REF ID:A72680 

_ ·. !~ECURllY IN~RMAT~©J~ 

SECRET 5Eel:1itI'fY IMFOR!~'fiON 22 October 1952 

MEMORAIIDUM FOR THE CONSULTANT 

SUBJECT: Comments on SCAMP 

Reference: Report on SCAMP by Stewart S. CAIRNS, dtd 8 September 1952 

1. I make t.he following comments concerning SCAMP: 

a. The idea of a two-month mathematical seminar on Agency 

problems is excellent. It provides three badly-needed things: 

(1) The int,roduction of new, competent scientific thought 

on important unsolved problems many of which have been 

around so long that the Agency personnel assigned to 

them have begun to grow stale; 

(2) The opportunity for the Agency's better cryptomathematicians, or mathematical cryptologists, to free themselves for.an extended period from the extensive morass · of administrative and executive detail with which all 

too many of them are saddled and to participate full 

time in the attempted solution of significant problems 

with which they are technically competent to cope; 

(3) The opportunity for bona-fide rrathematicians employed 

by AFSA to recover a bit of their professional skill 

through informal discussion with recognized leaders in 

mathematical specialties. 

b. The actual carrying-out of SCA!u1P during the summer of 1952 

left a good deal to be desired: 

(1) There was considerable uncertainty as to who would 

participate; this uncertainty persisted into the seminar 

itself, and seems to have been due, at least in pa.rt, 

to the late date at which invitations to participate 

were issued. 

(2) Clearance difficulties hampered the project immensely. 

These difficulties were of three kinds: 

(a) Some technically desirable people were excluded 

because of non-clearance or imcomplete clearance; 

(b) The highest clearance granted to visiting firemen 

was CONFIDEl'JTIAL; this was too low; 

(c) The heterogeneity of clearance levels made security 

leaks almost unavoidable • 

eclassified and approved for release by 

SA on 02-11-2014 ursuantto E.O. 1352 

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8EeftE'f SEemt!TY I!WOM'.tAi'ION 22 October 1952 

(3) The major SCAMP topic was the existence of finite 

projective planes of various orders, as set forth on 

pp. 4-5 of the reference-. The significance of this topic 

to AFSA seems small to me, and the argumentl adduced to 

support the idea that the topic is significant are, in my 

estimation, rather tenuous. I agree that the topic is 

of great mathematical interest; I agree further that 

certain steps forward were made; I question, however, the 

relevance of the subject and the adaptability of the 

methodology to AFSA problems. 

c. There is a very real danger in projects such as SCAMP and 

AFSASAB that the Agency may make itself an enthusiastic but unwitting sort 

of computing machine for the use of "outside experts" who do not have any 

real responsibility for the operation of the Agency but who are very much 

aware of the advantages to pure research of having so large and rich an 

organization to support their personal research goals. 

2. In line with these conunents, I make the following reconunendations: 

· ~ p· a. S.CAMP should be reconstituted next swmner. 

"' ~~\ . .J>V ,/ b. Participation lists should be made up now. 

~~- 0 . ~: crvY" ./ c. Clearances should be started now. All hands should have 

\l)~~ ~full cryptologic clearance and indoctrination. 

C..·~J . Ji. . .> d. The agenda should be established now, and thrashed out ~ by the of fices to insure that all subjects for discussion are in fact '\~ ~ closely related to the AFSA effort. I feel that the Agency should not ~ :~;,.y'·Pattempt to support pure research without some assurance that the results, ~- ~ .JJ'\.if any, will be appropriate to its mission • 

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//_,..,..~~--A;-'~:.:-_ -..A "4..llll!:::==-' ..... ___ m;a 

/ __ _,.,,. R. H. SHAW 

~ - Chief, Cryptosecurity Branch 

Copies to: 

Chief, Cryptomathemattcal Division (34) 

Chief, Technical Projects Group (206) .,. Technical Director, Office of Operations (feT) 

Chief, Office of Communication Security (04) 

Chief, Analysis and Evaluation Division (41) 

2 

SECRET 
00NF1BEiN'H#ii SenF.i.ty In£o:tmati.ou 

Report on SCAMP 

to the 

of the 

A:med Forces Security Agency 

Submitted by 

Stewart s. Cairns 

8 September 1952 

CONFIDENTIAL 
REF ID:A72680 

r -jONFIDENTI4 

I 

Report. on SCAMP 

TABLE OF CONTEN'l:S 

Secuon Title 

l. 

2. 

3. 

4. 

Appendices 

IntroductionJ origins of the sym.posi\Dll. 

