Commutative Matrix-based Diffie-Hellman-Like Key-Exchange Protocol

2013 ◽  
pp. 317-324 ◽  
Author(s):  
Alexander G. Chefranov ◽  
Ahmed Y. Mahmoud
Keyword(s):  
Key Exchange ◽  
Key Exchange Protocol ◽  
Diffie Hellman ◽  
Commutative Matrix

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.

A Faster Software Implementation of the Supersingular Isogeny Diffie-Hellman Key Exchange Protocol

2018 ◽  
Vol 67 (11) ◽  
pp. 1622-1636 ◽  
Author(s):  
Armando Faz-Hernandez ◽  
Julio Lopez ◽  
Eduardo Ochoa-Jimenez ◽  
Francisco Rodriguez-Henriquez
Keyword(s):  
Key Exchange ◽  
Software Implementation ◽  
Key Exchange Protocol ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange

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.

scholarly journals Extended supersingular isogeny Diffie–Hellman key exchange protocol: Revenge of the SIDH

2021 ◽  
Author(s):  
Daniel Cervantes‐Vázquez ◽  
Eduardo Ochoa‐Jiménez ◽  
Francisco Rodríguez‐Henríquez
Keyword(s):  
Key Exchange ◽  
Key Exchange Protocol ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange
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