Report discusses key generation for transmission of confidential data. A number of feedback functions are discussed for generation of long key sequences

Perlman, M.

English

NASA Technical Reports Server

•	 October 1975	 B75-10278 
NASA TECH BRIEF 
•	 NASA Pasadena Office 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Generation of Key In Cryptographic System

for Secure Communications 
.
A number of general-purpose digital computers are 
used for gathering, categorizing, and storing confi-
dential data. When these data are transmitted to a 
remotely located terminal, unauthorized access to it 
may be prohibited by using cryptographic encipher-
ment. An encipherment with a particular key is 
illustrated as follows: 
Sequence: 011010111101100
Key: 11110101 1001000

Cipher: 100111100100100 
The transformation consists of a bit-by-bit modulo 2 
sum (i.e., EXCLUSIVE-OR) of the data sequence 
with the key. 
An authorized user would have a priori knowledge 
of the key and of the corresponding inverse 
transformation. Thus deciphering proceeds as 
follows: 
Cipher: 100111100100100
Key: 11 1 10101 1001000

Sequence: 011010111101100 
Decipherment involves an inverse transformation 
whereby the key is subtracted bit-by-bit modulo 2 
from the cipher, yielding the data sequence. 
The cipher described is known as the Vigenere 
cipher. A Vigenre cipher with a key of unlimited 
length (i.e., nonrepeating) is called a Vernam system. 
A report has been published which discusses key 
generation for the Vigenre, the compound Vigenre 
(where two or more combined sequences comprise the 
key), and the Vernam systems, using feedback shift 
registers (FSR's). The report discusses the theoretical 
considerations necessary for key generation. One
major topic includes binary FSR's, particularly the 
nonsingular FSR's. The key sequences are generated 
using nonsingular FSR's. These FSR's are determined 
from factors of de Bruijn graphs of order r. A section 
of the report is devoted to linear feedback shift 
registers (LFSR's) and their role in generating binary 
sequences. These are compared with nonlinear FSR's. 
A number of feedback functions are discussed for 
the generation of long key sequences. The long 
sequences can be split and then rejoined to create 
additional nonrepetitive sequences. The report in-
cludes a number of examples. Projections for future 
work are also discussed. 
Note: 
Requests for further information may be directed 
to:
Technology Utilization Officer 
NASA Pasadena Office 
4800 Oak Grove Drive 
Pasadena, California 91103 
Reference: TSP75-10278 
Patent status: 
This invention has been patented by NASA (U.S. 
Patent No. 3,911,330). Inquiries concerning non-
exclusive or exclusive license for its commercial 
development should be addressed to: 
Patent Counsel 
NASA Pasadena Office 
4800 Oak Grove Drive 
Pasadena, California 91103 
Source: Marvin Perlman of 
Caltech/JPL 
(NPO-13451) 
•	 Categories: 09 (Mathematics and 
Information Sciences) 
02 (Electronics Systems) 
This document was prepared under the sponsorship of the National
	
Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States
	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States
	
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19750000278 2020-03-19T20:14:03+00:00Z


Generation of key in cryptographic system for secure communications

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