimised cryptanalysis of $$\mathsf {MP} \text{- }\mathsf {LWE} $$ that narrows the complexity gap between best known attacks on $$\mathsf {MP} \text{- }\mathsf {LWE} $$ and Polynomial $$\mathsf {LWE}$$ . To evaluate the practicality of $$\mathsf {MP} \text{- }\mathsf {LWE} $$ , we apply our results to construct, implement and optimise parameters for a practical $$\mathsf {MP} \text{- }\mathsf {LWE} $$ -based public-key cryptosystem, $$\mathsf {Titanium} $$ , and compare its benchmarks to other lattice-based systems. Our results show that $$\mathsf {MP} \text{- }\mathsf {LWE} $$ offers a new ‘security-risk vs. efficiency’ trade-off in lattice-based cryptography in practice, not only asymptotically in theory.

An efficient and practical public key cryptosystem with CCA-security on standard model

Chosen Ciphertext Attack (CCA) security on the standard model is widely accepted as the standard security notion for the public key cryptosystem. The existing CCA-secure public key cryptosystems on the standard model are expensive in terms of efficiency and practicality. In this paper, an efficient and practical public key cryptosystem is presented over the group of signed quadratic residues. It is provably secure against CCA on the standard model. Furthermore, public verifiability for this scheme is also realized in the way that projects the verification privacy key into public key on trapdoor pretending. It will be useful to devise efficient CCA-secure threshold and proxy re-encryption schemes on the standard model.

A Novel Combinatorial Public Key Cryptosystem

Combinatorial problems serve as an important resource for developing practical public key cryptosystems and several combinatorial cryptosystems have been proposed in the cryptographic community. In this paper, a combinatorial public key cryptosystem is proposed. The security of the proposed cryptosystem is dependent on a combinatorial problem involving matrices. The system features fast encryption and decryption. However, the system also suffers from some drawbacks. The ciphertext expansion is relatively large and the key sizes are somewhat larger than that of RSA. The security of the system is carefully examined by illustrating the computational infeasibilities of some attacks on the system.

Length-based cryptanalysis: the case of Thompson's group

The length-based approach is a heuristic for solving randomly generated equations in groups which possess a reasonably behaved length function. We describe several improvements of the previously suggested length-based algorithms, that make them applicable to Thompson's group with significant success rates. In particular, this shows that the Shpilrain-Ushakov public key cryptosystem based on Thompson's group is insecure, and suggests that no practical public key cryptosystem based on this group can be secure.

Towards Practical Non-interactive Public Key Cryptosystems Using Non-maximal Imaginary Quadratic Orders

We present a new non-interactive public-key distribution system based on the class group of a non-maximal imaginary quadratic order Cl( Δp). The main advantage of our system over earlier proposals based on (Z}/nZ)* [25,27] is that embedding id information into group elements in a cyclic subgroup of the class group is easy (straight-forward embedding into prime ideals suffices) and secure, since the entire class group is cyclic with very high probability. Computational results demonstrate that a key generation center (KGC) with modest computational resources can set up a key distribution system using reasonably secure public system parameters. In order to compute discrete logarithms in the class group, the KGC needs to know the prime factorization of ΔpeΔ1 p2. We present an algorithm for computing discrete logarithms in Cl(Δp) by reducing the problem to computing discrete logarithms in Cl(Δ1) and either F*p or F*p2. Our algorithm is a specific case of the more general algorithm used in the setting of ray class groups [5]. We prove—for arbitrary non-maximal orders—that this reduction to discrete logarithms in the maximal order and a small number of finite fields has polynomial complexity if the factorization of the conductor is known.

Discrete Logarithms: The Past and the Future

The first practical public key cryptosystem to be published, the Diffie–Hellman key exchange algorithm, was based on the assumption that discrete logarithms are hard to compute. This intractability hypothesis is also the foundation for the presumed security of a variety of other public key schemes. While there have been substantial advances in discrete log algorithms in the last two decades, in general the discrete log still appears to be hard, especially for some groups, such as those from elliptic curves. Unfortunately no proofs of hardness are available in this area, so it is necessary to rely on experience and intuition in judging what parameters to use for cryptosystems. This paper presents a brief survey of the current state of the art in discrete logs.