The scientific work of 'the symposium 

Administrative work 

Suggestions regarding possible future efforts 

I. List 0£ participants 

II. List ot -seminar meetings 

III. List o! conferences 

IV. List 0£ other reports 

v. Computations attacked 

VI. Reproduced seminar reports 

VII. Reproduced conference reports 

VIII. Other reproduced report.a 

IX. Budgetary material 

X. Suggestions trom SCAMP menil:>ers regarding future work 

XI. Miscellaneous selected correspondence 

GSN FIDEN'F IAL 
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I 

) 

Report on SCAMP 

l. Introduction 

The sununer symposiwn to which the name SC.AMP was fi.n~ly attached 

grew from discussions in SCAG. The initial proposals leading to SCA11P 

were made in 1951 by C. B. Tompkins in his role as a member o;f SCAG. 

Originally, a continuing project was intended. However, after various 

discussions, it was decided to conduct a sWIU1ler symposium and, on the 

basis of experience therewith, to consider the desirability of later 

efforts. This decision was reached in March 195~ 1 with the result that 

only about three months were available for the preliminaries to the · 

symposiwn. Among the proposals by Tompldns was the use of the primarily 

mathematical part or SCAG, referred to as SCAM (Speqfal Conunittee 

Advising in Mathematics), in an advisory capacity. The code name SCAMP 

~as created in AFSA by adding the letter P to SCAM. 

No fixed objectives were officially adopted for the symposium. A 

set of proposed objectives was contained in a document ''Notes on a 

proposed re~earch project and symposium" by Tompkins, 18 March 1952, 

subsequent to an agreement by tho writer to serve as leader of the 

symposium,, and these propo~ed objectives proved useful in preparing for 

and conducting the symposium. (The "Notes" are in Appendix XI.) · 

Because of the lateness of the decision to conduct the symposium,, 

difficulties were encolllltered in the recruitment of persoruiel. Many 
short for the normal clearance procedures. This led to the use largely 

of personnel for whom eVJ.dence of clearabili ty existed and also to the 

conduct of the symposium largely on a confidential level, though a 

higher security level would have been advantageo1,1S. (See Appendix for 

list or participants.) 

Through the cooperation or members of the start or the Institute 

for Nunerical Analysis in Los Angeles and ot the Um. verSJ. ty of California 

at Los Angeles, adequate office space was proVJ.ded and provisions made 

for the necessary office supplies am equipment. 

The symposium benefited in a numoer of' ways trom bemg located on 

the UCLA campus and associated ~th the Institute for Numerical Analym.s 

of the Nati.anal Bureau of Standards. A minor, but not inconsiderable, 

advantage was the comparat.i ve freedom from excessive summer heat, as a 

result of which more effective mrk can be accomplished there than in 

most parts of the country. Scientifically, SCAMP benefited by the 

availaln.li. ty of the computing equipment (SWAC and IBM) at the INA an::l 

by the proXlJlll. ty of mathematicians connected, at least for the summer, 

Wl. th UCLA, and INA and the Rand Corporation. This latter advantage extended. beyond the pleasure and the general stimulati.on of associatulg 

WJ..th colleagues. Si.nee one or the principal problems of the symposium 

was unclassified and or general mathema tJ..cal. interest,, SCAMP sponsored 

a seI11J.11ar on the subject (fi.m.te projecta.ve planes) and also a shorter 

seminar on mechanical a.ids to computation. Vanous mathematicians of 

the groups listed above not only attended the seminar meetings ard 

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, participated in discussions,, but also took pa.rt as invited speakers. 

C"ne such speaker, Assistant Proi'essor Lowell J. Pa.:i.ge 0£ UCLA, later 

became a member or SC.AMP for thre~ weeks. Conversely,, a number ot 

lectures sponsored by the INA and the Rand Corporation had a direct 

bean.ng on the interests or SCAMP and were attended wi.th profit by 

various participants. Particularly valuable were (1) a sen.es of talks 

at the INA on programming for computers,, and (2) lectures by John 

v-on Neumann and TJalling J(ooptT1ans at Rand or the so-called "assignment 

problem, 11 whose formulation in tenn.s -of matrices is very closely t."elated to one or the mathematical problems most SJ.gnificant to AFSA. 

