scholarly journals Non-Commutative Key Exchange Protocol

2021 ◽  
Author(s):  
Luis Adrián Lizama-Pérez ◽  
José Mauricio López Romero
Keyword(s):  
Discrete Logarithm ◽  
Matrix Multiplication ◽  
Key Exchange ◽  
Secret Key ◽  
Key Exchange Protocol ◽  
Promising Alternative ◽  
Private Key ◽  
Secret Communication ◽  
Perfect Forward Secrecy ◽  
Commutative Matrix

We introduce a novel key exchange protocol based on non-commutative matrix multiplication. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We claim that the unique opportunity for the eavesdropper to get the private key is by means of an exhaustive search which is equivalent to searching an unsorted database problem. Therefore, the algorithm becomes a promising candidate to be used in the quantum era to establish shared keys and achieve secret communication. Furthermore, to establish a 256-bit secret key the size of the public key only requires 256 bits while the private key occupies just 384 bits. Matrix multiplications can be done over a reduced 4-bit size modulo. Also, we show that in a generalized method, private numbers become indistinguishable and we discuss how to achieve Perfect Forward Secrecy (PFS). As a consequence, Lizama's protocol becomes a promising alternative for Internet-of-Things (IoT) computational devices in the quantum era.

scholarly journals Non-Commutative Key Exchange Protocol

2021 ◽  
Author(s):  
Luis Adrián Lizama-Pérez ◽  
José Mauricio López Romero
Keyword(s):  
Discrete Logarithm ◽  
Matrix Multiplication ◽  
Key Exchange ◽  
Security Level ◽  
Search Problem ◽  
Key Exchange Protocol ◽  
Secret Communication ◽  
Perfect Forward Secrecy ◽  
Iot Devices ◽  
Commutative Matrix

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{Z}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We claim that the unique eavesdropper's opportunity to get the secret/private key is by means of an exhaustive search which is equivalent to the unsorted database search problem. Furthermore, we show that the secret/private keys become indistinguishable to the eavesdropper. Remarkably, to achieve a 512-bit security level, the keys (public/private) are of the same size when matrix multiplication is done over a reduced 8-bit size modulo. Also, we discuss how to achieve key certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.

A key exchange protocol using matrices over group ring

2019 ◽  
Vol 12 (05) ◽  
pp. 1950075
Author(s):  
Indivar Gupta ◽  
Atul Pandey ◽  
Manish Kant Dubey
Keyword(s):  
Group Ring ◽  
Complexity Analysis ◽  
Discrete Logarithm ◽  
Key Exchange ◽  
Group Rings ◽  
Secret Key ◽  
Key Exchange Protocol ◽  
Diffie Hellman ◽  
Shared Secret ◽  
Invertible Matrices

The first published solution to key distribution problem is due to Diffie–Hellman, which allows two parties that have never communicated earlier, to jointly establish a shared secret key over an insecure channel. In this paper, we propose a new key exchange protocol in a non-commutative semigroup over group ring whose security relies on the hardness of Factorization with Discrete Logarithm Problem (FDLP). We have also provided its security and complexity analysis. We then propose a ElGamal cryptosystem based on FDLP using the group of invertible matrices over group rings.

scholarly journals LWR-Based Fully Homomorphic Encryption, Revisited

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Fucai Luo ◽  
Fuqun Wang ◽  
Kunpeng Wang ◽  
Jie Li ◽  
Kefei Chen
Keyword(s):  
Tensor Product ◽  
Gaussian Noise ◽  
Homomorphic Encryption ◽  
Matrix Multiplication ◽  
Public Key ◽  
Multiparty Computation ◽  
Secret Key ◽  
Fully Homomorphic Encryption ◽  
Private Key ◽  
Modulus Problem

Very recently, Costache and Smart proposed a fully homomorphic encryption (FHE) scheme based on the Learning with Rounding (LWR) problem, which removes the noise (typically, Gaussian noise) sampling needed in the previous lattices-based FHEs. But their scheme did not work, since the noise of homomorphic multiplication is complicated and large, which leads to failure of decryption. More specifically, they chose LWR instances as a public key and the private key therein as a secret key and then used the tensor product to implement homomorphic multiplication, which resulted in a tangly modulus problem. Recall that there are two moduli in the LWR instances, and then the moduli will tangle together due to the tensor product. Inspired by their work, we built the first workable LWR-based FHE scheme eliminating the tangly modulus problem by cleverly adopting the celebrated approximate eigenvector method proposed by Gentry et al. at Crypto 2013. Roughly speaking, we use a specific matrix multiplication to perform the homomorphic multiplication, hence no tangly modulus problem. Furthermore, we also extend the LWR-based FHE scheme to the multikey setting using the tricks used to construct LWE-based multikey FHE by Mukherjee and Wichs at Eurocrypt 2016. Our LWR-based multikey FHE construction provides an alternative to the existing multikey FHEs and can also be applied to multiparty computation with higher efficiency.

