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Computational cryptography deals with the storage and processing of sensitive information in computer systems by enciphering.
Typology: Summaries
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APPROVED FOR PUBLIC RELEASE. DISTRIBUTION UNLIMITED.
by Fred A. Stahl
This work was supported in part by the Joint Services Electronics Program (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB-07-72-C-0259.
Reproduction in whole or in part is permitted fo r any purpose o f the United States Government.
Approved fo r public release. Distribution unlimited.
this reason, simple ciphers can no longer be used to provide a great deal of secu rity. This carries over to computational cryptography also. Moreover, there are a number of desirable features that any ciphers to be used in computer systems should have. These include: 1* Encipherment and decipherment should be simple. That is , the computational complexity o f enciphering and deciphering information should be minimal.
which is extremely hard to remove. Simple substitution , for example, leaves for easy analysis a l l single le t t e r , and multiple le tte r frequencies, doublet and reversal frequencies, as w ell as contact variety information. Figure 1 is representative of this information for a standard text.
Linear Scale
Linear Scale
Log Scale
Log Scale
b) Digram Frequency
ETOANIRSHDLCFUMPYWGBVKX JQZ
T I A I E F T E H A V T T A H E H R I A C N A E I TH N N O NO IR E T EE H TA RI E LR OC LV T EE GD NT RO ER ER RAI TS SSL EN EL EHD
FP-
Figure 1. Various Frequency D istributions for English
Plaintext Symbol; A B C D E F G H I J K L M Number of Cipher Symbols: 81 13 31 4 3 1 3 3 2 9 14 61 71 2 5 38 27 N O P Q R S T U V W X Y Z 15 85 22 2 70 65 93 28 10 15 3 15 1 Figure 3
E T O A N I R S H D L C F U M P Y W G B V K X J Q Z F P -3 4 4 9 Figure 4
However, as noted above, the cryptanalyst uses other techniques for breaking codes. The cryptanalyst looks fo r the most deviant structural features f i r s t. Consider, for example, the abnormal reversal frequency of ER in Figure l e. I f this reversal can be located in the ciphertext the cryptanalyst is much closer to breaking the code. In contrast, he would not look for the reversal OF since there are many other reversals with nearly the same frequency occurrence. The cru cia l point to remember is that it is only the abnormal or deviant frequencies that can be used for clu es. C learly, i f a l l measurements of the ciphertext yielded nearly fla t distribu tions as in Figure 4 there would be no information gained from those measurements. Now let us generalize the homophonic technique to fla tten the other curves illu stra ted in Figure 1. This is easier said than accomplished, s since adjusting one curve to be fla t t e r w ill generally resu lt in making another one more curved. Let us return to the e a rlie r generalized homophonic enciphering hypothesis and modify it somewhat to allow for more f l e x i b i l i t y. Before we wanted the curve resulting from single le tte r enciphering to be nearly f l a t. I f we lessen this r e strictio n somewhat and allow for some d istrib u tion but not nearly as much we can avoid the abnormal or deviant frequencies that are normally used for clues on a ll the measurements found in Figure 1. Figure 5 gives one such homophonic cipher. The technique used to generate this code is fa ir ly simple. The frequencies are adjusted as for the code in Figure 3, and the corresponding frequency charts can be generated for the other measurement of the cipher- text. Next, the most deviant frequency in any measurement is examined. I f ,
fo r example, it is a reversal frequency the corresponding number o f cipher symbols used fo r each of the constituent symbols is raised accordingly. The process is repeated u n til the frequency curves are sa tisfa cto ry. I f there is no convergence the process can be started over again taking care to choose d ifferen t measurements f i r s t , I f a fter a number o f attempts are made appropriate curves cannot be gotten, it might be necessary to increase the number of ciphertext symbols by increasing the number o f b its used to represent each symbol. A cipher su ccessfu lly generated in the manner described has a ll the desirable features for computational cryptography set forth above. An extremely simple enciphering and deciphering scheme can be used since this is a substitution type cipher. A sample scheme w ill be given. With regard to