2. The Scientific Work of the Symposium 

The choice or the problems to wnich SCAMP devoted most of its effort 

war:. dcteI'111l.ned partly by the need for rnaintaining a low level of classification and partly, as the work progressed,, by the interests of the 

participants. Pn.or to the opening of the symposium,, a nwnber of problems 

were suggested and discussed with i\.FSA perso?lllel. In order to avoid a 

scattering of efforts over a variety 01' special questi.ons and to enhance . 

the likelihood of useful contributions,, attention was concentrated. on 

introducing and studying 

a. Combinatorial problems with possible n\1Il2rical solutions invalving permutab.ons. 

~. Computatl.onal scheries leading to exhaustive attacks on such 

problems~ 

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eeMF'iflBM'f!Afi 

c. Methods of attack involving the imbedding of such pro bl ems in a : 

continuous space am the study of appropriate func ti.ons defined 

over the convex hull of the discrete. set oi' potential solutions • 

. For a nwnber of reasons,,. these general subjects were specialized. 

to the question of the ~stence of finite projective pl~s of va~ous 

orilers. The participants devoted most of their efforts to items a. and. 

b.,, on which definite progress was made. Promising approaches exist to 

the attacks in continuous spaces,, and it is to be hoped that later efforts 

will involve their further development. 

The study of finite projective planes leads to gene~al questions involving pennutations. Since every pennutation can be realized as a 

cross-Wired rot.Or,, and since every cross-wired rotor yields a pennutation,, 

some fairly direct connec.tions between AFSA' s problems and those encountered in studying finite ~rojecti ve planes may be expected. These 

are outlined in the paper "Problems related to finite Geometries,,"· 

Conference No. 18,, Appendix VII,, but in sununary it might be pointed out 

that 

(1) The construction of a hitherto unknown finite'projective plane 

nd.ght lead to an example from which new arr:l valuable knowle_dge 

of permutations could be gleaned; 

(2) The problem of studying finite projectl.ve planes supports exhaustive attacks on SWAC which: are very likely to carry over to 

AFSA applications. 

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CONFIDENTIAL 
In acldi tion,, 1 t is true that finite proJecta.ve planes have long been 

of general mathematical interest, and research articles are currently 

being publl.shed concerm.ng them. Hence 1 t was possible to conduct open 

semind.rs (see Appendix for list) in connection with SCAMP, thus strengthem.ng our ta.es WJ.. th the considerable group of mathematicians in the Los 

Angeles area during the summer,, am stimulating their interest in a pure 

mathematical problem whose soluti.on would be of practical value to AFSA. 

Another short se11U.nar (four meetings) and several conferences were 

devoted to the capabilities of various computing deVJ.ces, especially with 

reference to the problems mentionE"d above. The talks given at these 

meeti.ngs were not reproduced,, since the existing litera"hlre covers their 

subJect matter. 

Supplementing the open seminars was a seI'l.es of conference (see 

Appendix III for list), some 0£ them classified and all of them confined. 

to SCAMP participants. 

With few exceptions,, the speakers at seminar meetings and at conferences wrote up the;i.r mateI'l.al._, which wac; reproduced. for later use. 

Copies of the resulting papers are in the appendices, as are a number of 

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other SCAMP reports written by the participants. The papers resulting 

I 

from the seminar on finite projective planes were reproduced in sufficient 

quantities to permit some distribution by the Institute :for Numerical. 

Analysis,, as well as WJ..thin AFSA and among members of SCAMP. The remaining papers were not made available to the INA but were entl.rely reserved 

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for AFSA and SCAMP uses. 

The purposes of the eonferences were (1) to present introductory 

material indicating, within se9¢ ty limitations, the general area of 

the sponsor's interest~ (2) to sug~est mathematical problems appropriate 

w SCAMP an:l (3) to discuss results' and methods. Conference topics in- . 

eluded depths, weights an:l faqtors, measures of rougtmess, _infonnajtiion 

theocy, and pennutata.on problems~ (See Appendix VI.) 

Research was pursued on both an individual am a collaborative basis. 

. . 'The spirit of tep.mwork was stfong, am the participants .Crom AFSA furnished 

valuable assistance in directing the other members along useful lines. 

Amo~ the results obtained, the following may be mentioned as samples. 

They are mere samples, and their listing here should not be taken to imply 

that they are considered more sigxtj..fieant than other results which might ' I 

have been listed: 

(1) In a paper by Paige and Wexler (Appendix VI,, No. 2) new light 

was thrown on methods for passing back and forth between an 

incidence matrix of a finite projective plane and a correspondi~g 

set of mutually orthogonal latin squares. 

(2) Certain rational matrices associated. with finite projective 

planes were developeq arx:1. presented in a seminar talk by Albert,, 

who plans, if ~pproval is gr~ted,, to publish the r~sults in a 

research jounial, 

(3) Dr. ward concentrated his efforts on computational procedures. 

