Sustainability of Public Key Cryptosystem in Quantum Computing Paradigm

2018 ◽  
pp. 563-588
Author(s):  
Krishna Asawa ◽  
Akanksha Bhardwaj
Keyword(s):  
Quantum Computing ◽  
Secure Communication ◽  
Prime Numbers ◽  
Cryptographic Protocols ◽  
Public Key ◽  
Quantum Computers ◽  
New Paradigm ◽  
Public Key Cryptosystems ◽  
Computing Paradigm ◽  
Diffie Hellman

With the emergence of technological revolution to host services over Internet, secure communication over World Wide Web becomes critical. Cryptographic protocols are being in practice to secure the data transmission over network. Researchers use complex mathematical problem, number theory, prime numbers etc. to develop such cryptographic protocols. RSA and Diffie Hellman public key crypto systems have proven to be secure due to the difficulty of factoring the product of two large primes or computing discrete logarithms respectively. With the advent of quantum computers a new paradigm shift on public key cryptography may be on horizon. Since superposition of the qubits and entanglement behavior exhibited by quantum computers could hold the potential to render most modern encryption useless. The aim of this chapter is to analyze the implications of quantum computing power on current public key cryptosystems and to show how these cryptosystems can be restructured to sustain in the new computing paradigm.

Sustainability of Public Key Cryptosystem in Quantum Computing Paradigm

2016 ◽  
pp. 664-688
Author(s):  
Krishna Asawa ◽  
Akanksha Bhardwaj
Keyword(s):  
Quantum Computing ◽  
Secure Communication ◽  
Prime Numbers ◽  
Cryptographic Protocols ◽  
Public Key ◽  
Quantum Computers ◽  
New Paradigm ◽  
Public Key Cryptosystems ◽  
Computing Paradigm ◽  
Diffie Hellman

With the emergence of technological revolution to host services over Internet, secure communication over World Wide Web becomes critical. Cryptographic protocols are being in practice to secure the data transmission over network. Researchers use complex mathematical problem, number theory, prime numbers etc. to develop such cryptographic protocols. RSA and Diffie Hellman public key crypto systems have proven to be secure due to the difficulty of factoring the product of two large primes or computing discrete logarithms respectively. With the advent of quantum computers a new paradigm shift on public key cryptography may be on horizon. Since superposition of the qubits and entanglement behavior exhibited by quantum computers could hold the potential to render most modern encryption useless. The aim of this chapter is to analyze the implications of quantum computing power on current public key cryptosystems and to show how these cryptosystems can be restructured to sustain in the new computing paradigm.

Hierarchical Certificate-Based Encryption: Definition and an Efficient Construction

2014 ◽  
Vol 513-517 ◽  
pp. 1971-1974 ◽  
Author(s):  
Hai Lin Xu ◽  
Yang Lu
Keyword(s):  
Random Oracle Model ◽  
Random Oracle ◽  
Public Key ◽  
New Paradigm ◽  
Public Key Cryptosystems ◽  
Identity Based Encryption ◽  
Diffie Hellman ◽  
Efficient Construction ◽  
Identity Based ◽  
Definition Of

Certificate-based encryption is a new paradigm which was introduced by Gentry to address the complex public key revocation problem in traditional public key cryptosystems. It represents an interesting and potentially useful balance between traditional public-key encryption and identity-based encryption. In this paper, we introduce the notion of hierarchical certificate-based encryption that preserves the advantages of certificate-based encryption such as implicit certificate and key-escrow free while inheriting the properties of hierarchical identity-based encryption. We formalize the definition of hierarchical certificate-based encryption and also propose a concrete hierarchical certificate-based encryption scheme that is chosen-ciphertext secure under the hardness of bilinear Diffie-Hellman problem in the random oracle model.

scholarly journals Improved cryptanalysis of a ElGamal Cryptosystem Based on Matrices Over Group Rings

2020 ◽  
Vol 15 (1) ◽  
pp. 266-279
Author(s):  
Atul Pandey ◽  
Indivar Gupta ◽  
Dhiraj Kumar Singh
Keyword(s):  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Public Key ◽  
Quantum Computers ◽  
Group Rings ◽  
Diffie Hellman ◽  
Algebra Approach ◽  
Elgamal Cryptosystem ◽  
Diffie Hellman Key Exchange ◽  
Equivalent Keys

