Quadratic compact knapsack public-key cryptosystem

AbstractKnapsack-type cryptosystems were among the first public-key cryptographic schemes to be invented. Their NP-completeness nature and the high speed in encryption/decryption made them very attractive. However, these cryptosystems were shown to be vulnerable to the low-density subset-sum attacks or some key-recovery attacks. In this paper, additive knapsack-type public-key cryptography is reconsidered. We propose a knapsack-type public-key cryptosystem by introducing an easy quadratic compact knapsack problem. The system uses the Chinese remainder theorem to disguise the easy knapsack sequence. The encryption function of the system is nonlinear about the message vector. Under the relinearization attack model, the system enjoys a high density. We show that the knapsack cryptosystem is secure against the low-density subset-sum attacks by observing that the underlying compact knapsack problem has exponentially many solutions. It is shown that the proposed cryptosystem is also secure against some brute-force attacks and some known key-recovery attacks including the simultaneous Diophantine approximation attack and the orthogonal lattice attack

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

Design and Application of Offset-Free Model Predictive Control Disturbance Observation Method

Model predictive control (MPC) with its lower request to the mathematical model, excellent control performance, and convenience online calculation has developed into a very important subdiscipline with rich theory foundation and practical application. However, unmeasurable disturbance is widespread in industrial processes, which is difficult to deal with directly at present. In most of the implemented MPC strategies, the method of incorporating a constant output disturbance into the process model is introduced to solve this problem, but it fails to achieve offset-free control once the unmeasured disturbances access the process. Based on the Kalman filter theory, the problem is solved by using a more general disturbance model which is superior to the constant output disturbance model. This paper presents the necessary conditions for offset-free model predictive control based on the model. By applying disturbance model, the unmeasurable disturbance vectors are augmented as the states of control system, and the Kalman filer is used to estimate unmeasurable disturbance and its effect on the output. Then, the dynamic matrix control (DMC) algorithm is improved by utilizing the feed-forward compensation control strategy with the disturbance estimated

Energy-efficient secure outsourcing decryption of attribute based encryption for mobile device in cloud computation

This is a copy of the author 's final draft version of an article published in the "Journal of ambient intelligence and humanized computing". The final publication is available at Springer via http://dx.doi.org/10.1007/s12652-017-0658-2In this paper two new ways for efficient secure outsourcing the decryption of key-policy attribute-based encryption (KP-ABE) with energy efficiency are proposed. Based on an observation about the permutation property of the access structure for the attribute based encryption schemes, we propose a high efficient way for outsourcing the decryption of KP-ABE, which is suitable for being used in mobile devices. But it can only be used for the ABE schemes having tree-like access structure for the self-enclosed system. The second way is motivated from the fact that almost all the previous work on outsourcing the decryption of KP-ABE cares little about the ciphertext length. Almost all the previous schemes for secure outsourcing the decryption of ABE have linear length ciphertext with the attributes or the policy. But transferring so long ciphertexts via wireless network for mobile phone can easily run out of battery power, therefore it can not be adapted to practical application scenarios. Thus another new scheme for outsourcing the decryption of ABE but with constant-size ciphertexts is proposed. Furthermore, our second proposal gives a new efficient way for secure outsourcing the decryptor’s secret key to the cloud, which need only one modular exponentiation while all the previous schemes need many. We evaluate the efficiency of our proposals and the results show that our proposals are practical.Peer ReviewedPostprint (author's final draft

SAT-aided Automatic Search of Boomerang Distinguishers for ARX Ciphers (Long Paper)

In Addition-Rotation-Xor (ARX) ciphers, the large domain size obstructs the application of the boomerang connectivity table. In this paper, we explore the problem of computing this table for a modular addition and the automatic search of boomerang characteristics for ARX ciphers. We provide dynamic programming algorithms to efficiently compute this table and its variants. These algorithms are the most efficient up to now. For the boomerang connectivity table, the execution time is $4^2(n − 1)$ simple operations while the previous algorithm costs $8^2(n − 1)$ simple operations, which generates a smaller model in the searching phase. After rewriting these algorithms with boolean expressions, we construct the corresponding Boolean Satisfiability Problem models. Two automatic search frameworks are also proposed based on these models. This is the first time bringing the SAT-aided automatic search techniques into finding boomerang attacks on ARX ciphers. Finally, under these frameworks, we find out the first verifiable 10-round boomerang trail for SPECK32/64 with probability $2^{-29.15}$ and a 12-round trail for SPECK48/72 with probability $2^{-44.15}$. These are the best distinguishers for them so far. We also perceive that the previous boomerang attacks on LEA are constructed with an incorrect computation of the boomerang connection probability. The result is then fixed by our frameworks

Efficient Construction for Full Black-Box Accountable Authority Identity-Based Encryption

Accountable authority identity-based encryption (A-IBE), as an attractive way to guarantee the user privacy security, enables a malicious private key generator (PKG) to be traced if it generates and re-distributes a user private key. Particularly, an A-IBE scheme achieves full black-box security if it can further trace a decoder box and is secure against a malicious PKG who can access the user decryption results. In PKC\u2711, Sahai and Seyalioglu presented a generic construction for full black-box A-IBE from a primitive called dummy identity-based encryption, which is a hybrid between IBE and attribute-based encryption (ABE). However, as the complexity of ABE, their construction is inefficient and the size of private keys and ciphertexts in their instantiation is linear in the length of user identity. In this paper, we present a new efficient generic construction for full black-box A-IBE from a new primitive called token-based identity-based encryption (TB-IBE), without using ABE. We first formalize the definition and security model for TB-IBE. Subsequently, we show that a TB-IBE scheme satisfying some properties can be converted to a full black-box A-IBE scheme, which is as efficient as the underlying TB-IBE scheme in terms of computational complexity and parameter sizes. Finally, we give an instantiation with the computational complexity as O(1) and the constant size master key pair, private keys, and ciphertexts

