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13 | 13 | ;; The basic question this article tries to answer is: Can fusing hashes |
14 | 14 | ;; together provide unique identifiers for arbitrary data? The answer is no. |
15 | 15 | ;; Specifically, we can not provide unique identifiers for sufficiently large |
16 | | -;; repeated sequences of values. That is, sufficiently low entrory dtat is not |
17 | | -;; reprentable by fusing hashes together. The good news is that low entropy |
| 16 | +;; repeated sequences of values. That is, sufficiently low entropy data is not |
| 17 | +;; representable by fusing hashes together. The good news is that low entropy |
18 | 18 | ;; data is compressible. |
19 | 19 |
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20 | 20 | ;; This is an article about fusing hashes together while having the key |
21 | | -;; properties of associativity and non-communativity. I describe the basic |
| 21 | +;; properties of associativity and non-commutativity. I describe the basic |
22 | 22 | ;; approach of using matrix multiplication of Upper Triangle Matricies and then |
23 | 23 | ;; show the results of two types experiments showing the quality and limits of |
24 | 24 | ;; this hash fusing approach. |
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29 | 29 | ;; as a way to efficiently share structured data between multiple clients. One |
30 | 30 | ;; of the key challenges in this area is being able to efficiently reference |
31 | 31 | ;; ordered collections of data. The usual apprach is to use Merkle Trees but, |
32 | | -;; since the immuable data structure for orderd collections is based on finger |
33 | | -;; trees, I need references that are insensivite to tree shape. This means that |
| 32 | +;; since the immuable data structure for ordered collections is based on finger |
| 33 | +;; trees, I need references that are insensitive to tree shape. This means that |
34 | 34 | ;; I need to be able to fuse hashes together in a way that is associative but |
35 | | -;; not communative. As a starting point, I have been reading the HP paper |
| 35 | +;; not commutative. As a starting point, I have been reading the HP paper |
36 | 36 | ;; describing hash fusing via matrix multiplication: |
37 | 37 | ;; https://www.labs.hpe.com/techreports/2017/HPE-2017-08.pdf |
38 | 38 |
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495 | 495 | ;; This article has described a method for fusing hashes together using upper |
496 | 496 | ;; triangular matrix multiplication. The method is associative and non-commutative. |
497 | 497 |
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498 | | -;; Final conclusion is to use 64 bit cells with 32 lower bits to tolarate many |
| 498 | +;; Final conclusion is to use 64 bit cells with 32 lower bits to tolerate many |
499 | 499 | ;; repeated values. |
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