Presentation on the topic of the mystery of cryptography. Cryptography Scientific supervisor: Ovcharenko Lyudmila Pavlovna computer science teacher Municipal educational institution Secondary school

Cryptography is the science of ensuring the secrecy of a message.

Cryptology is a branch of mathematics that studies the mathematical foundations of cryptographic methods

Periods of cryptography: 1. The first period (from approximately the 3rd millennium BC) is characterized by the dominance of mono-alphabetic ciphers (the basic principle is the replacement of the original text alphabet with another alphabet through the replacement of letters with other letters or symbols)

CAESAR CIPHER (shift cipher, Caesar shift) 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 D E F G H I J K L M N O P Q R S T U V W X Y Z A B C Example of Caesar cipher (encryption using key K=3): Encrypt the word “FAMILI” We get: IDPLOL (shift by 3)

An example of encryption using the key K=3 in the Russian alphabet. Original alphabet: A B C D E E F G H I J K L M N O P R S T U V X C CH W Y Y Y Z Ciphered: G E F G H I J K L M N O P R S T U V H C C H W S H Y Y Y A B V Original text: To succeed, students need to catch up with those who are ahead and not wait for those who are behind. The cipher text is obtained by replacing each letter of the original text with the corresponding letter of the encrypted alphabet: Tsъзрлнгп ъхсдиу тустзфтзхя ргжсжсёсрхя хзш НХС езузжл l рз йжгхя хзш НХС сткгжл

2. The second period (chronological framework - from the 9th century in the Middle East (Al-Kindi) and from the 15th century in Europe (Leon Battista Alberti) - until the beginning of the 20th century) was marked by the introduction of polyalphabetic ciphers into use

For example, in the encryption process, the Vigenère table is used, which is structured as follows: the entire alphabet is written out in the first line, and in each subsequent line a cyclic shift is carried out by one letter. This results in a square table, the number of rows of which is equal to the number of letters of the alphabet.

3. The third period (from the beginning to the middle of the 20th century) is characterized by the introduction of electromechanical devices into the work of cryptographers. At the same time, the use of polyalphabetic ciphers continued.

For example, the German Enigma machine was used to encrypt classified information during the Second World War. The Second World War served as a catalyst for the development of computer systems - through cryptography.

Wehrmacht Enigma ("Enigma") Cipher machine of the Third Reich. The code created using Enigma is considered one of the strongest used in World War II. Turing Bombe A decoder developed under the direction of Alan Turing. Its use allowed the Allies to crack the seemingly monolithic Enigma code.

4. The fourth period - from the mid to 70s of the XX century - the period of transition to mathematical cryptography. In Shannon's work, strict mathematical definitions of the amount of information, data transfer, entropy, and encryption functions appear. A mandatory step in creating a cipher is to study its vulnerability to various known attacks - linear and differential cryptanalysis. However, until 1975, cryptography remained “classical” or, more correctly, secret key cryptography.

5. The modern period of development of cryptography (from the late 1970s to the present) is distinguished by the emergence and development of a new direction - public key cryptography.

Cryptanalysis is the science of how to break an encrypted message, that is, how to extract the plaintext without knowing the key.

The relationship between algebra and critology

Def. 1. Encryption is the reversible transformation of plaintext into ciphertext. It is defined by two mutually inverse mappings, Ek: T →C and Dk: C→T, where T is the set of plaintexts, C is the set of all ciphertexts, k is the key chosen from the key space K. If we denote by E the set ( Ek : k∈K ) of all encryption mappings, and through D the set ( Dk: k∈K ) of all decryption mappings, then for any t ∈T, k∈K the equality Dk (Ek (t)) =t holds. Then the collection (T, C, K, E, D) is called a cipher, or cipher system. The simplest and oldest classes of ciphers are permutation and substitution ciphers. In these ciphers C = T =, where A is the text alphabet, n is the message length.

