.. REF ID:A60464 

5 April 1955 

The Basic Principles of Cryptanalysis 

The problem of understanding a message 'Which was not directed 

to one, and which is in fact intentionally obscured, is a broad one 

and has arisen in many fields, including the baseball diamond. It 

has reached its great-est difficulty and evoked the most ingenuity in 

solution in the field of military carmnunications. 

My object in this note is to point out some basic principles. 

There may be other ways of stating these principles, and there meybe other principles besides, but these are basic in the sense that 

they cannot be circumvented. 

In simple terms an interceptor B I listening to transnissions 

sent f'rom A to c, who are taking pains to keep B in ignorance. The 

only possible way that A and C can hope to succeed is to utilize some 

background information which is unknO'Wil to B. Generally this is prearranged material called "key". The message then fits into this background to make a coherent statement. 

This is principle n'W'!lber one; comrmmicat/.o/s A and C must have 

some infonnation not available to the interceptor • 

. If the link from A to C is to have utility it must be able to 

accommodate any messages fran a large bank of possibilities, and . ' . .. accommodate these in la:r:ge vol~e. ·' It ii;J ri~-- possible .for A to· assert. 

in advance what messages i'r~m this bank h_e· will send nor in what 

number. If it were possible, the communications link would nal:i be 

needed. 

The messages to be sent are not under the control of the communicator. 

A; he must take all comers. His key must have similar propert.ies; it must 

@'pp roved for Release by NSA on 09-06-2013 pursuantto E .0. 1352a 

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be unpredictable. ? 

If his keys are al.l from a clearly defined subset then the cryptanalyst 

B 11 once he recognizes this fact 11 has an excellent cha.nee to recover 

information. For instance, suppose the key were digits to be added to 

digital. plain text, and that the key had no zeros in it. 

This is the second principle. If the key comes from a subset 

which does not allow a.lrn.ost all the possibilities, then the cryptanalyst 

will eventually read some of the messages. 

The set of possible keys mBiY' have another weakness. If the key 

can be represented as a combination of sub-keys in such a way that this 

representation ca:tTies through the encipherment11 then the cryptanaJ.yst 

can deal merely with a sub-key. An example is the Hagel.in C-38, where 

the key is the result of contributions i'rom 6 dif f'erent 'Wheels. Solution 

is frequently achieved by attacking one of these lo.heels at a time. 

Principle number three is this. If the keys can be split such that 

the split carries throug~ the encipherment, then the cryptanalyst can 

attack one part at a tim.e~'he cryptogr~pher A is pl.eying a game, in 

the mathematical. sense, with the cryptan~yst B. The game is such that 

the gain of one is not necess.ari1y equ~ to .tP.e loss ~f the other. The - , 

game has significant chance el~ents, the message source ~d the risks . . . they may encounter en route (busts). Plqer A must s~lect _his strategy - ' 

in advance, and is on the defensive; -he cann~t afford mistakes. Player B 

can improvise his strategy as new infom.a.tion becomes available; he is 

on the offensive. The fact that this is a game explains the formidable 

complexity encountered in any attempt to catal.og crypt.analytic attacks. 

This complexity is frequently met in detailed prescription of a strategy. 

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REF ID:A60464 

The fourth principle is: the choices open to A and to B define 

game strategies., in which the effectiveness of each depends upon the 

actions of the other. 

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