Let p be a prime and a be any fixed positive integer such that gcd(a, Phi(p)) = 1. For 0 < x < p, define G(x) = #{m is an element of Z(& lowast;) p : | m-(m(a) mod p ) | < x }, where m(a) mod p is the least nonnegative residue of ma modulo p. We prove that G(x) = 2x-x (2) p(-1) + O ( p(1/2 )log(2) p) . This distribution result has an immediate cryptographic consequence. For RSA having public key (N , e) with small exponent e (such as 3 or 65537), we show that there exist at least Omega(N(3/4 )log(3) N) special plaintext-ciphertext pairs from which N can be factored in time O(log(12)N).
Calderini, Longo, Sala and Villa (Journal of Mathematical Cryptology 2024) proposed a public key encryption with keyword search (PKES) scheme which we call the CLSV scheme. They claim that the scheme provides Ciphertext-Indistinguishability (CI) security where no keyword information is leaked from ciphertexts. In this paper, we demonstrate a concrete attack that obtains keyword information from ciphertexts. We point out that a ciphertext of the CLSV scheme is an ElGamal ciphertext, which is malleable. By employing the malleability, we propose a ciphertext-trapdoor conversion algorithm that allows an CI adversary to generate a trapdoor for the challenge keyword without using the receiver’s secret key. We note that our attack follows a security model called full CI security, i.e., the attack needs an active adversary, and lies outside CI security considered in the CLSV paper. Thus, we do not claim to break the CLSV scheme. Due to this situation, we evaluate the validity of our attack model in light of the design objectives of the CLSV scheme. We also analyze the attack complexity, and show that our attack completes about 100 ms.
Ciphertext-Policy Attribute-Based Encryption (CP-ABE) is a cornerstone technique for fine-grained access control in encrypted data sharing, with pairing-based schemes having established the de facto standard. However, their vulnerability to quantum attacks generated growing interest in alternatives rooted in quantum-secure primitives, with Learning With Errors (LWE) emerging as a prominent candidate. In this work, we present the first direct performance benchmark of lattice-versus pairings-based CP-ABE implementations. We compare two mature, widely adopted implementations - PALISADE-ABE's LWE-based Zhang-Zhang scheme and OpenABE's pairing-based Waters scheme - selected for their comparable development environments and assumptions. Our results highlight the practical trade-offs - both costs and benefits - of each paradigm, quantifying where lattice-based designs offer advantages and where they incur extra overhead. This comparison addresses a critical gap in the literature and provides direction for the design of future post-quantum secure systems.
This work analyzes the probability of collisions in Merkle graphs, with a focus on a specific class of attacks in balanced Merkle trees. To provide a tractable model, each hash function is modeled as an independent random oracle with finite input space. We provided a general methodology for computing collision probabilities in arbitrary Merkle graphs, when an arbitrary amount of leaves is modified. The main finding of this study is the fact that an attack carried out modifying multiple leaves is not necessarily more powerful than the one carried out modifying only one leaf. Specifically, the collision probability depends on the height of the attacked Merkle tree, increasing for higher trees, and on the position of the modified nodes in the tree.
Integer sequences play a pivotal role in cryptography, acting as foundational elements for numerous cryptographic algorithms. This comprehensive investigation examines integer sequences that have significantly impacted the sector in domains such as key generation, hash function design, and encryption protocol development, including their specific implementations. We conduct an unprecedented systematic review of existing literature, analysing fundamental properties of these sequences and detailing their contributions to well-established cryptographic areas. In addition, the research emphasises the various strengths and limitations associated with these sequences, as well as their practical applications in the realm of digital information security. This is accomplished by developing a categorisation framework that facilitates mapping of their contributions. Furthermore, this framework can be used as a reference point for future analyses in this field. In conclusion, this research underscores the potential for further discovery and innovative applications of integer sequences in the cryptographic field.