scholarly journals A Prototype Model of Virtual Authenticated Key Exchange Mechanism over Secured Channel in Ad-Hoc Environment

2020 ◽  
Vol 8 (5) ◽  
pp. 5526-5532
Keyword(s):  
Ad Hoc ◽  
Vital Role ◽  
Key Exchange ◽  
Exchange Mechanism ◽  
Prototype Model ◽  
Secret Key ◽  
Private Key ◽  
Computational Overhead ◽  
Key Exchange Protocols ◽  
Symmetric Key

Key exchange protocols play a vital role in symmetric key cryptography. The transfer of private key through the secured medium is a challenging task because every day the intruders are evolved and the attacks are increasing constantly. The existing key exchange protocols such as Diffie-Hellman, Elgamal, and MQV, etc. are the old methods and many attacks happened on those protocols. That challenges demanding new protocol or methodology of transferring secret key between the parties. The paper proposes a new, secured, less computational overhead key exchange mechanism using short message service available in the cellular networks. GSM-SMS is a highly established secured channel and the research uses this facility to transfer the key between senders to a receiver of the symmetric key cryptosystem. The private key no need to reveal to third parties or even the receiver because the sender can directly communicate to the decryption system through the mobile SMS. After the decryption process, the secret key will be destroyed immediately. There is no possible attack during the key transfer and loss and error of the communication are very less.

scholarly journals Non-invertible Public Key Certificates

2020 ◽  
Author(s):  
Luis Lizama-Pérez ◽  
J. Mauricio López
Keyword(s):  
Public Key Infrastructure ◽  
Key Exchange ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Forward Secrecy ◽  
Certification System ◽  
Perfect Forward Secrecy

Post-quantum public cryptosystems introduced so far do not define an scalable public key infrastructure for the quantum era. We demonstrate here a public certification system based in Lizama’s non-invertible Key Exchange Protocol which can be used to implement a public key infrastructure (PKI), secure, scalable, interoperable and efficient. We show functionality of certificates across different certification domains. Finally, we discuss that non-invertible certificates can exhibit Perfect Forward Secrecy (PFS).

scholarly journals Compiled Constructions towards Post-Quantum Group Key Exchange: A Design from Kyber

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1853
Author(s):  
José Ignacio Escribano Pablos ◽  
María Isabel González Vasco ◽  
Misael Enrique Marriaga ◽  
Ángel Luis Pérez del Pozo
Keyword(s):  
Random Oracle Model ◽  
Building Blocks ◽  
Random Oracle ◽  
Key Exchange ◽  
Encryption Scheme ◽  
Secret Key ◽  
Key Exchange Protocol ◽  
Group Key ◽  
Group Key Exchange ◽  
Starting Point

A group authenticated key exchange (GAKE) protocol allows a set of parties belonging to a certain designated group to agree upon a common secret key through an insecure communication network. In the last few years, many new cryptographic tools have been specifically designed to thwart attacks from adversaries which may have access to (different kinds of) quantum computation resources. However, few constructions for group key exchange have been put forward. Here, we propose a four-round GAKE which can be proven secure under widely accepted assumptions in the Quantum Random Oracle Model. Specifically, we integrate several primitives from the so-called Kyber suite of post-quantum tools in a (slightly modified) compiler from Abdalla et al. (TCC 2007). More precisely, taking as a starting point an IND-CPA encryption scheme from the Kyber portfolio, we derive, using results from Hövelmanns et al. (PKC 2020), a two-party key exchange protocol and an IND-CCA encryption scheme and prove them fit as building blocks for our compiled construction. The resulting GAKE protocol is secure under the Module-LWE assumption, and furthermore achieves authentication without the use of (expensive) post-quantum signatures.

scholarly journals Enhancement of Security of Diffie-Hellman Key Exchange Protocol using RSA Cryptography.

2022 ◽  
Vol 2161 (1) ◽  
pp. 012014
Author(s):  
Chiradeep Gupta ◽  
N V Subba Reddy
Keyword(s):  
Key Exchange ◽  
Secret Key ◽  
Key Exchange Protocol ◽  
Diffie Hellman ◽  
Shared Secret ◽  
Diffie Hellman Key Exchange ◽  
Intended Receiver ◽  
Rsa Cryptography ◽  
Shared Secret Key ◽  
Mitm Attack

Abstract Cryptography is related and referred to as the secured transmission of messages amongst the sender and the intended receiver by ensuring confidentiality, integrity, and authentication. Diffie – Hellman (DH) key exchange protocol is a well-known algorithm that would generate a shared secret key among the sender and the intended receiver, and the basis of cryptosystems for using public and private key for encryption and decryption process. But it is severely affected by the Man in the Middle (MITM) attack that would intercept and manipulate thus eavesdropping the shared secret key. This paper proposes a model of integrating the public-key RSA cryptography system with the DH key exchange to prevent the MITM attack. The performance of the proposed work has been compared to the DH Key Exchange algorithm as well as RSA Cryptosystem to conclude for effectiveness of the proposed model.

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