Efficiency

Using Big 'O' notation, Gauss-Jacques Method's Computer Complexity is O(n^3 * log m). Where the logarithmic base is φ. Making it better than all previous methods for finding an 'n x n' Modular Inverse Matrix {mod m}, benefiting the Environmental, Social & Economic dimensions of Life.

[Jacques-García, Fausto & Uribe-Mejía, Daniel & Macías-Bobadilla, Gonzalo & Chaparro-Sánchez, Ricardo. (2022). On modular inverse matrices A computation approach. South Florida Journal of Development, Miami, vol.3, no.3. pp.3100-3111, 2022].

AI & Quantum Computer Attacks Resistant

First, there's no a dimensional theoretical limit for obtaining a Modular Inverse Matrix (MIM) with The Gauss-Jacques algorithm. Second, to get as many different MIM as required, Cantors' transfinite number Theory is thus extended to matrices. Third and last, if the number of symbols for certain coding system is a prime, there will be a MIM ready to be computed. Else a singular matrix could be obtained. [Fausto Abraham Jacques-García. Cryptography And Its Implications on Electronics and Devices: A Time-Complexity Algorithmical Analysis. COJ Elec Communicat. 2(3). COJEC.000538.2022. DOI: 10.31031/COJEC.2022.02.000538].

Ultimate Computing Method

Every Key-Set is computed using a Computer Algebraic System (CAS) with high level programming (functional), aiming ad-hoc implementation. [Alarcón-Narváez, D., Jacques García, F.A. (2021). Towards a Symmetric Crypto Algorithm: The HAJ. In: Latifi, S. (eds) ITNG 2021 18th International Conference on Information Technology-New Generations. Advances in Intelligent Systems and Computing, vol 1346. Springer, Cham. https://doi.org/10.1007/978-3-030-70416-2_15].

Finally, the research that was conducted to prove its reality since the beginning back then in 2015, has reported assimilation and approval by the scientific community. [F.A. Jacques-García and S.L. Canchola-Magdaleno, “Vector Cryptography System an appoach for the analysis of linear arithmetic spaces”, IEEE Transl. Las Vegas, NV, USA, pp. 522-527, April 2015. Digests 12th International Conference on Information Technology-New Generations, 2015].

World Wide Approval

FAQs

What is a Digital Key?

A cryptographic key is a matrix that helps encrypt your digital data.

What sizes do they offer?

We offer keys from 256 bits to 4096 bits, depending on your needs. Also, through scientific consulting we can compute a military grade reliable key-set or even a post-quantum key resistant; achieving Perfect Secrecy. Let us know!

How are the keys generated?

We use the Gauss-Jacques numerical method, recognized worldwide since 2018. [F.A. Jacques-García, “The proposed Gauss-Jacques method to obtain modular inverse matrices variable sized without a theoretical limit”, vol. XI, Querétaro, México: CIENCIA@UAQRO, 2018, pp. 193-203.]

Why to encrypt using this technology?

Our key-sets exceed the industry standard in digital security. Your clients will have the best information protection there is.

What are they for?

They protect information in symmetric cryptographic systems. The implementation of the digital keys is very simple, aiming that any user with a crypto-function would be able to import them in its project.

How do I manage a key-set?

Key-size along with data-security follows a linear proportion. Once you possess a pair of our digital crypto-keys, you'd be able to open any file in a text editor and see a square matrix composed by many natural numbers ready to be load to encrypt/decrypt any file. You can also distribute them in your tech-environment as needed. Hardware Security Module (HSM) is recommended.