CRYPTOGRAPHY Lecture 4. Secure transmission Steganographycryptography TranspositionSubstitution Monoalphabetic.

CRYPTOGRAPHY

Lecture 4

Secure transmission

Steganography cryptography

Transposition Substitution

Monoalphabetic

Mono-alphabetic Substitution Cipher

• Allow any permutation of the alphabet• Each letter is replaced by a different

letter or symbol• Roughly 288 possibilities: checking 1

billion per second, would take 12 billion years

• Too many possibilities to break by brute force! This is a major strength of the substitution cipher.

Mono-alphabeticSubstitution Cipher

• The major weakness: frequency analysis can help break this kind of cipher.

• But unlimited substitution ciphers require exchange of a lot of information – the entire alphabet!

• A good key would be something you can look up in a book.

Frequency Analysis

Problem # 4a: Monoalphabetic Substitution cipher

SK BKGKC FBTKCHZWBT W ZXUBA HM SKOO,

WBT EWQK UZ MFC MSB, WH SXKB SK XWGK

TUHJMGKCKT UZ DMC MFCHKOGKH

Problem # 4b: Mono-alphabetic Substitution cipher

CGXTOUNZL NQ UDOU HDNTD BCJONLQ

HDCL ZLC DOQ WZBMZUUCL CACBEUDNLM

DC KCOBLCG NL QTDZZK.

Problem # 4c: Mono-alphabetic Substitution cipher

UWZEZ VTPUW ZBEIK WVRWT UPUZT UWPUV YZFZE PAIQB

SISVT RBFZE TZJPR UNIKW PUUWZ GAVFZ ETZVT YBEPA

SKWIV UVTWZ EZVUK VNNVA TUPAU NISVT PCCZP EPASQ ZEZCN PRZSQ ITBOZ UWVAX ZFZAO BEZQV HPEEZ PASVA

ZJCNV RPQNZ UWZEZ VTPAB UWZEU WZBEI KWVRW TUPUZ

TUWPU UWVTW PTPNE ZPSIW PCCZA ZS

What can we do to improve the substitution cipher?In 1460 Battista Alberti wrote an essay on what he believed to be a new form of cipher: use two or more cipher alphabets alternately to encrypt a message.ABCDEFGHIJKLMNOPQRSTUVWXYZ plain text

GHIJKLMNOPQRSTUVWXYZABCDEF cipher1

RSTUVWXYZABCDEFGHIJKLMNOPQ cipher2

Let’s encrypt the statementIT IS WAY TOO EARLY IN THE DAY TO BE DOING THISOK OJ CRE KUF KRXCE ZT KNV JRE KU SK UUZTX ZYOJ12 34 567 890 12345 67 890 123 45 67 89012 3456

Ciphers• Monoalphabetic ciphers: each letter in the

plaintext is encoded by only one letter from the cipher alphabet, and each letter in the cipher alphabet represents only one letter in the plaintext.

• Polyalphabetic ciphers: each letter in the plaintext can be encoded by any letter in the cipher alphabet, and each letter in the cipher alphabet may represent different letters from the plaintext each time it appears.

What can we do to improve the substitution cipher?Alberti was followed by Johannes Trithemius (born 1462) and Giovanni Porta (born 1535) who developed his ideas. Finally, Vigenere put all these ideas together. Let’s take a whole table of Caesar shift alphabets. The first row will have a Caesar shift of 1, the second of 2, etc. Each letter in the plaintext message can be enciphered by a different row.

Vigenere cipher:Start with a table of Caesar shift alphabets.

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 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 A C D E F G H I J K L M N O P Q R S T U V W X Y Z A BD E F G H I J K L M N O P Q R S T U V W X Y Z A B CE F G H I J K L M N O P Q R S T U V W X Y Z A B C DF G H I J K L M N O P Q R S T U V W X Y Z A B C D EG H I J K L M N O P Q R S T U V W X Y Z A B C D E FH I J K L M N O P Q R S T U V W X Y Z A B C D E F GI J K L M N O P Q R S T U V W X Y Z A B C D E F G HJ K L M N O P Q R S T U V W X Y Z A B C D E F G H IK L M N O P Q R S T U V W X Y Z A B C D E F G H I JL M N O P Q R S T U V W X Y Z A B C D E F G H I J K M N O P Q R S T U V W X Y Z A B C D E F G H I J K L N O P Q R S T U V W X Y Z A B C D E F G H I J K L M O P Q R S T U V W X Y Z A B C D E F G H I J K L M N P Q R S T U V W X Y Z A B C D E F G H I J K L M N O Q R S T U V W X Y Z A B C D E F G H I J K L M N O P R S T U V W X Y Z A B C D E F G H I J K L M N O P Q S T U V W X Y Z A B C D E F G H I J K L M N O P Q R T U V W X Y Z A B C D E F G H I J K L M N O P Q R S U V W X Y Z A B C D E F G H I J K L M N O P Q R S T V W X Y Z A B C D E F G H I J K L M N O P Q R S T U W X Y Z A B C D E F G H I J K L M N O P Q R S T U V X Y Z A B C D E F G H I J K L M N O P Q R S T U V W Y Z A B C D E F G H I J K L M N O P Q R S T U V W X Z 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