He developed and successfl}lly tried out a ffivAC program of a 

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C'ON FI DENT I AL 
search for so-cal.led 11magic setsn or ntransversals" in a 

lat+n square, or ord~r 10; also for a test '00 see whether 

such a squa;i:-e CQnta:i.ns magic sets so related as to assure 

the existence o.f an orthogonal mate. Thl.s latter is a 

necessa;i:-y, but not sutficient, conch ti.on for the existence of 

a fl.ru.t~ projective plane of order 10. The methods can be 

used through order 12 on SWAC. (Report to be added to 

Appendix VI.) 

(4) Dr. Tompkins, besides stimulating arxi advising other members 

on a variety of problems~ obtained on SWAC a difference set 

or 513 numbers co:qnected Wl.th a fim.te proJectJ.ve plane of 

order 512. In connection therewith, he programmed a search 

tor a certi\Wl class of irreducible polynomials. (Appendix 

VI, Nos. 14, lS.} 

(5) A bn.ef method was presented by Botts for demonstrating the 

non-md,stence of five nutually orthogonal. 6 x 6 latl.n 

squares, hence the non-existence of a projecti.ve geometry ot 

order 6. While the r~sult was known, the method is new and 

may lead to successful a'(ftacks on unlmown cases. {Report to 

be added to Appendix VI. ) 

(6) A theorem was proved by Hanson on the number of permutations 

associated with a given di!ference set. (Report to be added 

to Appendix VI.) 

Various proJT1.1.s1ng attacks on problems were 1mtiated but left 

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incomplete at the end of the symposium. Among these may be mentioned 

a collaborative approach by D, w. Hall and G. A. Hedlund. to the probiem 

. . of the existence or a finite projective plane of onier 10. Furthermore, 

the results listed above are mere s~ges on the way toward larger problems and thus al.so represent in~omplete a_ttacks. In addition, members 

of SCAMP proposed, for possible future consideration, several problems 

related to those on w~ch actual. work was perfo~ed. 

The valuable work o:r the participants from 1-FSA is not individual.11 

recorded in this report, sinq~ it would be difficult to do so without 

seeming to make comparisons among them. Much or their contributions took 

the fo:nn c;>f oral discuss:i,ons and Qf direct assistance to tile other 

members of SC.AMP, who are relatively unfamiliar with the :problems of AFSA. 

J. ·Administrative work. 

As indicated in Section 1 above, SCAMP was brought into being.with 

little time for advance planning. The writer, as chairman, assumed 

responsibility for almost all phases of the arrangements: (1) administration of funds, (2) recfU,itment or personnel, (3) scheduling of conferences and ffeminars, (4) general supervision or research acti.Vities, 

and of the r.epro~uction of reports. Thf!se duties nd.ght well have been 

divided among a number of people. The important matter 0£ a,rangtng for 

o.ffice space a~ equipmept was handled with the aid or c. B, Tompkins, 

who was in the Lo~ Angeles area in advance of the sympo.sium, am. with 

the cooperation of staff ~mberliJ ot INA ·am. UCLA. 

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GONFIDENTIAL 
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The space occupied by SCAMP consisted of Rooms 323 and 32,-329 inclusive in the old Chemistry Building at UCLA. Room 323 has a capacity 

of six persons without crowding, as does 32', which is divided into two 

.· rooms holding three each. Room 327 is likewise thus divided, with three 

.. desks in one part and appropriate space in the other tor the safe file, 

the librarian and the chairman. Rooms 326 ani 329 are offices for three 

each, and Room 328 was-used as ~ conference room. Such space is 

adequate for~ symposium of the· size of SCAMP. 

The SCAMP budget was set at a lump sum of $2.S,ooo, tran~ferred from 

/!FSA through t~e ONR to the IN.i\ 1 with assurances or further funds it 

essential to the success or the Wldertaking. Roughly speaking, about 

$18,ooo was allocated to salaries,, travel expenses an:i associated overhead, about $6,ooo to computing (SWAC and IBM), and about $11 000 to_ 

office. equipment, supplies,, telephone charges, and so on. Some computing 

on SWAC is still, in progr~ss, a.¢ some other addi Uonal expenses are yet 

to be incurred before the worl<: of SCAMP is completed. In a supplenait 

to this report, a breakdown of actual. expenditures as of 15 September 

will be gi. ven. It appears likely that some unexpended. funds will remain 

after that date and might well be used for further computation growing 

directly out of the work of SCAMP. Appendix IX contains correspond~~e 

relating to budgetary ma ttez:os. 