Def. 2. The role of key k in the permutation cipher is played by an arbitrary permutation k∈Sn from the permutation group of the set (1, ..., n); Thus, the key space K=Sn, the encryption mapping is determined by the equality: and the decryption mapping is determined by the equality:

Def. 3. The role of key k in the substitution cipher is played by an arbitrary permutation k ∈ Sn from the group of permutations of the alphabet A; Thus, the key space K = Sn, the encryption mapping is given by: and the decryption mapping is given by:

Example. 1. If history is to be believed, the first permutation cipher was used in Sparta. A narrow parchment ribbon was wound tightly, turn to turn, around the cylinder, which was called a scital. Then, text was written along the axis of the cylinder. When the tape was removed from the cylinder, a chain of letters remained on it, at first glance, completely disordered. The tape was wound up and handed over to the recipient, who read the message by winding the tape around the same citala. After this, the text again became understandable. The key to the cipher is the diameter of the scital. Therefore, she did not protect trusted secrets very well, because soon enough, Aristotle came up with the device of the “anti-scital,” who proposed winding a tape around a cone, moving it from the top to the base of the cone. Where the diameter of the conical section coincided with the diameter of the scital, meaningful syllables and words appeared on the tape, after which a scital of the appropriate diameter was made and the letters were combined into a coherent text.

Example 2: The first substitution cipher was invented by Julius Caesar. To rearrange the letters of the alphabet, he simply used a cyclic shift of three letters. The reverse permutation is also, naturally, a cyclic shift. In general, this cipher used a shift type and the key was the number k. Since the key space is small, Caesar’s encryption algorithm apparently did not advertise much.

Example 3. The class of permutation ciphers includes route permutation ciphers. This is their idea. The message is written to the table along one route, for example along horizontal lines, and read through another, for example along vertical lines. To increase the key space, the table columns were also rearranged.

CIPHER WITH LETTERS REPLACED BY NUMBERS 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 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 For example: “LIFE” - “12 9 6 5"

NUMERIC TABLE The first digit in the code is a column, the second is a row, or vice versa. So the word “MIND” can be encrypted as “33 24 34 14”.

POLYBIUS SQUARE 1 METHOD. Instead of each letter in a word, the corresponding letter below is used (A = F, B = G, etc.). Example: CIPHER - HOUNIW. 2 METHOD. The numbers corresponding to each letter from the table are indicated. The first number is written horizontally, the second – vertically. (A = 11, B = 21...). Example: CIPHER = 31 42 53 32 51 24

Color chart A B C D E E F G H I J K L M N O P R S T U V H C CH W S H Y J 0 1 2 3 4 5 6 7 8 9 . , : ; ! ? The first color in the code is a row, the second is a column

Source text: The purpose of studying this topic is to familiarize students with the theory of text encryption, as well as to develop skills in studying mathematical objects and methods of using them in teaching and organizing research work for schoolchildren; involving students in research activities. Encrypted text:

Julian Assange R. 1971 On his portal, WikiLeaks publicly demonstrated to everyone the underbelly of many government structures. Corruption, war crimes, top-secret secrets - in general, everything that an active libertarian could get his hands on became public knowledge. In addition, Assange is the creator of an infernal cryptosystem called “Deniable encryption”. This is a way of arranging encrypted information that allows for plausible deniability of its presence.

Bram Cohen R. 1975 American programmer, originally from sunny California. To the delight of the whole world, he came up with the BitTorrent protocol, which is still successfully used to this day.

Films Zodiac 2007. An intense thriller by David Fincher, based on real events. For most of the film, the smartest San Francisco police officers try in vain to crack the code of the presumptuous maniac. Enigma 2001. A live-action film set in the backdrop of World War II: brilliant mathematicians gather in Bletchley Park to solve the new code of the insidious Nazis. The picture is full of inexplicable mysteries and secrets - however, you can guess this from the title.

Every user of electronic means of information exchange will need familiarity with cryptography, so cryptography in the future will become a “third literacy” on a par with the “second literacy” - computer and information technology skills.

Classification of ciphers and their features

Cryptography

The work was completed by: Artamonova Ekaterina gr.6409-ok

Subject of research: cryptographic systems and types of ciphers

Purpose of the study: study of cryptographic methods for encrypting information

Research objectives:

• Study the features of various cryptographic systems;
• Explore different types of ciphers.

Research methods: literature analysis, comparison, synthesis.

