dorsal/arxiv
View SchemaPrivacy Amplification in Quantum Key Distribution: Pointwise Bound versus Average Bound
| Authors | G. Gilbert, M. Hamrick, F. J. Thayer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108013 |
| URL | https://arxiv.org/abs/quant-ph/0108013 |
Abstract
In order to be practically useful, quantum cryptography must not only provide a guarantee of secrecy, but it must provide this guarantee with a useful, sufficiently large throughput value. The standard result of generalized privacy amplification yields an upper bound only on the average value of the mutual information available to an eavesdropper. Unfortunately this result by itself is inadequate for cryptographic applications. A naive application of the standard result leads one to incorrectly conclude that an acceptable upper bound on the mutual information has been achieved. It is the pointwise value of the bound on the mutual information, associated with the use of some specific hash function, that corresponds to actual implementations. We provide a fully rigorous mathematical derivation that shows how to obtain a cryptographically acceptable upper bound on the actual, pointwise value of the mutual information. Unlike the bound on the average mutual information, the value of the upper bound on the pointwise mutual information and the number of bits by which the secret key is compressed are specified by two different parameters, and the actual realization of the bound in the pointwise case is necessarily associated with a specific failure probability. The constraints amongst these parameters, and the effect of their values on the system throughput, have not been previously analyzed. We show that the necessary shortening of the key dictated by the cryptographically correct, pointwise bound, can still produce viable throughput rates that will be useful in practice.
{
"annotation_id": "eaa4d5ee-dab3-4b66-bb3f-0441153c4e1b",
"date_created": "2026-03-02T18:01:46.209000Z",
"date_modified": "2026-03-02T18:01:46.209000Z",
"file_hash": "2f3b861dfcf1dc4234515b126b5bfc0b83f1cb1107e140ee0bb706cb9d55b2aa",
"private": false,
"record": {
"abstract": "In order to be practically useful, quantum cryptography must not only provide\na guarantee of secrecy, but it must provide this guarantee with a useful,\nsufficiently large throughput value. The standard result of generalized privacy\namplification yields an upper bound only on the average value of the mutual\ninformation available to an eavesdropper. Unfortunately this result by itself\nis inadequate for cryptographic applications. A naive application of the\nstandard result leads one to incorrectly conclude that an acceptable upper\nbound on the mutual information has been achieved. It is the pointwise value of\nthe bound on the mutual information, associated with the use of some specific\nhash function, that corresponds to actual implementations. We provide a fully\nrigorous mathematical derivation that shows how to obtain a cryptographically\nacceptable upper bound on the actual, pointwise value of the mutual\ninformation. Unlike the bound on the average mutual information, the value of\nthe upper bound on the pointwise mutual information and the number of bits by\nwhich the secret key is compressed are specified by two different parameters,\nand the actual realization of the bound in the pointwise case is necessarily\nassociated with a specific failure probability. The constraints amongst these\nparameters, and the effect of their values on the system throughput, have not\nbeen previously analyzed. We show that the necessary shortening of the key\ndictated by the cryptographically correct, pointwise bound, can still produce\nviable throughput rates that will be useful in practice.",
"arxiv_id": "quant-ph/0108013",
"authors": [
"G. Gilbert",
"M. Hamrick",
"F. J. Thayer"
],
"categories": [
"quant-ph"
],
"title": "Privacy Amplification in Quantum Key Distribution: Pointwise Bound versus Average Bound",
"url": "https://arxiv.org/abs/quant-ph/0108013"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "d259da7c-251a-4d17-ad2a-98def427cd22",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}