Lattice-based Attacks Research Articles

Cryptographic primitives based on compact knapsack problem

The present paper builds upon prior research on an id scheme that utilizes a compact knapsack problem defined by a single equation. We introduce a three-move id scheme founded on a compact knapsack problem defined by an integer matrix. Through our analysis, we investigate the possible lattice-based attacks on this problem. Additionally, we present the corresponding digital signature gained through the Fiat–Shamir transform and demonstrate its security under ROM. These cryptographic primitives are potentially post quantum resistant.

On Efficient Parallel Secure Outsourcing of Modular Exponentiation to Cloud for IoT Applications

Modular exponentiation is crucial for secure data exchange in cryptography, especially for resource-constrained Internet of Things (IoT) devices. These devices often rely on third-party servers to handle computationally intensive tasks like modular exponentiation. However, existing outsourcing solutions for the RSA algorithm may have security vulnerabilities. This work identifies a critical flaw in a recent outsourcing protocol for RSA proposed by Hu et al. We demonstrate how this flaw compromises the security of the entire RSA system. Subsequently, we propose a robust solution that strengthens the RSA algorithm and mitigates the identified vulnerability. Furthermore, our solution remains resilient against existing lattice-based attacks. The proposed fix offers a more secure and efficient way for IoT devices to leverage the power of third-party servers while maintaining data integrity and confidentiality. An extensive performance evaluation confirms that our solution offers comparable efficiency while significantly enhancing security compared to existing approaches.

Ciphertext-Only Attacks Against Compact-LWE Submitted to NIST PQC Project

As a candidate of the standard of post-quantum cryptography for NIST, Liu, et al. submitted a new public-key encryption scheme Compact-LWE, whose structure is similar to LWE, but with different distribution of errors. They thought that the special error distribution would protect Compact-LWE from known lattice-based attacks. Furthermore, they recommended a set of small parameters to improve the efficiency of Compact-LWE and claimed it can offer 192-bit security. However, in this paper, the authors show that Compact-LWE is not secure under recommended parameters by presenting two ciphertext-only attacks. First, the authors show that the message can be recovered efficiently from the ciphertext. Then the authors go further to recover an equivalent private key efficiently from the public key by exploiting the special structure of Compact-LWE.

A Group-Based NTRU-Like Public-Key Cryptosystem for IoT

The Internet of things have been widely used to improve our daily life. Public-key cryptosystem plays a central role in the security of IoT. However, classic public-key cryptosystems such as RSA and ECC are not suitable for IoT because of the complicated encryption and decryption operations. NTRU is an efficient public-key cryptosystem. In this paper, we first generalize NTRU and propose a group-based NTRU-like public-key cryptosystem, namely GTRU. Then, we construct high-performance GTRU for IoT. Finally, security analysis shows that our proposed GTRU for IoT is more secure than NTRU against lattice-based attacks.

Generalizing cryptosystems based on the subset sum problem

We identify a generic construction of cryptosystems based on the subset sum problem and characterize the required homomorphic map. Using the homomorphism from the Damgard-Jurik cryptosystem, we then eliminate the need for a discrete logarithm oracle in the key generation step of the Okamoto et al. scheme to provide a practical cryptosystem based on the subset sum problem. We also analyze the security of our cryptosystem and show that with proper parameter choices, it is computationally secure against lattice-based attacks. Finally, we present a practical application of this system for RFID security and privacy.