Cryptography as a Privacy Tool

Cryptography(from ancient Greek κρυπτός - hidden and γράφω - I write) - the science of privacy practices(impossibility for outsiders to read information) and authenticity(integrity and authenticity of authorship, as well as the impossibility of renouncing authorship) information.

History of the development of the science of cryptography

Formally, cryptography (from Greek - “secret writing”) is defined as a science that ensures the secrecy of a message.

The history of cryptography goes back about 4 thousand years. As the main criterion for the periodization of cryptography, it is possible to use the technological characteristics of the encryption methods used:

1.First period(3 thousand BC e.)

Monoalphabetic ciphers

The basic principle is to replace the alphabet of the source text with another alphabet by replacing letters with other letters or symbols

2.Second period(9th century in the Middle East(Al-Kindi) and 15th century in Europe(Leon Battista Alberti) - early 20th century) - polyalphabetic ciphers.

Leon Battiste Alberti

3. Third period(from the beginning to the middle of the 20th century) - the introduction of electromechanical devices into the work of cryptographers.

Continued use of polyalphabetic ciphers.

4.Fourth period -from the 50s to the 70s of the XX century- transition to mathematical cryptography. In Shannon's work, strict mathematical definitions of the amount of information, data transfer, entropy, and encryption functions appear.

Claude Shannon

5.Modern period(from the late 1970s to the present time) the emergence and development of a new direction - public key cryptography.

Another periodization of the history of cryptography is also known:

1.Aeneas Tactician wrote the first scientific work on cryptography.

The Scytala cipher is widely known - Sparta against Athens in the 5th century BC. uh.

2. Middle Ages

-Code Copiale- an elegantly designed manuscript with watermarks, which has not yet been fully deciphered.

Code Copiale

3.Renaissance - the golden age of cryptography: Francis Bacon studied it and proposed a binary encryption method.

Francis Bacon

4. The appearance of the telegraph- the fact of data transfer is no longer secret.

5.World War I-cryptography has become a recognized combat tool.

6.World War II-development of computer systems. The encryption machines used clearly demonstrated the vital importance of information control.

Wehrmacht Enigma (“Enigma”)-

Cipher machine of the Third Reich.

Turing Bombe

A decoder developed under the direction of Alan Turing.

Classification of cryptographic systems

General use cryptosystems

Restricted Cryptosystems

1. By area of ​​application

2. According to the features of the encryption algorithm

Single-key

Two-key

Substitutions (substitutions)

Rearrangements

Additive (gamming)

Deterministic

Probabilistic

Quantum

Combined (composite)

3. By the number of message characters

Streaming

4. According to the strength of the cipher

unstable

practically resistant

perfect

Basic requirements for cryptosystems

• The complexity and laboriousness of encryption and decryption procedures;
• Time and cost costs for information protection;
• Encryption and decryption procedures;
• The number of all possible cipher keys;

• Redundancy of messages;
• Any key from a variety of possible ones;
• Minor key change;
• Encrypted message.

Code (from French. chiffre"digit" from Arabic. صِفْر‎‎, sifr“zero”) - any text conversion system with a secret (key) to ensure the secrecy of transmitted information.

Cipher classification

Rearrangements

Compositional

Multiple-valued

Single digit

Symmetrical

Asymmetrical

In-line

Mono-alphabetic

Polyalphabetic

Gamma ciphers

Affine cipher

An affine cipher is a simple substitution cipher that uses two numbers as a key. The linear dependence of an affine cipher can be like this:

Caesar Cipher

Replacing plaintext characters according to formula, for example like this:

N is the number of the character in the alphabet

INFORMATION LRISUQDWMDSR

Dancing men code

Advantage - due to shorthand properties encryption can be written anywhere. Disadvantage - does not provide sufficient confidentiality or authenticity.

P R O T I V O I D I E

Vigenère cipher

A word (phrase) that is convenient for memorization is taken as the key of the Vigenère cipher; the word (code phrase) is repeated until it becomes equal to the length of the message.

Vigenère table

To encrypt a message with a Vigenère cipher using a Vigenère table, select the column starting with the first character of the plaintext and the row starting with the first character of the key. At the intersection of these columns and rows there will be the first encryption character.