4. Proposals for the future. 

Suggestion~ for the immediate future were made to the Director of 

the Armed Forces S~curi ty Agency when he visited SCAMP on 14 August and 

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EONFIDENTI:A·L 
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eeNPmEN'i'Itii 

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conferred with the available SCAG members: s·. s. Cairns,, H. p. Robertson 

an:i c. B. Tompkins. It was recommended (1) tha't AFSA Spf:>nsor a second 

swnmer symposiwn similar '00 SCAMP at the sam~ location in 19~3, (2) that . . 

there be some work ~ t UCLA. on a red~ceq scale_ dutj.ng the academic year 

1952-J,, to avoid a·dis~ontinuity between the two symposiwns·ani (3) that 

decisions conc~J;'Ilin~ later efforts be re~ery-ed \lllti+ the work of SCAMP 

has been suitably evaluated. 

The foll9wi.ng suggestions·,,. SOJ!le or. -them -obvious ~ some resul. ting 

. . . from the experience of thi~ year'~ sympos:i,.uin,, may l'rove helptu;J.. in·f'uture 

planning. 

(1) It is of the greate~t i~portanc.e .to- start as early as practicable 

on the t~sk of recruiting arxi cleEμ'ing personn~l,, since clearance procedures are notoriously ti.me-consuming arxi. since the 

most de~irable matheinat.tcians are· likely '00 make other commit ... 

ments fo~ ·the summer, if n<,>t app~a.Ched early. 

(2) Alt.O.ough the resear~h program w~l~ be pa~tly dictated by the 

talents a.Iii interests of the particip$!1ts, there should be an 

early de9ision as tq·general objectives. Reference is made to I 

the following i terns in Appendix XI: 

(a) "N<!>tes on a proposed research project ard symposiwn, 11 

18 March 1952 by c. B. Tompkins. 

(b) Le~ter of 24 June 1~52 £rom Tompkins to D. c. 

Spencer. 

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t:.:. 

06lf PmEHYtrtL 

(c) Memorandum on "The Objectives of SCAMP" from 

s. s. Cairns to· the members of SCAMP, l/) July 19S2. 

Prospective participants should be informed or the 

general objecti·ve~ in advance and al.so, insofar as 

possi'Qle, of particular problems proposed l'or attack. 

(3) °It might be we}J. to have both an administrative an:l a technical 

· chainnan. The technical chairman, \IDO .might be chosen from . . 

.the INA or £ram UCLA, l«i~d assume responsibility for financial 

11eg<?~ ti.o~s wi-1:-h prospect:i.. ve participants and for the proVi.sion 

· of suitable wrking -space, office equi·pment so on. Some 

secretarial· assistance might be provided by the· INA, al though 

an AFSA lib;rarian is a+so· nee4ed to take care or th~ classified 

file~·~· .to ·prepare. cia·s.sified reports and to supervise their . : ' . . -

reproctucti,~rt. The technic.al chairman could concentrate on the 

research program, including tne planning or expository background .lectures,. presentation of ne"t-1 results and conferenoe 

d:i.scussi~ns devo·ted ·to work in proe,z:esa. He should also have 

the duty of preparing a-fina'.!- report. If thus freed from the 

non-"research administrative burden~ he might have time to do 

some mathematics h:j.111self. This division of duties,, or some 

modification the~eor, should make it easter to secure a good 

technical. chairman. 

(4) From. the first. planning stage on,, there might well be an advisory commit tee or fUlly cl eared nia thema ticians 1 who would 

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nominate the chairman or chainnen, ·establish a calendar of 

deadlines, nominate key personnel, an:l who would be kept informed of signific.'.l.Ilt developments both before and during 

. the symposium, so as to be in a posi ti.on to render the most 

useful advice. The advisory committee should,, ill: cooperation 

with the chairman, ensure that the problem& attacked during 

the symposium are relevant arxl important to· applications on a 

high security level. 

(5) A few carefully selected AFSA personnel should be assigned to 

the symposium for its entire duration arrl others, as this summer, 

for shorter periods o£ time. Those assigned for the whole 

period should include persons thoroughly familiar both with· the 

mathP.ma tical problems of AFSA and wi. th their prospective applications. Questions of secur.i ty (classification of problems,, 

reports and so on) should be decided by AFSA representatives. 

Appendix X contains suggestions from .SCP.MP participants relating to. 

various aspects of pos~ible future projects analogous to SCAMP. 

GOUFffif.N !!AL 

CONFIDENTIAL