• Corpus ID: 235294109

MOBS (Matrices Over Bit Strings) public key exchange

@article{Rahman2021MOBSO,
  title={MOBS (Matrices Over Bit Strings) public key exchange},
  author={Nael Rahman and Vladimir Shpilrain},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.01116}
}
We use matrices over bit strings as platforms for Diffie-Hellman-like public key exchange protocols. When multiplying matrices like that, we use Boolean OR operation on bit strings in place of addition and Boolean AND operation in place of multiplication. As a result, (1) computations with these matrices are very efficient; (2) standard methods of attacking Diffie-Hellman-like protocols are not applicable. 

Figures from this paper

Cryptanalysis of Semidirect Product Key Exchange Using Matrices Over Non-Commutative Rings

It is demonstrated that group rings R[G], where R is a commutative ring and G is a non-abelian group, are examples of non-commutative rings that satisfy these conditions.

On the efficiency of a general attack against the MOBS cryptosystem

Computational evidence is presented suggesting that an instance of the scheme called “MOBS (matrices over bitstrings)” is an example of a scheme where the telescoping equality has too many solutions to be a practically viable means to conduct an attack.

MAKE: A matrix action key exchange

A public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z p so standard classical attacks on Diffie–Hellman-like protocols are not applicable.

A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

This paper gives the first dedicated security analysis of a central problem in group-based cryptography: the so-called Semidirect Product Key Exchange ( SPDKE), and presents a subexponential quantum algorithm for solving SPDKE.

Semidirect Product Key Exchange: the State of Play

The various platforms proposed and an overview of the main cryptanalytic ideas relevant to each scheme are given, as well as a comparison of current and proposed schemes.

Monoidal categories, representation gap and cryptography

This work considers simple examples of monoidal categories of diagrammatic origin, including the Temperley–Lieb, the Brauer and partition categories, and discusses lower bounds for their representations.

Remarks on MOBS and cryptosystems using semidirect products

  • C. Monico
  • Mathematics, Computer Science
    IACR Cryptol. ePrint Arch.
  • 2021
This section describes the general framework encompassing several recently proposed algebraic cryptosystems, and gives a general observation which applies to them all, which will be used in the next section to give a polynomial-time attack on the proposed MOBS system.

References

SHOWING 1-10 OF 10 REFERENCES

MAKE: A matrix action key exchange

A public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z p so standard classical attacks on Diffie–Hellman-like protocols are not applicable.

Public Key Exchange Using Semidirect Product of (Semi)Groups

In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on

Key Agreement

Here, A and B are the identities of the two communicating parties, Alice and Bob. EncPKB (·) is the public key encryption algorithm with respect to Bob’s public key PKB, while EK(·) denotes a

Using Semidirect Product of (Semi)groups in Public Key Cryptography

  • Delaram KahrobaeiV. Shpilrain
  • Mathematics, Computer Science
    CiE
  • 2016
It is shown, in particular, that one can get a variety of new security assumptions by varying an automorphism used for a (semi)group extension, in terms of security and efficiency.

New directions in cryptography

This paper suggests ways to solve currently open problems in cryptography, and discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing.

Tropical Cryptography

We employ tropical algebras as platforms for several cryptographic schemes that would be vulnerable to linear algebra attacks were they based on “usual” algebras as platforms.

Tropical cryptography II: Extensions by homomorphisms

Extensions of tropical algebras are used as platforms for very efficient public key exchange protocols and show great promise in solving the challenge of efficient and scalable public key exchanges in the rapidly changing environment.

The Algebraic Eraser and Lightweight Cryptography, in: Algebraic methods in cryptography

  • Contemp. Math
  • 2006

Landau's function

    Cryptanalysis of 'MAKE', preprint