AbstractElGamal cryptosystem has emerged as one of the most important construction in Public Key Cryptography (PKC) since Diffie-Hellman key exchange protocol was proposed. However, public key schemes which are based on number theoretic problems such as discrete logarithm problem (DLP) are at risk because of the evolution of quantum computers. As a result, other non-number theoretic alternatives are a dire need of entire cryptographic community.In 2016, Saba Inam and Rashid Ali proposed a ElGamal-like cryptosystem based on matrices over group rings in ‘Neural Computing & Applications’. Using linear algebra approach, Jia et al. provided a cryptanalysis for the cryptosystem in 2019 and claimed that their attack could recover all the equivalent keys. However, this is not the case and we have improved their cryptanalysis approach and derived all equivalent key pairs that can be used to totally break the ElGamal-like cryptosystem proposed by Saba and Rashid. Using the decomposition of matrices over group rings to larger size matrices over rings, we have made the cryptanalysing algorithm more practical and efficient. We have also proved that the ElGamal cryptosystem proposed by Saba and Rashid does not achieve the security of IND-CPA and IND-CCA.

scholarly journals Delegating a Product of Group Exponentiations with Application to Signature Schemes (Submission to Special NutMiC 2019 Issue of JMC)

2020 ◽  
Vol 14 (1) ◽  
pp. 438-459
Author(s):  
Giovanni Di Crescenzo ◽  
Matluba Khodjaeva ◽  
Delaram Kahrobaei ◽  
Vladimir Shpilrain
Keyword(s):  
Elliptic Curves ◽  
Digital Signature ◽  
Cryptographic Protocols ◽  
Public Key ◽  
Small Probability ◽  
Signature Schemes ◽  
Cyclic Groups ◽  
Public Key Cryptosystems ◽  
Fixed Base

AbstractMany public-key cryptosystems and, more generally, cryptographic protocols, use group exponentiations as important primitive operations. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that a computationally weaker client (i.e., capable of performing a relatively small number of modular multiplications) delegates such primitive operations to a computationally stronger server. Important requirements for such delegation protocols include privacy of the client’s input exponent and security of the client’s output, in the sense of detecting, except for very small probability, any malicious server’s attempt to convince the client of an incorrect exponentiation result. Only recently, efficient protocols for the delegation of a fixed-based exponentiation, over cyclic and RSA-type groups with certain properties, have been presented and proved to satisfy both requirements.In this paper we show that a product of many fixed-base exponentiations, over a cyclic groups with certain properties, can be privately and securely delegated by keeping the client’s online number of modular multiplications only slightly larger than in the delegation of a single exponentiation. We use this result to show the first delegations of entire cryptographic schemes: the well-known digital signature schemes by El-Gamal, Schnorr and Okamoto, over the q-order subgroup in ℤp, for p, q primes, as well as their variants based on elliptic curves. Previous efficient delegation results were limited to the delegation of single algorithms within cryptographic schemes.

scholarly journals Towards security recommendations for public-key infrastructures for production environments in the post-quantum era

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Sergey E. Yunakovsky ◽  
Maxim Kot ◽  
Nikolay Pozhar ◽  
Denis Nabokov ◽  
Mikhail Kudinov ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Public Key Cryptography ◽  
Public Key ◽  
Quantum Computers ◽  
Security Systems ◽  
Security Issues ◽  
Production Environments ◽  
Cryptographic Algorithms ◽  
Primary Focus ◽  
The Impact

AbstractQuantum computing technologies pose a significant threat to the currently employed public-key cryptography protocols. In this paper, we discuss the impact of the quantum threat on public key infrastructures (PKIs), which are used as a part of security systems for protecting production environments. We analyze security issues of existing models with a focus on requirements for a fast transition to post-quantum solutions. Although our primary focus is on the attacks with quantum computing, we also discuss some security issues that are not directly related to the used cryptographic algorithms but are essential for the overall security of the PKI. We attempt to provide a set of security recommendations regarding the PKI from the viewpoints of attacks with quantum computers.

scholarly journals Modification of Traditional RSA into Symmetric-RSA Cryptosystems

Cryptography ◽  
2020 ◽  
pp. 120-128
Author(s):  
Prerna Mohit ◽  
G. P. Biswas
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Prime Numbers ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Factorization Problem ◽  
Rsa Algorithm ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange ◽  
Rsa Cryptography

