Temasek Academy
Math of Passwords
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Chapter 1: Introduction to Cryptography
Cryptography is the study of message secrecy. Historically, cryptography has been used to encode
information to conceal secret messages from unauthorised parties and, as such, it is important for military and
national security use.
The development of information and communications technologies that allow vast quantities of data to
be transmitted, copied and stored quickly and easily has prompted a growing concern for the protection of privacy
and the confidentiality of data, including personal data, government administrative records, and business and
financial information. Effective cryptography is an essential tool in a network environment for addressing these
concerns. It is also used to protect classified government information.
In this course, we will study the developments of code writing from ancient times to our modern era, and
learn some of the classical ciphers, a modern cryptosystem, and certain aspects of Coding Theory.
Section
1.1
Terminology
Before we embark on this journey of discovery into the art of secrecy, let us introduce some special
words that we will be using in this elective.
“Cryptography” came from two root Greek words, meaning “secret writing”. (kryptós, meaning “hidden,”
and gráphein, meaning “to write”). In general, the study of the field of secret writing is called cryptography. In
layman terms, cryptography is the art of creating and studying secret “codes”.
“Cryptoanalysis” is the study of how to circumvent the use of cryptography, or in layman terms, the art
of codebreaking.
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“Cryptology” is the whole field of secret writing in general, comprising of both cryptoanalysis and
cryptography, i.e., the study of both making and cracking secret “codes”.
“Encryption” is the process of converting ordinary readable information, plaintext, into unreadable
gibberish, ciphertext.
“Decryption” is just the reverse process of converting the unreadable ciphertext back into the original
readable message, plaintext.
“Code or cipher” in layman terms, is the method used to encrypt the information. However, specifically,
the two terms mean different things in cryptography. Thus we will use the term cipher to represent the method.
Strictly speaking, cipher refers to the set of algorithms used in encryption and decryption.
A “key” refers to the parameters used in the cipher. A cipher can have many possible keys. (i.e., the more
keys a cipher has, the harder it is to crack the cipher.)
Note: The field of cryptography or cryptology should not be confused with the field of Coding Theory, which
involves the study of accuracy of transmission of data across channels, an error prone process.
Typing in Secret Message
Plaintext
Hacker
(Doing Cryptoanalysis)
Encryption
Stealing Secret Message
Ciphertext
Transmitting Secret Message
Ciphertext
Decryption
The Real Da Vinci Code
Leonardo DA Vinci wrote his notes with his
left hand using a technique of mirror
writing. The mirror script made his work
Figure1.2
1:
Development
of Cryptography
very Section
difficult to read.
To compound
the
Illustration of processes in
difficulty, he also made use of unusual
Cryptography
spellings and abbreviations, while
arranging his notes in no logical order.
Receiving Secret Message
Plaintext
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Task: Research on the development of cryptography and fill up the table below with the major events that
occurred during each period of time.
Read up on the ciphers you come across in your research and other classical ciphers.
1900 BC
Egyptian Hieroglyphic writing. The first known incidence of cryptography. A scribe used
nonstandard hieroglyphs in an inscription. This is the picture language that was used most often
to decorate temples and monuments. [Originally used to draw kings possessions]
600 BC
500 - 600 B.C. - ATBASH Cipher.
Hebrew scribes writing down the book of Jeremiah used a reverse-alphabet simple substitution
cipher known as the ATBASH cipher. The ATBASH cipher is a Hebrew code which substitutes the
first letter of the alphabet for the last and the second letter for the second last, and so on.
ATBASH to English
Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher: ZYXWVUTSRQPONMLKJIHGFEDCBA
500 BC
486 B.C. - Greek Skytale
Ancient Greeks invented the "Skytale" (rhymes with Italy), which was a stick wrapped with narrow
strips of papyrus, leather, or parchment.
The message was written on the wrapping; then the strip was removed and passed to the
messenger. Only if the receiver had the same size tube would they be able to read the message.
50 BC
Julius Caesar's simple substitution cipher.
This type of encryption is one of the simplest and most widely known encryption techniques. Each
letter of the plaintext is replaced by a letter some fixed number of positions further down the
alphabet. For example, a shift of 4 would move A to E, B to F, etc. Such as:
Plain: abcdefghijklmnopqrstuvwxyz Cipher: DEFGHIJKLMNOPQRSTUVWXYZABC
800
Around 800 AD, religiously motivated textual analysis of the Qur’an led to the invention of the
frequency analysis technique for breaking monoalphabetic substitution ciphers by al-kindi.
1500
In 1467,Leon Alberti invented the cipher disk and cryptographic key. Alberti's cipherdisk was
polyalphabetic, meaning that a new alphabet could be created each time by turning the disk. This
type of disk was the only method of using this type of cipher until the 16th century. This
assumption was based on his inquiries into frequency analysis, which is the most effective
method of deciphering monoalphabetic cryptograms.
