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 bidimensional array { Matrix } of Natural Numbers, that along with a crypto-algorithm, encrypts selected digital data.

What kind of digital keys do you offer?

We offer private cryptographic keys from 256 bits to 4096 bits, working with variable number of symbols for your coding system; depending on your needs. Also, through scientific consulting, we can help you compute a military grade reliable key-set or even a solution resistant to quantum computing threats; Let us know!

How are the keys generated?

We use the Gauss-Jacques numerical method to compute every key-set; 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?

Because the products we offer are Officially Licenced. On the other hand, we possess competitive advantage by computing the biggest crypto-key sets in the market as they surpass industry standards. So, your clients will have the best information protection there is.

Do I need something else to protect my data?

Yes. We work with a triadic model. First element, The data to be encrypted. Second, an encryption algorithm. Third and last, a pair of keys to encrypt (close) and decrypt (open) selected information. It's a symmetric crypto-system. Implement this in your project!

Do you guarantee Perfect Secrecy?

Key-size along with data-security follows a linear proportion, this is, the bigger the matrix (key) the better the encryption. To accomplish entropy, a block cipher scheme is then recommended; using one key-set for each block of information. You can also manage the private  keys in your tech-environment through Hardware Security Module (HSM).