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Summer 2010.

Paper & PencilCryptography

Handy Security ToolsGideon Samid Lectures

Cryptology and Data ProtectionINFA640

Cryptography, INFA 640, Gideon Samid [email protected] March 2010

Prof. G. Samid, (INFA 640)

Prof. G. Samid, (INFA 640)Your Personal Notebook

• Many record their passwords and secret keys on a personal notebook they carry everywhere – and lose everywhere.

• Once in the wrong hands, its totally compromised.

• It’s advisable to use ‘last defense’ cryptography to protect your secrets, or have a chance to, once you lose your note book.

• This last defense crypto tool will have to be easy for ordinary use..



Prof. G. Samid, (INFA 640)Last defense Crypto

• Usable by hand, (paper and pencil), easy, and fast way to conceal (encrypt) data.

• Should be very easy to encrypt and decrypt.

• Should be ‘additive’ – ready for re-encryption.

• Should be usable in extreme circumstances –without computers.



Prof. G. Samid, (INFA 640)Categories

• Arithmetic1. Digital Confusion

· 2. Modular Arithmetic · 3. Sieve Operations · 4. Memorized Formula

• Graphic



Prof. G. Samid, (INFA 640)Marked Expansion

Given P, a plain numeric (decimal) secret comprised of n digits, one is to inject m digits after digit number s, then concatenate P with sm, (resulting in the ciphertext number C). Decryption is in reverse, ignore m digits after digit s and ignore sm.

Example: P = 567812We add 7 digits (8321054), after the 3rd digit,

then concatenate the result with “37”, to result in:

C = 567832105481237 To decrypt: delete 7 digits from C starting from after the 3rd digit, remove the "37" at the end. It is advisable to mark the expanded number in a clear way, say a prefix of a symbol, like "&".

Note that the expanded number (cryptogram), C, may be re-expanded, like: C=567832105481237, add "312" at position 4, resulting in:

C' = 56783123210548123743 It would be advisable to mark C' with a prefix of "&&" to indicate two rounds of

expansion



Prof. G. Samid, (INFA 640)Digital Split

• Given P, a plain numeric (decimal) secret comprised of n digits, one is to split each of the n digits to two digits that add up to the split digit. This creates a cryptogram twice the size of the plaintext, P. Decryption is the same, in reverse: add all successive pairs of digits to recover the plaintext.

• Example: P =5871290 • One possible cryptogram: 23445210113600 • and another: 14624310209000 • The two cryptograms decrypt back to the same

plain text.



Prof. G. Samid, (INFA 640)Modular 100

• Given a numerical string, P, divide it from left to right to groups of 2 digits each, leaving an odd digit at the rightmost edge, if necessary. Let us denote the first pair as s1, the second pair as s2, etc. The number P will then be written as:

• P = s1* s2* ........ * sn

• where sn may be of one or two digits, the rest s numbers are two digits each.

• We now perform: • s'i= (si+ s1) Mod 100

• for all values of i=2,...n • The resultant cryptogram will be: C = s1* s'2* ........ * s'n Note that

the first group remains in tact, so that the decryptor will know which number to subtract from the written numbers.



Prof. G. Samid, (INFA 640)Modular 100 Exercise

• Example: P = 456723875 •

The groups are 45, 67, 23, 87, 5 Each group is computed to be:

67 + 45 = 112 Mod 100 = 12 23 + 45 = 68 Mod 100 = 68 87 + 45 = 132 Mod 100 = 32 5 + 45 = 50 Mod 100 = 50

• And the corresponding cryptogram: 4512683250 • To decrypt compute: 12 - 45 = -33 Mod 100 = 67 68 - 45 = 23 Mod 100 = 23 32 - 45 = -13 Mod 100 = 87

50 - 45 = 5 Mod 100 = 5 • This method is open to many modifications. It is possible to implement it

as Modular 10 doing the same one digit at a time, or Modular 1000, processing three digits at a time.



Prof. G. Samid, (INFA 640)Sieve Operation

• Transposition of digits according to sieve operation: Let P be a string of n decimal digits to be encrypted. Pick a natural number, r, and count r places from the left-most digit of P. The digit where the count stopped will become the first digit for the encrypted (transposed) cryptogram, mark that digit off from the original P string. Resume counting from the next (right next) digit, or from the beginning (left most) digit if you reached the end of P. The digit that stopped your second counting of r digits will become the second digit in the cryptogram, C. Mark that digit off from the P string. Continue counting r digits at the time over the remaining P digits, and each round of r counts (cycling back to the beginning when the end is reached) identifies the next digit in the cryptogram and causes that digit to be marked of P. This will continue until the original P has only one digit left. That digit becomes the last digit of the cryptogram. This process amounts to transposing the original order on a new one. Decryption goes in reverse.