the a b ility to adjust the cipher to meet security needs one need only increase the number o f b its used to represent each ciphertext symbol (e ffe c t iv e ly , increasing the ciphertext alphabet). Since there is one ciphertext symbol for each plaintext symbol the messages can be of arbitrary length. An error in one symbol does not extend errors even to adjacent symbols of the message; thereby keeping losses of information to a minimum. Note in particular that since i t is a substitution cipher the 'in te g rity through e d itin g ' condition is met. That is , strings (including individual characters) of enciphered message may be moved with respect to each other without going through a deciphering and reenciphering process. This property makes it invaluable for large dynamic data-bases. The length of the message only increases with the security needed. For a typ ical low security cipher 8-bits should be su fficie n t for a 64
symbol plaintext alphabet. A homophonie cipher can e ffe c t iv e ly destroy a l l standard language frequency information as shown in Figure 1. In addition, information in ciphered form may be received by the computer from a terminal and be edited without it ever being deciphered at the central f a c i l i t y. As mentioned e a rlie r the device to encipher the plain text message need not be very complex. Consider a key of 256 characters; each o f the 64 characters appears in the key the number of times desired fo r the particular application (see Figure 6 ). The key is loaded into a 256 word memory. Deciphering consists of returning the contents of the address sp ecified by the 8 -b it cipher. Enciphering involves generating an address randomly and then searching sequentially u n til a matching character is found and then transmitting its address (see Figure 7). The amount of secrecy needed can be con trolled by the number of b it s. So, fo r instance with 9 b its there would be 418 remaining b it patterns; with 10 b its it would be 984, e tc. Each additional b it increases the secu rity.
6, Additional Problems Associated With Computational Cryptography There are a number of additional problems associated with keeping sensitive information secure in computer systems. These include the follow ing: 1« The decoded message problem. This comes about when a block of decoded or unenciphered message is known by the analyst. With this type o f information available very few cipher systems are s a fe. The limited syntax problem. When dealing with limited languages such as programming languages the analyst can break the cipher
Address Memory O O O O O O O O
Search sequentially for Plaintext Character s ' P
F P -3 4 4 7 Figure 7
by knowing the r e strictiv e properties of the language involved.
Security Classification ( S e c u r i t y c l a s s i f i c a t i o n o f t i t l e , bo'dy o f^ DOCUMENT CONTROL DATA ■ a b s t r a c t a n d i n d e x i n g a n n o t a t i o n m u s t be^ R & D e n t e r e d w h e n the o v e r a l l r e p o r t is c l a s s i f i e i
2 a. R E P O R T S E C U R I T Y C L A S S I F I C A T I O N 2 b. G R O U P^ UNCLASSIFIED
7 a. T O T A L N O. O F P A G E S 15
7 b. N O. O F R E F S 8a. C O N T R A C T O R G R A N T N O. (^) 9 a. O R I G I N A T O R ’ S R E P O R T N U M B E R ( S )^13 b. P R O J E C T N O.^ DAAB-07-72-C- R- c. (^) 9 b. (^) t h is O T H E R r e p o r t ) R E P O R T N O ( S ) ( A n y o t h e r n u m b e rs t h a t m a y be a s s i g n e d d. UILU-ENG 73-
D istribution unlimited.
A simple enciphering technique that can be used to encode sen sitive data in computer systems is described. This cipher has properties that make i t possible to do editing on data within the computer without decoding. Thus, the key need not be available to the computer nor anyone who has access to the computer system since the data can easily enter and leave the system in ciphered form. It need only appear decipheredprocedure. at it s origin or it s destination by use of a very simple ciphering Requirements for computational cryptography are also discussed along with a short reviewFinally, of some problemscryptographic thattechniques s t i l l remain unsolved w illthat have already been be usedillu stra te d. for computer systems.
DD A”™, Security Classification
Security Classification 1 4 K E Y W O R D S L I N K A L I N K B L I N K^ C R O L E. W T^ R O L E^ W T^ R O L E^ W T
Homophonic substitution cipher Computational cryptography Data-base security Text-editing System security Cryptography
Security Classification
