Post-Quantum Cryptography PQC attempts to find cryptographic protocols resistant to attacks using Shors polynomial time algorithm for numerical field problems or Grovers algorithm to find the unique input to a black-box function that produces a particular output value. The use of non-standard algebraic structures like non-commutative or non-associative structures, combined with one-way trapdoor functions derived from combinatorial group theory, are mainly unexplored choices for these new kinds of protocols and overlooked in current PQC solutions. In this paper, we develop an algebraic extension ring framework who could be applied to different asymmetric protocols, i.e. key exchange, key transport, enciphering, digital signature, zero-knowledge authentication, oblivious transfer, secret sharing etc.. A valuable feature is that there is no need for big number libraries as all arithmetic is performed in F256 extension field operations (precisely the AES field). We assume that the new framework is cryptographical secure against strong classical attacks like the sometimes-useful length-based attack, Romankovs linearization attacks and Tsabans algebraic span attack. This statement is based on the non-linear structure of the selected platform which proved to be useful protecting the AES protocol. Otherwise, it could resist post-quantum attacks Grover, Shor and be particularly useful for computational platforms with limited capabilities like USB cryptographic keys or smartcards. Semantic security IND-CCA2 could also be inferred for this new platform.
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover's search algorithm gives a square root time boost for the searching of the key in symmetric schemes like AES and 3DES. The security of asymmetric algorithms like RSA, Diffie Hellman, and ECC is based on the mathematical hardness of prime factorization and discrete logarithm. The best classical algorithms available take exponential time. Shor's factoring algorithm can solve the problems in polynomial t…
With the advent of advanced technology, IoT introduces a vast number of devices connecting with each other and collecting a sheer volume of data. Thus, the demands of IoT security is paramount. Cryptography is being used to secure the networks for authentication, confidentiality, data integrity and access control. However, due to the resource constraint nature of IoT devices, the traditional cryptographic protocols may not be suited in all IoT environments. Researchers, as a result, have been proposing various lightweight cryptographic algorithms and protocols. In this paper, we discuss the st…
Currently used digital signatures based on asymmetric cryptography will be vulnerable to quantum computers running Shor's algorithm. In this work, we propose a new quantum-assisted digital signature protocol based on symmetric keys generated by QKD, that allows signing and verifying messages in a simple way implementing an integration of currently available classical and quantum technologies. The protocol is described for a three-user scenario composed of one sender and two receivers. In contrast to previous schemes, it is independent of the message length. The security of the protocol has bee…
The planted tensor problem over finite fields: algorithms and cryptography
State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所处理器重点实验室）；School of Computer Science and Technology, University of Chinese Academy of Sciences（中国科学院大学计算机科学与技术学院）；University of Technology Sydney（悉尼科技大学）；Wuhan University（武汉大学）；Monash University（蒙纳士大学）
Circulant matrices are an important tool widely used in coding theory and cryptography. A circulant matrix is a square matrix whose rows are the cyclic shifts of the first row. Such a matrix can be efficiently stored in memory because it is fully specified by its first row. The ring of $n \times n$ circulant matrices can be identified with the quotient ring $\mathbb{F}[x]/(x^n-1)$. In consequence, the strong algebraic structure of the ring $\mathbb{F}[x]/(x^n-1)$ can be used to study properties of the collection of all $n\times n$ circulant matrices. The ring $\mathbb{F}[x]/(x^n-1)$ is a speci…
Many IoT use cases involve constrained battery-powered devices offering services in a RESTful manner to their communication partners. Such services may involve, e.g., costly computations or actuator/sensor usage, which may have significant influence on the power consumption of the service Providers. Remote attackers may excessively use those services in order to exhaust the Providers' batteries, which is a form of a Denial of Service (DoS) attack. Previous work proposed solutions based on lightweight symmetric authentication. These solutions scale poorly due to requiring pre-shared keys and do…
Hacking Cryptographic Protocols with Advanced Variational Quantum Attacks
Multiverse Computing（多元宇宙计算公司）；Tecnun - University of Navarra（纳瓦拉大学 Tecnun 学院）；Donostia International Physics Center（多诺斯蒂亚国际物理中心）；Ikerbasque Foundation for Science（伊克尔巴斯克科学基金会）