1600
In 1626, the Great Cipher was developed by the rossignols. Each number stood for a French
syllable rather than single letters.
1800
In 1845, Samuel Morse created the Morse Code - Morse code represents letters, numbers and
punctuation marks by means of a code signal sent intermittently. This is an early form of digital
communication. It uses to states(on and off) composed into five symbols: dit('), dah(-), short gap
(between letters), medium gap (between words) and long gap (between sentences). Morse code
differed from the telegraph in the fact that it sent code for each letter on a single wire rather than
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a wire for each letter. In 1863, the European Morse Code was created.
1900
In 1917, the Zimmerman telegram was a secret telegram which included proposals for a German
alliance with Mexico. The telegram was intercepted and decrypted by the British Government.
1920
Arthur Scherbius designed the Enigma in 1918 - a device which allowed businesses to
communicate confidential documents without having to resort to clumsy and slow codebooks.
The device consisted of many rotors turning on a common axis. The rotors had numbers 1
through 26 marked on the edge, or the alphabet A-Z, and were equipped with 26 electrical
contacts (one for each letter of the alphabet) so that when a letter was pressed, the output would
depend on the position of the rotor and its cross wiring. Within that year, the Enigma was put to
use by the Nazi Germans before and during WWII.
1940
Captain Midnight radio show featured the “Code-O-Graph” at the finishing of each transmission,
where fans could request the program’s sponsors to get the Code-O-Graph and decode the secret
messages from the program. (Classic example of a cipher disk except that it used numbers instead
of letters.
1968
It is the start of John Walker’s 17 years of copying keys and sending them to the Soviet Union
during the Cold War. He helped the Soviet Union garner more than one million messages and
compromised US codes.
1976
1976 - Diffie Hellman
Whitfield Diffie & Martin Hellman publish Public-key Cryptography. This asymmetric key
cryptosystem was known as the Diffie-Hellman key exchange, and was the first published practical
method for establishing a secret key through unprotected communications channels without a
prior shared secret.
Note: In public key cryptography, a user has a pair of cryptographic keys—a public key and a
private key. The private key is kept secret, while the public key may be widely distributed.
Incoming messages would have been encrypted with the recipient's public key and can only be
decrypted with his corresponding private key. The keys are related mathematically, but the private
key cannot be practically derived from the public key.
Also, In encryption, a key specifies the particular transformation of plaintext into ciphertext, or
vice versa during decryption.
1991
Pretty Good Privacy (PGP)
PGP is a computer program that provides cryptographic privacy and authentication. PGP is often
used for signing, encrypting and decrypting e-mails to increase the security of e-mail
communications. It was originally created by Philip Zimmermann in 1991.
1999-2000
1999 -January RSA Data Security, establishes worldwide distribution of encryption product
outside the USA
National Institute of Standards and Technologies announces that 56-bit DES is not safe
compared to Triple DES
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German government wants to elaborate a cryptography-law, different organizations start a
campaign against that law.
computer hackers do no longer only visit websites and change little details there but cause
breakdowns of entire systems, producing big economic losses.
2010
Section 1.3
Related Readings
The list of readings below will be useful in this elective to understand more about the art of secrecy, but it is not
exhaustive. Feel free to find more related readings.
Readings (Books)
1)
The cracking code book: how to make it, break it, hack it, crack it
Author: Simon Singh
2)
The science of secrecy: the secret history of codes and code breaking
Author: Simon Singh
3)
652.8 SIN
652.8 SIN[BIZ], 652.809 SIN[BIZ],
Cryptography Demystified
Author: John E. Hershey
4)
Crypto: secrecy and privacy in the new code war
Author: Steven Levy
5)
005.82 HER[COM]
652.8 LEV[BIZ]
Cryptography for dummies
Author: Chey Cobb
005.82 COB[COM]
Available: Tampines Regional Library
Readings (Websites)
1)
Wikipedia Website
Cryptography Portal: http://en.wikipedia.org/wiki/Portal:Cryptography
Cryptography:
2)
http://en.wikipedia.org/wiki/Cryptography
Website of Author of “The Code Book”, Simon Singh:
http://www.simonsingh.net/
3)
Frode Weierud’s CryptoCellar: Cryptology and Its History
http://mad.home.cern.ch/frode/crypto/
4)
Beyond Discovery Website
http://www.beyonddiscovery.org/content/view.article.asp?a=3420
5)
Cryptology Essay by Oliver Pell
http://www.ridex.co.uk/cryptology/
6)
National Security Agency (USA)
http://www.nsa.gov/museum/
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