Post-quantum public cryptosystems introduced so far do not define an scalable public key infrastructure for the quantum era. We demonstrate here a public certification system based in Lizama’s non-invertible Key Exchange Protocol which can be used to implement a public key infrastructure (PKI), secure, scalable, interoperable and efficient. We show functionality of certificates across different certification domains. Finally, we discuss that non-invertible certificates can exhibit Perfect Forward Secrecy (PFS).

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{F}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We show that the public, secret and channel keys become indistinguishable to the eavesdropper under matrix multiplication. Remarkably, for achieving a 512-bit security level, the public key is 1024 bits and the private key is 768 bits, making them the smallest keys among post-quantum key exchange algorithms. Also, we discuss how to achieve key authentication, interdomain 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.

We present an error reconciliation method for Quantum Key Distribution (QKD) that corrects 100% of errors generated in regular binary frames transmitted over a noisy quantum channel regardless of the quantum channel error rate. In a previous investigation, we introduced a novel distillation QKD algorithm whose secret key rate descends linearly with respect to the channel error rate. Now, as the main achievement of this work, we demonstrate an improved algorithm capable of retaining almost all the secret information enclosed in the regular binary frames. Remarkably, this technique increases quadratically the secret key rate as a function of the double matching detection events and doubly quadratically in the number of the quantum pulses. Furthermore, this reconciliation method opens up the opportunity to use less attenuated quantum pulses, would allow greater QKD distances at drastically increased secret key rate. Since our method can be implemented as a software update, we hope that quantum key distribution technology would be fast deployed over global data networks in the quantum era.

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.

We present a new post-processing method for Quantum Key Distribution (QKD) that raise cubically the secret key rate in the number of double matching detection events. In Shannon’s communication model information is prepared at Alice’s side then it is intended to pass it over a noisy channel. In our approach, secret bits do not rely in Alice’s transmitted quantum bits but in Bob’s basis measurement choices. Therefore measured bits are publicly revealed while bases selections remain secret. Our method implements sifting, reconciliation and amplification in a unique process, it just require a round iteration, no redundancy bits are sent and there is no limit in the correctable error percentage. Moreover, this method can be implemented as a post processing software into QKD technologies already in use.

Previously, using the conjugate frame-based reconciliation approach, we defined a method to correct errors produced in pairs of non-orthogonal quantum states that are transmitted through a quantum key distribution (QKD) link. The security of the frame-based reconciliation was discussed in order to deal with Photon Number Division (PNS) attack and Intercept and Forward (IR) attack, among others. However, until the time of publication we did not have the distillation software to test our method. In this article, following the conjugate frame distillation method, we present the implementation of the post-processing system that demonstrates that it is capable of correcting errors in the presence of error rates close to unity. The system shows that when the number of double-sensing events at Bob's station is as low as 100, the number of secret bits stays above 4500 bits in about 12 seconds, giving a secret rate of 375 bits per second while that the channel error rate reaches 90\%.