Li Yang
We present a quantum public-key cryptosystem based on a classical NP-complete problem related with finding a code word of a given weight in a linear binary code.
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It is well known that Shor's quantum algorithm for integer factorization can break down the RSA public-key cryptosystem, which is widely used in many cryptographic applications. Thus, public-key cryptosystems in the quantum computational setting are longed for cryptology. In order to define the security notions of public-key cryptosystems, we have to model the power of the sender, receiver, adversary and channel. While we may consider a setting where quantum computers are available only to adversaries, we generally discuss what are the right security notions for (quantum) public-key cryptosyst…
Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum computing indicate that many of the public key cryptosystems currently in use could easily be broken if large-scale quantum computers become technologically feasible. Further, encrypted messages captured and stored in the past could also be decrypted by a future quantum attacker. Since large-scale quantum computers may one day be developed, We need to prepar…
Inspired by Fujita's analysis [Quantum inf. & comput. 12(3&4), 2012], we suggest a twice-encryption scheme to improve the security of the original quantum McEliece public-key encryption algorithm.
In this paper, we improve Bruschweiler's algorithm such that only one query is needed for searching the single object z from N=2^n unsorted elements. Our algorithm construct the new oracle query function g(.) satisfying g(x)=0 for all input x, except for one, say x=z, where g(z)=z. To store z, our algorithm extends from one ancillary qubit to n ancillary qubits. We then measure these ancillary qubits to discover z. We further use our ensemble search algorithm to attack classical public key cryptosystems. Given the ciphertext C=Ek(m, r) which is generated by the encryption function Ek(), a publ…
A concept named induced trapdoor one-way quantum transformation (OWQT) has been introduced, and a theoretical framework of public-key encryption (PKE) of quantum message is presented based on it. Then several kinds of quantum public-key encryption (QPKE) protocols, such as quantum version PKE of RSA, ElGamal, Goldwasser-Micali, elliptic curve, McEliece, Niederreiter and Okamoto-Tanaka-Uchiyama, are given within this framework. Though all of these protocols are only computationally secure, the last three are probably secure in post-quantum era. Besides, theoretical frameworks for public-key aut…
We discuss cryptographic applications of single-qubit rotations from the perspective of trapdoor one-way functions and public-key encryption. In particular, we present an asymmetric cryptosystem whose security relies on fundamental principles of quantum physics. A quantum public key is used for the encryption of messages while decryption is possible by means of a classical private key only. The trapdoor one-way function underlying the proposed cryptosystem maps integer numbers to quantum states of a qubit and its inversion can be infeasible by virtue of the Holevo's theorem.
Public-key cryptosystems for quantum messages are considered from two aspects: public-key encryption and public-key authentication. Firstly, we propose a general construction of quantum public-key encryption scheme, and then construct an information-theoretic secure instance. Then, we propose a quantum public-key authentication scheme, which can protect the integrity of quantum messages. This scheme can both encrypt and authenticate quantum messages. It is information-theoretic secure with regard to encryption, and the success probability of tampering decreases exponentially with the security …
Quantum computers can break the RSA and El Gamal public-key cryptosystems, since they can factor integers and extract discrete logarithms. If we believe that quantum computers will someday become a reality, we would like to have \emph{post-quantum} cryptosystems which can be implemented today with classical computers, but which will remain secure even in the presence of quantum attacks. In this article we show that the McEliece cryptosystem over \emph{well-permuted, well-scrambled} linear codes resists precisely the attacks to which the RSA and El Gamal cryptosystems are vulnerable---namely, t…
Decision of whether a Boolean equation system has a solution is an NPC problem and finding a solution is NP hard. In this paper, we present a quantum algorithm to decide whether a Boolean equation system FS has a solution and compute one if FS does have solutions with any given success probability. The runtime complexity of the algorithm is polynomial in the size of FS and the condition number of FS. As a consequence, we give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are small, say polynomial in the size of FS. We apply our quantum algo…
Lectures on classical and quantum cryptography. Contents: Private key cryptosystems. Elements of number theory. Public key cryptography and RSA cryptosystem. Shannon`s entropy and mutual information. Entropic uncertainty relations. The no cloning theorem. The BB84 quantum cryptographic protocol. Security proofs. Bell`s theorem. The EPRBE quantum cryptographic protocol.
Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
本研究从NTRU密码体制的密码分析出发，提出一类兼具恒定码率、√n量级平均距离且自带高效解码器的优质随机NTRU-GKP码，揭示了GKP码对经典纠错、量子纠错与后量子密码的衔接作用，并提出基于NTRU安全性的公钥量子通信协议。
Due to Shor's algorithm, quantum computers are a severe threat for public key cryptography. This motivated the cryptographic community to search for quantum-safe solutions. On the other hand, the impact of quantum computing on secret key cryptography is much less understood. In this paper, we consider attacks where an adversary can query an oracle implementing a cryptographic primitive in a quantum superposition of different states. This model gives a lot of power to the adversary, but recent results show that it is nonetheless possible to build secure cryptosystems in it. We study application…
On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
本文将最坏情况格问题（如GapSVP和SIVP）量子归约到带误差学习问题，并提出一种基于该问题的高效公钥密码系统，显著降低了公钥和密文扩展开销。
Downtime Required for Bitcoin Quantum-Safety
本文分析了比特币为抵御量子攻击而升级到后量子密码系统的技术成本，计算出所需累计停机时间下界为1827.96小时，并强调必须尽快启动升级以保障网络安全。
Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest known classical algorithm takes exponential time, and prior to our work no faster quantum algorithm was known. Recently, public-key cryptosystems based on the presumed hardness of this problem have been proposed as candidates for post-quantum cryptography. In this paper, we give a subexponential-time quantum algorithm for constructing isogenies, assuming th…
Towards post-quantum blockchain: A review on blockchain cryptography resistant to quantum computing attacks
该综述研究后量子密码系统及其在区块链与分布式账本技术中的应用，分析代表性后量子区块链系统的挑战，对比主流后量子公钥加密和数字签名方案的特性与性能，为相关研究者和开发者提供后量子区块链安全的全面视角与指导。
The HyperFrog Cryptosystem: High-Genus Voxel Topology as a Trapdoor for Post-Quantum KEMs
HyperFrog是一种实验性后量子密钥封装机制，通过体素网格拓扑结构生成强约束的稀疏二进制秘密向量，结合拓扑挖掘算法和Fujisaki-Okamoto变换实现IND-CCA安全，探讨拓扑秘密与已知格攻击的交互及安全分析问题。
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