An integral security kernel

As the user base of the Internet has grown tremendously, the need for secure services has increased accordingly. Most secure protocols, in digital business and other fields, use a combination of symmetric and asymmetric cryptography, random generators and hash functions in order to achieve confidentiality, integrity, and authentication. Our proposal is an integral security kernel based on a powerful mathematical scheme from which all of these cryptographic facilities can be derived. The kernel requires very little resources and has the flexibility of being able to trade off speed, memory or security; therefore, it can be efficiently implemented in a wide spectrum of platforms and applications, either software, hardware or low cost devices. Additionally, the primitives are comparable in security and speed to well known standards.

Fast pseudorandom generator based on packed matrices

Pseudorandom generators are a basic foundation of many cryptographic services and information security protocols. We propose a modification of a previously published matricial pseudorandom generator that significantly improves performance and security. The resulting generator is successfully compared to world class standards.

A public key cryptosystem based on block upper triangular matrices

We propose a public key cryptosystem based on block upper triangular matrices. This system is a variant of the Discrete Logarithm Problem with elements in a finite group, capable of increasing the difficulty of the problem while maintaining the key size. We also propose a key exchange protocol that guarantees that both parties share a secret element of this group and a digital signature scheme that provides data authenticity and integrity.

An optimized pseudorandom generator using packed matrices

Most cryptographic services and information security protocols require a dependable source of random data; pseudorandom generators are convenient and efficient for this application working as one of the basic foundation blocks on which to build the required security infrastructure. We propose a modification of a previously published matricial pseudorandom generator that significantly improves performance and security by using word packed matrices and modifying key scheduling and bit extraction schemes. The resulting generator is then successfully compared to world class standards.

A secret sharing scheme based on exponentiation in Galois fields

To provide more efficient and flexible alternatives for the applications of secret sharing schemes, this paper describes a threshold sharing scheme based on exponentiation of matrices in Galois fields. A significant characteristic of the proposed scheme is that each participant has to keep only one master secret share which can be used to reconstruct different group secrets according to the number of threshold values.