Prof. G. Samid, (INFA 640)Sieve Illustration

• Example: P =568234. We choose r=4 and start counting from the left-most digit of P, namely "5". The digit "2" stops the count, and becomes the first in the cryptogram:

• C = 2 _ _ _ _ _ • P has now shrunk to 56834. The counting resume at digit "3" and ends at digit "6",

which becomes the second digit in the cryptogram: • C = 26_ _ _ _ • P has now shrunk to 5834, and the next counting start at "8" and ends at "5",

therefore: • C = 265 _ _ _ • The new P now looks as 834, and the new round of counting starts at "8" and ends at

"8", so we can write: • C = 2658 _ _ • and P has now shrunk to "34". The new count starts at "3" and ends at "4" so the final

result is: • C = 265843 • The same method would yield another cryptogram for r=3, namely:

Cr=3= 842635 •



Prof. G. Samid, (INFA 640)Tabular Cryptography

y,z,1,2,3,

4 Y Z 0 1 2 3

5,6,7,8,9,

0 4 5 6 7 8 9

a,b,c,d,e,f g,h,i,j,k,l m,n,o,p,q,r s,t,u,v,w,x y,z,1,2,3,4 5,6,7,8,9,0

a,b,c,d,e,f A B C D E F

g,h,i,j,k,l G H I J K L

m,n,o,p,q,r M N O P Q R

s,t,u,v,w,x S T U V W X

y,z,1,2,3,4 Y Z 0 1 2 3

5,6,7,8,9,0 4 5 6 7 8 9

26 letters + 10 digits marked by 6x6 options



Prof. G. Samid, (INFA 640)Tabular Crypto -- How

• This table encrypt any symbol of the chosen 36 capital letters and digits to a pair of lower-case letters and digits. Each encrypted symbol may be encrypted to 36 possible combinations of defining letters (marked on the vertical and horizontal edges of the matrix). This means that this encryption is polyalphabetical. The choice of letters may be random, or it may be used to deliver a subliminal message.

• Example: Let the plaintext be: P ="I LOVE LUCY," one corresponding cryptogram will be:

• C = gnAk9rpswayBg5xofmze (Capital letter follows a space)



Prof. G. Samid, (INFA 640)Subliminal Cryptography

• When a ciphertext will decrypt to one plaintext, and then decrypt further to a second plaintext.

• The cryptanalyst celebrates cracking the first level, leaving the deeper level undetected.

• The user of the subliminal cryptography will find that the first layer has been cracked by some actions on the part of the cryptanalyst, and use it to assess risk for breaking the deeper layer.



Prof. G. Samid, (INFA 640)Tabular Subliminal Cryptography

• . Since the plaintext here is comprised of 9 letters (ignoring spaces), there are 369 strings that converge, or decrypt to the same plaintext. This variety may be used to convey a subliminal message of same or shorter size. Note that each symbol inside the 6x6 matrix may be expressed via one of six symbols that identify the row of the encrypted symbol, and one of six symbols that identify the column of the encrypted symbol, together this computes to 36 combinations, which is sufficient to express the 26 letters of the alphabet and the digits 0-9. That means that any encrypted symbol will be able to deliver a subliminal symbol. So while the primary encrypted message might be "I LOVE LUCY" the subliminal one might say: "NOT TRUE".



Prof. G. Samid, (INFA 640)Configuration



Prof. G. Samid, (INFA 640)Summary

• Pencil & Paper cryptography is the last line of defense

• Used to record sensitive information in personal notebooks, and private pads.

• Used in special cases where computers are not operationally available.

• Used as added security in normal computing environment.

• Used as building blocks for high-variety professional complexity computing.



Prof. G. Samid, (INFA 640)Context

Cryptology is a weapon in the Unending CyberWar and must be considered in that context.

The CyberWar is a race of imagination. If your adversary can imagine ways to violate you, which you are too stream-lined to conceive of – then you are done for.



Prof. G. Samid, (INFA 640)Course Outline

• Review of modern day CyberWar• Cryptology in Context Overview• The History of Cryptology• Cryptology Today• Outlook• The Prevailing Cryptographic Tools• Deployment and Usage• Intractability Appraisal



Prof. G. Samid, (INFA 640)Course Objectives:

• To help you become an effective computer security executive by becoming profoundly educated about the use, the benefit, and the implications of modern cryptographic tools.

• To provide you with the tools to effectively negotiate, activate, and use professional cryptographers for your cyber security needs.



Prof. G. Samid, (INFA 640)INFA640 - Abstract

• An overview of the theory of encryption using symmetric and asymmetric keys, current protocols for exchanging secure data (including the Data Encryption Standard and the Advanced Encryption Standard) and secure communication techniques. A review of the historical development of cryptographic methods and cryptanalysis tools is provided. Public key infrastructure and the use of digital signatures and certificates for protecting and validating data are examined. Strategies for the physical protection of information assets are explored

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