Barcodes

Linear barcode

Bar code (barcode) is graphic information applied to the surface, marking or packaging of products, making it readable by technical means - a sequence of black and white stripes or other geometric shapes.

Information encoding methods:

1.Linear

2.Two-dimensional

Areas of application

• Increasing the speed of document flow of payment systems;
• Minimizing data reading errors by automating the process;
• Employee identification;
• Organization of time recording systems;
• Unification of forms for collecting different types of data;
• Simplification of warehouse inventory;
• Monitoring the availability and promotion of goods in stores, ensuring their safety.

The main advantage of a QR code is its easy recognition by scanning equipment.

Conclusion

1. There is a unified classification of cryptographic systems according to various parameters, each of which has its own distinctive features, advantages and disadvantages.

2. There are a huge number of ciphers in the world, which in turn can be combined into groups according to individual characteristics.

3. Cryptography is relevant now, because information protection today is one of the most serious problems of humanity in the information society.

Sources

http://shifr-online-ru.1gb.ru/vidy-shifrov.htm

http://studopedia.org/3-18461.html

KeyKEY
Key - a cipher parameter that determines
selection of a specific transformation of a given
text.
In modern ciphers the algorithm
encryption is known, and cryptographic
the strength of the cipher is entirely determined
key secrecy (Kerkhoffs principle).

Encryption-applications
cryptographic conversion
plaintext based algorithm and
key
ciphertext.
Decryption is a normal process
application of cryptographic
converting ciphertext to
open.

Types of text

TYPES OF TEXT
Open (source) text - data
transmitted without use
cryptography
Closed (ciphered) text - data,
received after application
cryptosystems with the specified key.

History of cryptography

HISTORY OF CRYPTOGRAPHY
Methods of secret correspondence were invented
independently in many ancient states,
such as Egypt, Greece and Japan.

The first examples of cryptography

tattoo

TATTOO
Herodotus (484 BC – 425 BC)
Tattoo made on shaved
slave's head, hidden under
regrown hair.

Scytala (cipher of Ancient Sparta)

SCYTALA (CIPHER OF ANCIENT SPARTA)
The hermitage was first mentioned in Greek
the poet Archilochus.
A scytale is a wooden cylinder.
(from Greek Σκυτάλη - rod)
Crypto communication requires two cylinders (one
wandered from the one who will send the message,
the other is at the addressee.
The diameter of both should be
strictly the same.

Encryption principle

ENCRYPTION PRINCIPLE
1
4
Sending to recipient
3
2

Bible

BIBLE
Book of the prophet Jeremiah (22.23): "...and the king
Sessakha will drink after them."
In the original language we have the word
Babylon.

Atbash

ATBASH
Original text:
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Encrypted text:
ZYXWVUTSRQPONMLKJIHGFEDCBA

Alberti ciphertext disk

DISC WITH ALBERTI CIPHERTEXT
Leon Battista Alberti
(1404-1472)
"Treatise on Ciphers"
The first letter is encrypted by
the first cipher alphabet,
second by second, etc.

Cardan grille

GRILLE TO CARDAN
Gerolamo Cardano (1501-1576)
"YOU KILL AT ONCE"
"I LOVE YOU. I HAVE YOU DEEP UNDER MY
SKIN. MY LOVE LASTS
FOREVER IN
HYPERSPACE."

Pyotr and Modest Tchaikovsky

PETER AND MODEST TCHAIKOVSKY
Replacing each vowel of the Russian language with
another vowel, each consonant - to another
I agree:
"shyr-pir yu pyapyuzhgy zelemgy gesryg"
instead of:
“Once upon a time there lived a gray boy with his grandmother
goat."

Vigenère cipher

VIGENÉRE CIPHER
Key - ABC

Literature about cryptography

LITERATURE ABOUT CRYPTOGRAPHY
"Treatise on Ciphers" by Gabriel de Lavind
"Encyclopedia of all sciences", Shehaba
Kalkashandi (classification methods
content of correspondence)
Intelligence Service, Oliver Cromwell
(decryption section)
"Military Cryptography" by Auguste Kerghoffs
…

Cipher

CIPHER
(from Arabic: ص ْفر
ِ,ṣifr “zero”, fr. chiffre "digit";
related to the word number)
Cipher - a set of algorithms
cryptographic transformations.

