# Privately Generated Key Pairs for Post Quantum Cryptography in a Distributed Network
## 4 Experimental Validation
### Biometry as a Multi-Factor with [PERSON]  
After the completion of the verification cycle, the CA and the client device can use \(K_{i}\) as a cryptographic key to protect the exchange of information between them. A public-private key pair for an asymmetric cryptosystem is generated from a random seed. If the entropy of the space that this seed is chosen from is not high enough, the cryptosystem becomes vulnerable to a brute-force search. Recall that in the new protocol discussed here, each user is equipped with a cryptographic table (CT) that can be generated from, for example, a Physical Unclonable Function (PUF), a biometric image, or simply a digital file. During  
Figure 10: Latency graph for different fragmentation levels. an initial enrollment cycle that is performed securely, the users share their cryptographic tables with the CA. A string of bits related to identifying information is fed into the table and a deterministic output is then used as the source of the secret key. Until the present work, it has not been possible to use a biometric image for this function without facing some serious disadvantages. This is because the mapping must be deterministic, that is, the same input must always produce the same output. This can be accomplished with a biometric source if many images are combined and averaged into a template, which is then stored. This template can then be leveraged into a cryptographic table, but there are some serious security issues. First, if the information is stored anywhere, then a breach of the security of that storage space reveals sensitive biometric information. Second, if the image is lost or corrupted, at the current level of technology, the creation of a new template would not produce the same lookup table. Biometric information is simply too fluid and changeable for a second set of measurements to produce an identical lookup table or even a particularly close approximation to the original. However, if a solution could be found whereby a biometric source could be consistently mapped to the same lookup table, then a person's biometric characteristics could be tied directly to the creation of an asymmetric key pair--a very desirable objective. In the following, we will use the example of a face as a source of biometric information, but this is only one of a variety of different possibilities. A face has several characteristics that can be very easily, at low computational cost, detected and measured. For example, the centers of the eyes and the tips of the nose can be identified and used to establish a coordinate system, and the relative positions of various points on the face such as the corners of the eye, cheekbones, etc. can be recorded. Approximately 400 of such \"landmarks\" can be identified and assigned coordinates. At this point, a random subset of these landmarks can be chosen, and distances between landmarks and angles between  
Figure 11: Average latencies for important factors of the protocol. lines connecting one point to two distinct points can be measured and recorded as a several-hundred-dimensional vector. The naive thing to do at this point would be to use this vector as a source of \"deterministic\" randomness and map it to a private key, from which an associated public key would be created. This would suffer from several defects and security flaws. First of all, there is sufficient randomness and variability in the process of taking a photo and performing these measurements that an attempt to reconstruct the same vector from a different photo would fail. A new vector would be created that would be, from the point of view of Euclidean distance, close to the original vector, but if this new vector were mapped to, for example, a second 256 bit long sequence to be used for key creation, it would differ from the 256 bit sequence created by the first vector at enough points to make it computationally infeasible to reconstruct the original key.