Hash-based Multivariate Public Key Cryptosystems

Many efficient attacks have appeared in recent years, which have led to serious blow for the traditional multivariate public key cryptosystems. For example, the signature scheme SFLASH was broken by Dubois et al. at CRYPTO\u2707, and the Square signature (or encryption) scheme by Billet et al. at ASIACRYPTO\u2709. Most multivariate schemes known so far are insecure, except maybe the sigature schemes UOV and HFEv-. Following these new developments, it seems that the general design principle of multivariate schemes has been seriously questioned, and there is a rather pressing desire to find new trapdoor construction or mathematical tools and ideal. In this paper, we introduce the hash authentication techniques and combine with the traditional MQ-trapdoors to propose a novel hash-based multivariate public key cryptosystems. The resulting scheme, called EMC (Extended Multivariate Cryptosystem), can also be seen as a novel hash-based cryptosystems like Merkle tree signature. And it offers the double security protection for signing or encrypting. By the our analysis, we can construct the secure and efficient not only signature scheme but also encryption scheme by using the EMC scheme combined some modification methods summarized by Wolf. And thus we present two new schems: EMC signature scheme (with the Minus method ``- ) and EMC encryption scheme (with the Plus method ``+ ). In addition, we also propose a reduced scheme of the EMC signature scheme (a light-weight signature scheme). Precise complexity estimates for these schemes are provided, but their security proofs in the random oracle model are still an open problem

FPGA implementation of post-quantum DME cryptosystem

The rapid development of quantum computing constitutes a significant threat to modern Public-Key Cryptography (PKC). The use of Shor's algorithm with potential powerful quantum computers could easily break the two most widely used public key cryptosystems, namely, RSA and Elliptic Curve Cryptography (ECC), based on integer factorization and discrete logarithm problems. For this reason, Post-Quantum Cryptography (PQC) based on alternative mathematical features has become a fundamental research topic due to its resistance against quantum computers. The National Institute of Standards and Technology (NIST) has even opened a call for proposals of quantum-resistant PKC algorithms in order to standardize one or more PQC algorithms. Cryptographic systems that appear to be extremely difficult to break with large quantum computers are hash -based cryptography, lattice -based cryptography, code -based cryptography, and multivariate -quadratic cryptography. Furthermore, efficient hardware implementations are highly required for these alternative quantum -resistant cryptosystems

Group theory in cryptography

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor typographical changes. To appear in Proceedings of Groups St Andrews 2009 in Bath, U

On a new fast public key cryptosystem

This paper presents a new fast public key cryptosystem namely : a key exchange algorithm, a public key encryption algorithm and a digital signature algorithm, based on the difficulty to invert the following function : $F(x) =(a\times x)Mod(2^p)Div(2^q)$ .\\* Mod is modulo operation , Div is integer division operation , a , p and q are integers where $( p > q )$ .\\* In this paper we also evaluate the hardness of this problem by reducing it to SAT

Towards Post-Quantum Blockchain: A Review on Blockchain Cryptography Resistant to Quantum Computing Attacks

[Abstract] Blockchain and other Distributed Ledger Technologies (DLTs) have evolved significantly in the last years and their use has been suggested for numerous applications due to their ability to provide transparency, redundancy and accountability. In the case of blockchain, such characteristics are provided through public-key cryptography and hash functions. However, the fast progress of quantum computing has opened the possibility of performing attacks based on Grover's and Shor's algorithms in the near future. Such algorithms threaten both public-key cryptography and hash functions, forcing to redesign blockchains to make use of cryptosystems that withstand quantum attacks, thus creating which are known as post-quantum, quantum-proof, quantum-safe or quantum-resistant cryptosystems. For such a purpose, this article first studies current state of the art on post-quantum cryptosystems and how they can be applied to blockchains and DLTs. Moreover, the most relevant post-quantum blockchain systems are studied, as well as their main challenges. Furthermore, extensive comparisons are provided on the characteristics and performance of the most promising post-quantum public-key encryption and digital signature schemes for blockchains. Thus, this article seeks to provide a broad view and useful guidelines on post-quantum blockchain security to future blockchain researchers and developers.10.13039/501100010801-Xunta de Galicia (Grant Number: ED431G2019/01) 10.13039/501100011033-Agencia Estatal de Investigación (Grant Number: TEC2016-75067-C4-1-R and RED2018-102668-T) 10.13039/501100008530-European Regional Development FundXunta de Galicia; ED431G2019/0

Quantum Algorithms for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems

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 algorithm for solving Boolean equations to the cryptanalysis of several important cryptosystems: the stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, and the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the condition numbers of the corresponding equation systems are large. This leads to a new criterion for designing cryptosystems that can against the attack of quantum computers: their corresponding equation systems must have large condition numbers

Introduction to Post-Quantum Cryptography in Scope of NIST's Post-Quantum Competition

Tänapäeval on andmeturve paljudes valdkondades määrava tähtsusega, kuid hiljutised edusammud kvantmehhaanika valdkonnas võivad tänased interneti turvaprotokollid ohtu seada. Kuna kvantvutid on tõenäoliselt võimelised murdma meie praeguseid krüptostandardeid, tekib vajadus tugevamate krüpteerimisalgoritmide järele. Viimaste kümnendite jooksul on postkvantkrüptograafia saanud palju tähelepanu, kuid siiani pole ükski postkvantkrüptograafiline algoritm standardiseeritud ulatuslikuks kasutamiseks. Seetõttu algatati NIST programm, mille eesmärk on valida uued krüptostandardid, mis säilitaks oma turvalisuse ka kvantarvutite vastu. Käesolev lõputöö annab ülevaate postkvantkrüptograafia erinevatest valdkondadest - võrepõhine, koodipõhine, räsipõhine ja mitmemuutujaline krüptograafia - kasutades näiteid NIST standardiseerimisprogrammist. Lõputöö eesmärk on koostada ülevaatlik materjal, mis annaks informaatika või matemaatika taustaga tudengile laiahaardelised algteadmised postkvantkrüptograafia valdkonnast.Nowadays, information security is essential in many fields, ranging from medicine and science to law enforcement and business, but the developments in the area of quantum computing have put the security of current internet protocols at risk. Since quantum computers will likely be able to break most of our current cryptostandards in trivial time, a need for stronger and quantum-resistant encryption algorithms has arisen. During the last decades, a lot of research has been conducted on the topic of quantum-resistant cryptography, yet none of the post-quantum algorithms have yet been standardized. This has encouraged NIST to start a program to select the future post-quantum cryptography standards. This thesis gives an overview of different types of quantum-resistant algorithms, such as lattice-, code-, hash- and multivariate polynomial based algorithms, for public key encryption and signature schemes, using the examples from NIST’s postquantum cryptography standardization program. The aim of this paper is to compose a compact material, which gives a person with computer science background a basic understanding of the main aspects of post-quantum cryptography