arXiv subjects

Keita Xagawa

Publications and source records attributed to Keita Xagawa.

5 recordsLinked to original sources

arXiv2024

Secure multi-party quantum computation protocol for quantum circuits: the exploitation of triply-even quantum error-correcting codes

Secure multi-party quantum computation (MPQC) protocol is a cryptographic primitive allowing error-free distributed quantum computation to a group of $n$ mutually distrustful quantum nodes even when some quantum nodes disobey the instructions of the protocol. Here we suggest a modified MPQC protocol that adopts unconventional quantum error-correcting codes and as a consequence reduces the number of qubits required for the protocol execution. In particular, the replacement of the self-dual Calderbank-Shor-Steane quantum error-correcting codes with triply-even ones permits us to avoid the previously indispensable but resource-intensive procedure of the ``magic'' state verification. Besides, since every extra qubit reduces the credibility of physical devices, our suggestion makes the MPQC protocol more accessible for the near-future technology by reducing the number of necessary qubits per quantum node from $n^2 + Θ(r)n$, where $r$ is the security parameter, to $n^2 + 3n$.

quant-ph↗

arXiv2024

Quantum Group Actions

In quantum cryptography, there could be a new world, Microcrypt, where cryptography is possible but one-way functions (OWFs) do not exist. Although many fundamental primitives and useful applications have been found in Microcrypt, they lack ``OWFs-free'' concrete hardness assumptions on which they are based. In classical cryptography, many hardness assumptions on concrete mathematical problems have been introduced, such as the discrete logarithm (DL) problems or the decisional Diffie-Hellman (DDH) problems on concrete group structures related to finite fields or elliptic curves. They are then abstracted to generic hardness assumptions such as the DL and DDH assumptions over group actions. Finally, based on these generic assumptions, primitives and applications are constructed. The goal of the present paper is to introduce several abstracted generic hardness assumptions in Microcrypt, which could connect the concrete mathematical hardness assumptions with applications. Our assumptions are based on a quantum analogue of group actions. A group action is a tuple $(G,S,\star)$ of a group $G$, a set $S$, and an operation $\star:G\times S\to S$. We introduce a quantum analogue of group actions, which we call quantum group actions (QGAs), where $G$ is a set of unitary operators, $S$ is a set of states, and $\star$ is the application of a unitary on a state. By endowing QGAs with some reasonable hardness assumptions, we introduce a natural quantum analogue of the decisional Diffie-Hellman (DDH) assumption and pseudorandom group actions. Based on these assumptions, we construct classical-query pseudorandom function-like state generators (PRFSGs). Because classical group actions are instantiated with many concrete mathematical hardness assumptions, our QGAs could also have some concrete (even OWFs-free) instantiations.

quant-ph↗

arXiv2022

An improvement on the versatility of secure multi-party quantum computation protocol: exploitation of triorthogonal quantum error-correcting codes

Secure multi-party quantum computation (MPQC) protocol is a versatile tool that enables error-free distributed quantum computation to a group of $n$ mutually distrustful quantum nodes even when some of the quantum nodes do not follow the instructions of the protocol honestly. However, in case of the MPQC protocols built on top of the quantum error correction technique, the versatility is significantly affected by the fact that one has to choose a particular quantum error-correcting code (QECC), which immediately applies a constraint on the number of quantum nodes $n$. Therefore, in this talk, we suggest a modified MPQC protocol based on triorthogonal QECCs which applies significantly less constraint on the number of quantum nodes $n$ if compared to the previously suggested MPQC protocol based on triply-even QECCs. Especially, the variety of available options in the region of a small number of quantum nodes $n$ becomes important in the noisy intermediate-scale quantum (NISQ) era.

quant-ph↗

arXiv2019

Quantum Algorithm for the Multicollision Problem

The current paper presents a new quantum algorithm for finding multicollisions, often denoted by $\ell$-collisions, where an $\ell$-collision for a function is a set of $\ell$ distinct inputs that are mapped by the function to the same value. The tight bound of quantum query complexity for finding a $2$-collisions of a random function has been revealed to be $Θ(N^{1/3})$, where $N$ is the size of the range of the function, but neither the lower nor upper bounds are known for general $\ell$-collisions. The paper first integrates the results from existing research to derive several new observations, e.g.,~$\ell$-collisions can be generated only with $O(N^{1/2})$ quantum queries for any integer constant $\ell$. It then provides a quantum algorithm that finds an $\ell$-collision for a random function with the average quantum query complexity of $O(N^{(2^{\ell-1}-1) / (2^{\ell}-1)})$, which matches the tight bound of $Θ(N^{1/3})$ for $\ell=2$ and improves upon the known bounds, including the above simple bound of $O(N^{1/2})$. More generally, the algorithm achieves the average quantum query complexity of $O\big(c_N \cdot N^{({2^{\ell-1}-1})/({ 2^{\ell}-1})}\big)$ and runs over $\tilde{O}\big(c_N \cdot N^{({2^{\ell-1}-1})/({ 2^{\ell}-1})}\big)$ qubits in $\tilde{O}\big(c_N \cdot N^{({2^{\ell-1}-1})/({ 2^{\ell}-1})}\big)$ expected time for a random function $F\colon X\to Y$ such that $|X| \geq \ell \cdot |Y| / c_N$ for any $1\le c_N \in o(N^{{1}/({2^\ell - 1})})$. With the same complexities, it is actually able to find a multiclaw for random functions, which is harder to find than a multicollision.

quant-ph↗

arXiv2019

Improved Quantum Multicollision-Finding Algorithm

The current paper improves the number of queries of the previous quantum multi-collision finding algorithms presented by Hosoyamada et al. at Asiacrypt 2017. Let an $l$-collision be a tuple of $l$ distinct inputs that result in the same output of a target function. In cryptology, it is important to study how many queries are required to find $l$-collisions for random functions of which domains are larger than ranges. The previous algorithm finds an $l$-collision for a random function by recursively calling the algorithm for finding $(l-1)$-collisions, and it achieves the average quantum query complexity of $O(N^{(3^{l-1}-1) / (2 \cdot 3^{l-1})})$, where $N$ is the range size of target functions. The new algorithm removes the redundancy of the previous recursive algorithm so that different recursive calls can share a part of computations. The new algorithm finds an $l$-collision for random functions with the average quantum query complexity of $O(N^{(2^{l-1}-1) / (2^{l}-1)})$, which improves the previous bound for all $l\ge 3$ (the new and previous algorithms achieve the optimal bound for $l=2$). More generally, the new algorithm achieves the average quantum query complexity of $O\left(c^{3/2}_N N^{\frac{2^{l-1}-1}{ 2^{l}-1}}\right)$ for a random function $f\colon X\to Y$ such that $|X| \geq l \cdot |Y| / c_N$ for any $1\le c_N \in o(N^{\frac{1}{2^l - 1}})$. With the same query complexity, it also finds a multiclaw for random functions, which is harder to find than a multicollision.

cs.CR↗