Faster Bootstrapping of FHE over the integers with large prime message space

Bootstrapping of FHE over the integer with large message is a open problem, which is to evaluate double modulo $(c ~\text{mod}~ p )~\mod~ Q$ arithmetic homomorphically for large $Q$. In this paper, we express this double modulo reduction circuit as a arithmetic circuit of degree at most $\theta^2 \log^2\theta/2$, with $O(\theta \log^2\theta)$ multiplication gates, where $\theta= \frac{\lambda}{\log \lambda}$ and $\lambda$ is the security parameter. The complexity of decryption circuit is independent of the message space size $Q$ with a constraint $Q> \theta \log^2\theta/2$

Notes on Reusable Garbling

Garbling is a cryptographic primitive which has many applications. It is mainly used for scenes of limited authority, such as multi-party computation (MPC), attribute-based encryption (ABE), functional encryption (FE), indistinguishability obfuscation (IO), etc. Garbling schemes before 2013 are of one-time garbling. Goldwasser et al and Agrawal presented a reusable garbling scheme, which made use of a symmetric encryption scheme and an FE scheme as the components. In this paper we discuss the validity and the efficiency of reusable garbling scheme. We present the following three notes on the scheme. (1) Reusable garbling scheme does not provide new applications, and it is still a one-time garbling scheme. (2) Even reusable garbling scheme is taken as a one-time garbling scheme, sometimes it is not usable. More detailedly, it can only be used for Basic Scene 2, and cannot be used for Basic Scene 1. For example, it cannot be used for MPC. (3) Even reusable garbling scheme is taken as a one-time garbling scheme used for Basic Scene 2, there is no evidence to show that its efficiency is better than a former one-time garbling scheme

Improved Progressive BKZ with Lattice Sieving and a Two-Step Mode for Solving uSVP

The unique Shortest Vector Problem (uSVP) is one of the core hard problems in lattice-based cryptography. In NIST PQC standardization (Kyber, Dilithium), leaky-LWE-Estimator is used to estimate the hardness of LWE-based cryptosystems by reducing LWE to uSVP and considers the primal attack using Progressive BKZ (ProBKZ). ProBKZ trivially increases blocksize β and lifts the shortest vector in the final BKZ block to find the unique shortest vector in the full lattice. In this paper, we show that a ProBKZ algorithm as above (we call it a BKZ-only mode) is not the best way to solve uSVP. So we present a two-step mode to solve it, where the ProBKZ algorithm is followed by a sieving algorithm with the dimension larger than the blocksize of BKZ. While instantiating our two-step mode with the sieving algorithm Pump and Pump-and-jump BKZ (PnjBKZ) presented in G6K, which are the state-of-art sieving and BKZ implementations, we show that our algorithm is not only better than the BKZ-only mode but also better than the heuristic uSVP solving algorithm in G6K. However, a ProBKZ with the heuristic parameter selection in leaky-LWE-Estimator or the optimized parameter selection in the literature (Yoshinori Aono et al. at Asiacrypt 2016), is insufficient in optimizing the efficiency of a two-step solving algorithm. To find the best param- eters, we design a PnjBKZ simulator which allows the choice of value jump to be more than 1. Based on the newly designed simulator, we give a blocksize and jump strategy selection algorithm, which can achieve the best simulated efficiency in solving uSVP instances. Combining all the things above, we get a new lattice solving algorithm called Improved Progressive PnjBKZ (ProPnjBKZ for short). We test the efficiency of our ProPnjBKZ with the TU Darmstadt LWE Challenge. The experiment result shows that our ProPnjBKZ is 7.6∼12.9 times more efficient than the heuristic uSVP solving algorithm in G6K. Besides, we break the TU Darmstadt LWE Challenges with (n, α) ∈{(40, 0.035), (40, 0.040), (50, 0.025), (55, 0.020), (90, 0.005)}. Finally, we give a newly refined security estimator of LWE. The evaluation results indicate that the concrete hardness of the lattice-based NIST candidate schemes from LWE primal attack will decrease by 1.9∼4.2 bits when using our optimized blocksize and jump selection strategy and two-step solving mode. In addition, when using the list-decoding technology proposed by MATZOV in 2022, it further decreased by 8∼10.7 bits

Quantum Rotational Cryptanalysis for Preimage Recovery of Round-Reduced Keccak

This paper considers the capability of 4-round Keccak-224/256/384/512 against the cryptanlysis involved by the quantum algorithm. In order to effectively find the corresponding rotational number for the rotational counterpart of preimage, we first establish a probabilistic algorithm based on the Grover search to guess a possible rotational number by using the fixed relations of bits pairs in some coordinates. This is committed to achieving that each iteration of searching the rotational counterparts contains only one run of 4-round Keccak variant applied for the verification, which can reduce the attack complexity in the quantum setting. Based on finding the rotational number under an acceptable randomness, we construct two attack models to focus on the recovery of preimage. In the first model, the Grover’s algorithm serves as finding out a rotational counterpart of the preimage. Through 64 attempts of checking the correct rotational number, the desired preimage can be obtained. In the second model, we abstract the finding of rotational counterparts into searching vertexes on a hypercube, and then, the SKW quantum algorithm is used to deal with the finding of the vertexes acted as rotational counterparts. Compared to the recent works in classical setting, we greatly reduce the attack complexity of preimage recovery. Furthermore, the first attack model is superior to the generic quantum preimage attack for 4-round Keccak-224/256/384/512, and the second model has slightly lower attack effect but more practicality on the 4-round Keccak-512/384, that is, the model is exponentially easier to implement in quantum circuit than both our first attack model and the generic quantum preimage attack