Cipher
symmetric
asymmetrical

classic types of encryption

CLASSICAL TYPES OF ENCRYPTION

easy replacement

EASY REPLACEMENT
a b c d e f... i
1 2 3 4 5 6 ... 33
Or:
A b c d t f ...
! @ # $ % *...
Example:
33 9 29 12 16 9 15 1 15 10 6
LINGUISTICS

Permutation view

PERMANENT VIEW
The letters of the message are rearranged:
"help me"
"I'll come on Tuesday"
"remember me"
"rpdiu ov tvroink"

Replacement view

SUBSTITUTE VIEW
Replace each letter with the next one in
alphabet:
"very fast"
"pshzhoy vutusp"
“good bye”
"hppe czf"

Caesar's cipher

CAESAR'S CIPHER
N
o p Rs...
Julius Caesar used a cipher with
offset 3 when communicating with your
commanders during military campaigns.

Cryptography and other sciences

CRYPTOGRAPHY AND OTHER SCIENCES
Until the 20th century, cryptography dealt only with
linguistic samples.
Now:
use of mathematics
part of engineering
application in quantum cryptography
physicists

CRYPTOGRAPHY
PERSISTENT
WEAK

Cryptographic attack

CRYPTOGRAPHIC ATTACK
Cryptographic attack - results
cryptanalysis of a specific cipher.
Successful
cryptographer
attack
breaking
opening

Enigma rotary crypto machine

ROTARY CRYPTOMACHINE ENIGMA
First encryption
car.
Used
German troops
from the late 1920s to
end of World War II
war.

Disassembled rotor
1. ring with notches
2. marking point
3. for pin "A"
4. alphabet ring
5. tinned contacts
6. electrical wiring
7. pin contacts
8. spring lever for
9. ring settings
10. bushing
11. finger ring
12. ratchet wheel

Enigma rotors assembled

ENIGMA ROTORS ASSEMBLED

Enigma encryption examples

EXAMPLES OF ENIGMA ENCRYPTION
E = PRMLUL − 1M − 1R − 1P − 1
E = P(ρiRρ − i)(ρjMρ − j)(ρkLρ − k)U(ρkL − 1ρ −
k)(ρjM − 1ρ − j)(ρiR − 1ρ − i)P − 1

German crypto machine Lorenz

GERMAN CRYPTOMACHINE LORENZ

Cryptanalysis

CRYPTOANALYSIS
Cryptanalysis is the science of methods of obtaining
original encrypted value
information without having access to secret
information (key) necessary for this.
(William F. Friedman, 1920)

A cryptanalyst is a person who creates and
using cryptanalysis methods.

cryptology

CRYPTOLOGY
Cryptology is a science that deals with methods
encryption and decryption.

modern cryptography

MODERN CRYPTOGRAPHY
Includes:
asymmetric cryptosystems
electronic digital signature systems
(EDS) hash functions
key management
obtaining hidden information
quantum cryptography

Modern cryptography

MODERN CRYPTOGRAPHY
Common algorithms:
symmetric DES, Twofish, IDEA, etc.;
asymmetric RSA and Elgamal
hash functions MD4, MD5, GOST R 34.11-94.

List of manufacturers using microdots:

LIST OF MANUFACTURERS USING
MICRODOTS:
Audi
BMW in Australia
Mitsubishi Ralliart
Porsche
Subaru
Techmashimport in Russia
Toyota

Digital watermarks

DIGITAL WATERMARKS
Digital watermark is a special
a label embedded in digital content with
for the purpose of copyright protection.