This paper addresses the modification of RSA cryptography namely Symmetric-RSA, which seem to be equally useful for different cryptographic applications such as encryption, digital signature, etc. In order to design Symmetric-RSA, two prime numbers are negotiated using Diffie-Hellman key exchange protocol followed by RSA algorithm. As the new scheme uses Diffie-Hellman and RSA algorithm, the security of the overall system depends on discrete logarithm as well as factorization problem and thus, its security is more than public-key RSA. Finally, some new cryptographic applications of the proposed modifications are described that certainly extend the applications of the existing RSA.

scholarly journals Committing to quantum resistance: a slow defence for Bitcoin against a fast quantum computing attack

2018 ◽  
Vol 5 (6) ◽  
pp. 180410 ◽  
Author(s):  
I. Stewart ◽  
D. Ilie ◽  
A. Zamyatin ◽  
S. Werner ◽  
M. F. Torshizi ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Digital Signature ◽  
Public Key Cryptography ◽  
Public Key ◽  
Quantum Computers ◽  
Signature Scheme ◽  
Integer Factorization ◽  
Digital Signature Algorithm ◽  
Mathematical Problems ◽  
Digital Signature Scheme

Quantum computers are expected to have a dramatic impact on numerous fields due to their anticipated ability to solve classes of mathematical problems much more efficiently than their classical counterparts. This particularly applies to domains involving integer factorization and discrete logarithms, such as public key cryptography. In this paper, we consider the threats a quantum-capable adversary could impose on Bitcoin, which currently uses the Elliptic Curve Digital Signature Algorithm (ECDSA) to sign transactions. We then propose a simple but slow commit–delay–reveal protocol, which allows users to securely move their funds from old (non-quantum-resistant) outputs to those adhering to a quantum-resistant digital signature scheme. The transition protocol functions even if ECDSA has already been compromised. While our scheme requires modifications to the Bitcoin protocol, these can be implemented as a soft fork.

Modification of Traditional RSA into Symmetric-RSA Cryptosystems

2017 ◽  
Vol 13 (1) ◽  
pp. 66-73
Author(s):  
Prerna Mohit ◽  
G. P. Biswas
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Prime Numbers ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Factorization Problem ◽  
Rsa Algorithm ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange ◽  
Rsa Cryptography

This paper addresses the modification of RSA cryptography namely Symmetric-RSA, which seem to be equally useful for different cryptographic applications such as encryption, digital signature, etc. In order to design Symmetric-RSA, two prime numbers are negotiated using Diffie-Hellman key exchange protocol followed by RSA algorithm. As the new scheme uses Diffie-Hellman and RSA algorithm, the security of the overall system depends on discrete logarithm as well as factorization problem and thus, its security is more than public-key RSA. Finally, some new cryptographic applications of the proposed modifications are described that certainly extend the applications of the existing RSA.

scholarly journals SPDH - A Secure Plain Diffie-Hellman Algorithm

2012 ◽  
Author(s):  
Henrik Tange ◽  
Birger Andersen
Keyword(s):  
Elliptic Curve ◽  
Secure Communication ◽  
Public Key Cryptography ◽  
Public Key ◽  
Wireless System ◽  
Eavesdropping Attack ◽  
Replay Attacks ◽  
Diffie Hellman ◽  
Man In The Middle ◽  
Shared Secret

Secure communication in a wireless system or end-to-end communication requires setup of a shared secret. This shared secret can be obtained by the use of a public key cryptography system. The most widely used algorithm to obtain a shared secret is the Diffie–Hellman algorithm. However, this algorithm suffers from the Man-in-the-Middle problem; an attacker can perform an eavesdropping attack listen to the communication between participants A and B. Other algorithms as for instance ECMQV (Elliptic Curve Menezes Qo Vanstone) can handle this problem but is far more complex and slower because the algorithm is a three-pass algorithm whereas the Diffie–Hellman algorithm is a simple two-pass algorithm. Using standard cryptographic modules as AES and HMAC the purposed algorithm, Secure Plain Diffie–Hellman Algorithm, solves the Man-in-the-Middle problem and maintain its advantage from the plain Diffie–Hellman algorithm. Also the possibilities of replay attacks are solved by use of a timestamp.

Sign in / Sign up

Export Citation Format

Share Document