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 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 A C D E F G H I J K L M N O P Q R S T U V W X Y Z A BD E F G H I J K L M N O P Q R S T U V W X Y Z A B CE F G H I J K L M N O P Q R S T U V W X Y Z A B C DF G H I J K L M N O P Q R S T U V W X Y Z A B C D EG H I J K L M N O P Q R S T U V W X Y Z A B C D E FH I J K L M N O P Q R S T U V W X Y Z A B C D E F GI J K L M N O P Q R S T U V W X Y Z A B C D E F G HJ K L M N O P Q R S T U V W X Y Z A B C D E F G H IK L M N O P Q R S T U V W X Y Z A B C D E F G H I JL M N O P Q R S T U V W X Y Z A B C D E F G H I J K M N O P Q R S T U V W X Y Z A B C D E F G H I J K L N O P Q R S T U V W X Y Z A B C D E F G H I J K L M O P Q R S T U V W X Y Z A B C D E F G H I J K L M N P Q R S T U V W X Y Z A B C D E F G H I J K L M N O Q R S T U V W X Y Z A B C D E F G H I J K L M N O P R S T U V W X Y Z A B C D E F G H I J K L M N O P Q S T U V W X Y Z A B C D E F G H I J K L M N O P Q R T U V W X Y Z A B C D E F G H I J K L M N O P Q R S U V W X Y Z A B C D E F G H I J K L M N O P Q R S T V W X Y Z A B C D E F G H I J K L M N O P Q R S T U W X Y Z A B C D E F G H I J K L M N O P Q R S T U V X Y Z A B C D E F G H I J K L M N O P Q R S T U V W Y Z A B C D E F G H I J K L M N O P Q R S T U V W X Z 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

SAVEMEPLEASE plain text

CRYPTOGRAMCR keyword

URTTFSVCEMUV enciphered

The first letter, S is encrypted using the row beginning with CThe second letter, A is encryted using the row beginning with RThe third letter, V is encrypted using the row beginning with YThe fourth letter, E, is encrypted using the row beginning with P.And so on . . .

You can use http://www.simonsingh.net/The_Black_Chamber/v_square.html

Vigenere cipher

• The Vigenere cipher is a polyalphabetic cipher.

• Frequency analysis does not apply.• Enormous number of possible keys• It was then neglected for 2 centuries

– it is hard to break but also hard to encrypt.

Vigenere cipher: the unbreakable code

• At first glance the Vigenère Cipher appears to be unbreakable, due to its use of up to 26 different cipher alphabets. Ciphers like this, which use more than one cipher alphabet are known as Polyalphabetic Ciphers. These can be incredibly difficult to decipher, because of their resistance to letter frequency analysis. Indeed, over time, the Vigenère cipher became known as 'Le Chiffre Undechiffrable', or 'The Unbreakable Cipher'.

This slide and the next few copied directly from Simon Singh’s website.

Vigenere cipher: the unbreakable code

• It wasn't until 1854, over two hundred years later, that the Vigenère Cipher was finally cracked by the British cryptographer Charles Babbage. Babbage employed a mix of cryptographic genius, intuition and sheer cunning to break the Vigenère Cipher. Amazingly, his work was never published in his lifetime, and it was over a hundred years later, in the 1970's, that his technique was finally made public.

This slide and the next few copied directly from Simon Singh’s website.

Vigenere cipher: the unbreakable code

The strength of the Vigenère Cipher is that the same letter can be encrypted in different ways. For example, if the keyword is KING, then every plaintext letter can be encrypted in 4 ways, because the keyword contains 4 letters. Each letter of the keyword defines a different cipher alphabet in the Vigenère Square. . . whole words will be enciphered in different ways - the word 'the' could be enciphered as DPR, BUK, GNO and ZRM depending on its position relative to the keyword. Although this makes cryptanalysis difficult, it is not impossible.

This slide and the next few copied directly from Simon Singh’s website.

Next time . . .How Babbage cracked the

undecipherable cipher.

HW #4a: Vigenere

• 1. Encrypt the sentence “Simon Singh is a singularly talented writer” using the keyword “CODE”

• 2. Encrypt 1 message (at least 100 words long) using a chosen keyword. Swap and try to crack it.

HW # 4b: Monoalphabetic Substitution cipher

NBSQF VKLUV GZSGN BGVZQ SZMCR GZUVG RHABI FHSVW XGZMTVLMVE LQSGV LSGVQ TRUVM RGLKC GRHCV ZQZMC NRMVG VXZMM LSNRH HSGVQ VMVUV QDZHZ AZQTZ RMAVS SVQCQ RUVMG RHGVZ QSRMN VPVVO HNVZM CGRNR MLMVN BGVZQ SRMGR NGRHS GLFTG SHZMC HVMHV HTFRC VHGVK LUVHN BGVZQ SELQL MXVRS DZHGR HLDMR XGVQR HGGRH AVXZF HVRMN VRSAR CVHGR HGVZQ SGRHD LFMCQ VXVRU VCEQL NNBHR TGSNB GVZQS DZHDL FMCVC DRSGG RHDLF MCVCG VZQSE LQZHE QLNNV LMGRN GRHGF QSCRC KRTGS HLHSR KKNVS GLFTG SRMNV GRHGF QSCRC HNZQS ALSGV JFZKG FQSRM SGRHX GZMTV HLFTG SLFQA KRHHN BSQFV KLUVG ZSGNB GVZQS ZMCRG ZUVGR H

HW # 4c: Mono-alphabetic Substitution cipher

826821526251162515231172625148114  14826232621111161411615142623722526  14826168262326172213262514826232621111  11221614231252212142221622161827182625  8262326116252026232671782152625148114  14826232621111161411615142623722526  252610711112512011 

Websites which help

http://www.geocities.com/cryptogramcorner/

http://cs.colgate.edu/faculty/nevison/Core139Web/tools/substitution.html