# Mathematical investigation of one-way transform matrix options.

## Abstract

One-way transforms have been used in weapon systems processors since the mid- to late-1970s in order to help recognize insertion of correct pre-arm information while maintaining abnormal-environment safety. Level-One, Level-Two, and Level-Three transforms have been designed. The Level-One and Level-Two transforms have been implemented in weapon systems, and both of these transforms are equivalent to matrix multiplication applied to the inserted information. The Level-Two transform, utilizing a 6 x 6 matrix, provided the basis for the ''System 2'' interface definition for Unique-Signal digital communication between aircraft and attached weapons. The investigation described in this report was carried out to find out if there were other size matrices that would be equivalent to the 6 x 6 Level-Two matrix. One reason for the investigation was to find out whether or not other dimensions were possible, and if so, to derive implementation options. Another important reason was to more fully explore the potential for inadvertent inversion. The results were that additional implementation methods were discovered, but no inversion weaknesses were revealed.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Laboratories

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 877142

- Report Number(s):
- SAND2006-0193

TRN: US0601294

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEFENSE; AIRCRAFT; COMMUNICATIONS; DIMENSIONS; IMPLEMENTATION; MATRICES; SAFETY; WEAPONS; NUCLEAR WEAPONS; Nuclear weapons; United States-Safety measures.; Matrices.

### Citation Formats

```
Cooper, James Arlin.
```*Mathematical investigation of one-way transform matrix options.*. United States: N. p., 2006.
Web. doi:10.2172/877142.

```
Cooper, James Arlin.
```*Mathematical investigation of one-way transform matrix options.*. United States. doi:10.2172/877142.

```
Cooper, James Arlin. Sun .
"Mathematical investigation of one-way transform matrix options.". United States.
doi:10.2172/877142. https://www.osti.gov/servlets/purl/877142.
```

```
@article{osti_877142,
```

title = {Mathematical investigation of one-way transform matrix options.},

author = {Cooper, James Arlin},

abstractNote = {One-way transforms have been used in weapon systems processors since the mid- to late-1970s in order to help recognize insertion of correct pre-arm information while maintaining abnormal-environment safety. Level-One, Level-Two, and Level-Three transforms have been designed. The Level-One and Level-Two transforms have been implemented in weapon systems, and both of these transforms are equivalent to matrix multiplication applied to the inserted information. The Level-Two transform, utilizing a 6 x 6 matrix, provided the basis for the ''System 2'' interface definition for Unique-Signal digital communication between aircraft and attached weapons. The investigation described in this report was carried out to find out if there were other size matrices that would be equivalent to the 6 x 6 Level-Two matrix. One reason for the investigation was to find out whether or not other dimensions were possible, and if so, to derive implementation options. Another important reason was to more fully explore the potential for inadvertent inversion. The results were that additional implementation methods were discovered, but no inversion weaknesses were revealed.},

doi = {10.2172/877142},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Jan 01 00:00:00 EST 2006},

month = {Sun Jan 01 00:00:00 EST 2006}

}