No Arabic abstract
Many commonly used public key cryptosystems will become insecure once a scalable quantum computer is built. New cryptographic schemes that can guarantee protection against attacks with quantum computers, so-called post-quantum algorithms, have emerged in recent decades. One of the most promising candidates for a post-quantum signature scheme is SPHINCS$^+$, which is based on cryptographic hash functions. In this contribution, we analyze the use of the new Russian standardized hash function, known as Streebog, for the implementation of the SPHINCS$^+$ signature scheme. We provide a performance comparison with SHA-256-based instantiation and give benchmarks for various sets of parameters.
In the $left( {t,n} right)$ threshold quantum secret sharing scheme, it is difficult to ensure that internal participants are honest. In this paper, a verifiable $left( {t,n} right)$ threshold quantum secret sharing scheme is designed combined with classical secret sharing scheme. First of all, the distributor uses the asymmetric binary polynomials to generate the shares and sends them to each participant. Secondly, the distributor sends the initial quantum state with the secret to the first participant, and each participant performs unitary operation that using the mutually unbiased bases on the obtained $d$ dimension single bit quantum state ($d$ is a large odd prime number). In this process, distributor can randomly check the participants, and find out the internal fraudsters by unitary inverse operation gradually upward. Then the secret is reconstructed after all other participants simultaneously public transmission. Security analysis show that this scheme can resist both external and internal attacks.
Cryptographic hash functions from expander graphs were proposed by Charles, Goren, and Lauter in [CGL] based on the hardness of finding paths in the graph. In this paper, we propose a new candidate for a hash function based on the hardness of finding paths in the graph of Markoff triples modulo p. These graphs have been studied extensively in number theory and various other fields, and yet finding paths in the graphs remains difficult. We discuss the hardness of finding paths between points, based on the structure of the Markoff graphs. We investigate several possible avenues for attack and estimate their running time to be greater than O(p). In particular, we analyze a recent groundbreaking proof in [BGS1] that such graphs are connected and discuss how this proof gives an algorithm for finding paths
Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that allow for that reduction. Hash functions which are additive or multiplicative are vulnerable to a quantum attack using the hidden subgroup problem algorithm for quantum computers. Using a quantum oracle to the hash, we can reconstruct the kernel of the hash function, which is enough to find collisions and second preimages. When the hash functions are additive with respect to the group operation in an Abelian group, there is always an efficient implementation of this attack. We present concrete attack examples to provable hash functions, including a preimage attack to $oplus$-linear hash functions and for certain multiplicative homomorphic hash schemes.
This paper proposes a new signature scheme based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli, IFP) and the discrete logarithm problem(DLP). By combining these two cryptographic assumptions, we introduce an efficient and strongly secure signature scheme. We show that if an adversary can break the new scheme with an algorithm $mathcal{A},$ then $mathcal{A}$ can be used to sove both the DLP and the IFP. The key generation is a simple operation based on the discrete logarithm modulo a composite moduli. The signature phase is based both on the cube root computation and the DLP. These operations are computationally efficient.
To examine the integrity and authenticity of an IP address efficiently and economically, this paper proposes a new non-Merkle-Damgard structural (non-MDS) hash function called JUNA that is based on a multivariate permutation problem and an anomalous subset product problem to which no subexponential time solutions are found so far. JUNA includes an initialization algorithm and a compression algorithm, and converts a short message of n bits which is regarded as only one block into a digest of m bits, where 80 <= m <= 232 and 80 <= m <= n <= 4096. The analysis and proof show that the new hash is one-way, weakly collision-free, and strongly collision-free, and its security against existent attacks such as birthday attack and meet-in-the- middle attack is to O(2 ^ m). Moreover, a detailed proof that the new hash function is resistant to the birthday attack is given. Compared with the Chaum-Heijst-Pfitzmann hash based on a discrete logarithm problem, the new hash is lightweight, and thus it opens a door to convenience for utilization of lightweight digital signing schemes.