New Directions in Multivariate Public Key Cryptography

Most public key cryptosystems used in practice are based on integer factorization or discrete logarithms (in finite fields or elliptic curves). However, these systems suffer from two potential drawbacks. First, they must use large keys to maintain security, resulting in decreased efficiency. Second, if large enough quantum computers can be built, Shor\u27s algorithm will render them completely insecure. Multivariate public key cryptosystems (MPKC) are one possible alternative. MPKC makes use of the fact that solving multivariate polynomial systems over a finite field is an NP-complete problem, for which it is not known whether there is a polynomial algorithm on quantum computers. The main goal of this work is to show how to use new mathematical structures, specifically polynomial identities from algebraic geometry, to construct new multivariate public key cryptosystems. We begin with a basic overview of MPKC and present several significant cryptosystems that have been proposed. We also examine in detail some of the most powerful attacks against MPKCs. We propose a new framework for constructing multivariate public key cryptosystems and consider several strategies for constructing polynomial identities that can be utilized by the framework. In particular, we have discovered several new families of polynomial identities. Finally, we propose our new cryptosystem and give parameters for which it is secure against known attacks on MPKCs

New directions in cryptography.

Abstract Two kinds of contemporary developments in cryp-communications over an insecure channel order to use cryptogtography are examined. Widening applications of teleprocess-raphy to insure privacy, however, it currently necessary for the ing have given rise to a need for new types of cryptographic communicating parties to share a key which is known to no systems, which minimize the need for secure key distribution one else. This is done by sending the key in advance over some channels and supply the equivalent of a written signature. This secure channel such a private courier or registered mail. A paper suggests ways to solve these currently open problems. private conversation between two people with no prior acquainIt also discusses how the theories of communication and compu-tance is a common occurrence in business, however, and it is tation are beginning to provide the tools to solve cryptographic unrealistic to expect initial business contacts to be postponed problems of long standing. long enough for keys to be transmitted by some physical means. The cost and delay imposed by this key distribution problem is a major barrier to the transfer of business communication

New directions in cryptography.

Abstract Two kinds of contemporary developments in cryp-communications over an insecure channel order to use cryptogtography are examined. Widening applications of teleprocess-raphy to insure privacy, however, it currently necessary for the ing have given rise to a need for new types of cryptographic communicating parties to share a key which is known to no systems, which minimize the need for secure key distribution one else. This is done by sending the key in advance over some channels and supply the equivalent of a written signature. This secure channel such a private courier or registered mail. A paper suggests ways to solve these currently open problems. private conversation between two people with no prior acquainIt also discusses how the theories of communication and compu-tance is a common occurrence in business, however, and it is tation are beginning to provide the tools to solve cryptographic unrealistic to expect initial business contacts to be postponed problems of long standing. long enough for keys to be transmitted by some physical means. The cost and delay imposed by this key distribution problem is a major barrier to the transfer of business communication

Quantum Communication

Quantum communication, and indeed quantum information in general, has changed the way we think about quantum physics. In 1984 and 1991, the first protocol for quantum cryptography and the first application of quantum non-locality, respectively, attracted a diverse field of researchers in theoretical and experimental physics, mathematics and computer science. Since then we have seen a fundamental shift in how we understand information when it is encoded in quantum systems. We review the current state of research and future directions in this new field of science with special emphasis on quantum key distribution and quantum networks.Comment: Submitted version, 8 pg (2 cols) 5 fig

Curves, Jacobians, and Cryptography

The main purpose of this paper is to give an overview over the theory of abelian varieties, with main focus on Jacobian varieties of curves reaching from well-known results till to latest developments and their usage in cryptography. In the first part we provide the necessary mathematical background on abelian varieties, their torsion points, Honda-Tate theory, Galois representations, with emphasis on Jacobian varieties and hyperelliptic Jacobians. In the second part we focus on applications of abelian varieties on cryptography and treating separately, elliptic curve cryptography, genus 2 and 3 cryptography, including Diffie-Hellman Key Exchange, index calculus in Picard groups, isogenies of Jacobians via correspondences and applications to discrete logarithms. Several open problems and new directions are suggested.Comment: 66 page

A comprehensive meta-analysis of cryptographic security mechanisms for cloud computing

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The concept of cloud computing offers measurable computational or information resources as a service over the Internet. The major motivation behind the cloud setup is economic benefits, because it assures the reduction in expenditure for operational and infrastructural purposes. To transform it into a reality there are some impediments and hurdles which are required to be tackled, most profound of which are security, privacy and reliability issues. As the user data is revealed to the cloud, it departs the protection-sphere of the data owner. However, this brings partly new security and privacy concerns. This work focuses on these issues related to various cloud services and deployment models by spotlighting their major challenges. While the classical cryptography is an ancient discipline, modern cryptography, which has been mostly developed in the last few decades, is the subject of study which needs to be implemented so as to ensure strong security and privacy mechanisms in today’s real-world scenarios. The technological solutions, short and long term research goals of the cloud security will be described and addressed using various classical cryptographic mechanisms as well as modern ones. This work explores the new directions in cloud computing security, while highlighting the correct selection of these fundamental technologies from cryptographic point of view

A Comprehensive Survey on the Implementations, Attacks, and Countermeasures of the Current NIST Lightweight Cryptography Standard

This survey is the first work on the current standard for lightweight cryptography, standardized in 2023. Lightweight cryptography plays a vital role in securing resource-constrained embedded systems such as deeply-embedded systems (implantable and wearable medical devices, smart fabrics, smart homes, and the like), radio frequency identification (RFID) tags, sensor networks, and privacy-constrained usage models. National Institute of Standards and Technology (NIST) initiated a standardization process for lightweight cryptography and after a relatively-long multi-year effort, eventually, in Feb. 2023, the competition ended with ASCON as the winner. This lightweight cryptographic standard will be used in deeply-embedded architectures to provide security through confidentiality and integrity/authentication (the dual of the legacy AES-GCM block cipher which is the NIST standard for symmetric key cryptography). ASCON's lightweight design utilizes a 320-bit permutation which is bit-sliced into five 64-bit register words, providing 128-bit level security. This work summarizes the different implementations of ASCON on field-programmable gate array (FPGA) and ASIC hardware platforms on the basis of area, power, throughput, energy, and efficiency overheads. The presented work also reviews various differential and side-channel analysis attacks (SCAs) performed across variants of ASCON cipher suite in terms of algebraic, cube/cube-like, forgery, fault injection, and power analysis attacks as well as the countermeasures for these attacks. We also provide our insights and visions throughout this survey to provide new future directions in different domains. This survey is the first one in its kind and a step forward towards scrutinizing the advantages and future directions of the NIST lightweight cryptography standard introduced in 2023