The relevance of encryption today

RELEVANCE OF ENCRYPTION TODAY
widespread use of the World Wide Web
the emergence of modern heavy-duty
computers

the scope of application has expanded
computer networks
possibility of discrediting encryption
systems that just yesterday were considered completely
safe

Information security tools today

INFORMATION SECURITY TODAY

Bibliography

BIBLIOGRAPHY
o
o
o
o
o
o
o
o
o
o
o
Practical cryptography, A.V. Agranovsky
English-Russian dictionary-reference book on cryptography
Encryption algorithms, S. Panasenko
Dictionary of cryptographic terms, Pogorelova
B.A.
http://crypto-r.narod.ru
http://www.cryptopro.ru
http://dic.academic.ru
http://www.citforum.ru
http://www.krugosvet.ru
http://cryptolog.ru
http://www.kpr-zgt.ru

• generalize and systematize knowledge of basic concepts: code, coding, cryptography;
• get acquainted with the simplest encryption methods and their creators;
• practice the ability to read codes and encrypt information.

Developmental:

• develop cognitive activity and creative abilities of students;
• form logical and abstract thinking;
• develop the ability to apply acquired knowledge in non-standard situations;
• develop imagination and attentiveness.

Educational:

• cultivate a communicative culture;
• develop cognitive interest.

Slide 1. « Cryptography Basics »

Recently, more and more attention has been paid to ensuring the security of communications, data storage, confidentiality of data access and similar aspects. Numerous solutions are offered, both at the hardware and software levels.

Please note that the use of data encryption does not guarantee the confidentiality of this data. The simplest example is to intercept an encrypted message, determine the block/blocks corresponding to the sending time, and then use the same encrypted message, but with a different sending time. This technique can be used to falsify messages between banks, for example to transfer sums of money to an attacker's account.

Cryptography only provides algorithms and some techniques for client authentication and information encryption. How did encryption come about in the first place?

Slide 2.

Cryptography(from ancient Greek κρυπτ?ς - hidden and γρ?φω - write) - (impossibility of reading information by outsiders) and authenticity(integrity and authenticity of authorship, as well as the impossibility of renouncing authorship) information.

Slide 3.

Cryptanalysis(from ancient Greek κρυπτ?ς - hidden and analysis) - the science of methods for deciphering encrypted information without a key intended for such decryption.

The most famous ciphers are:

Slide 4: The cipher of the wanderer

Lycurgus was the king of Sparta from the Eurypontid family, who ruled from 220 to 212 BC. e.

In cryptography wandered(or scitala from Greek σκυτ?λη , rod), also known as Ancient Sparta code, is a device used to perform permutation encryption, consisting of a cylinder and a narrow strip of parchment wound around it in a spiral, on which a message was written. The ancient Greeks and the Spartans in particular used this code to communicate during military campaigns.

Slide 5: Caesar Cipher

Gaius Julius Caesar (100 BC - 44 BC) - ancient Roman statesman and politician, dictator, commander, writer.

Caesar Cipher, also known as shift cipher, Caesar code or Caesar's shift is one of the simplest and most widely known encryption methods.

Slide 6: Francois? Vie?t

Francois? Vie?t (1540 - 1603) - French mathematician, founder of symbolic algebra.

At the royal court, François Viète showed himself to be a talented specialist in deciphering complex ciphers (secret writing) used by inquisitorial Spain in the war against France. Thanks to its complex code, militant Spain could freely communicate with the opponents of the French king even within France, and this correspondence remained unsolved all the time.

As one would expect, after the French deciphered the intercepted Spanish secret reports, the Spaniards began to suffer one defeat after another. The Spaniards were perplexed for a long time about the unfavorable turn in military operations for them. Finally, from secret sources they learned that their code was no longer a secret to the French and that the person responsible for deciphering it was François Viête. The Spanish Inquisition declared Vieta an apostate and sentenced the scientist in absentia to be burned at the stake, but was unable to carry out his barbaric plan.

Slide number 7: John Wallis

The term “cryptography” was introduced into widespread use by the English mathematician, one of the predecessors of mathematical analysis as a science, John Wallis.

In 1655, Wallis published a large treatise, The Arithmetic of the Infinite, where he introduced the infinity symbol he invented. In the book, he formulated a strict definition of the limit of a variable quantity, continued many of Descartes’ ideas, introduced negative abscissas for the first time, and calculated the sums of infinite series - essentially integral sums, although the concept of an integral did not yet exist.

Slide number 8: Leon Batista Alberti

Batista Alberti, Italian architect, sculptor, art theorist, artist and musician. He made a revolutionary breakthrough in European cryptographic science in the 15th century. In the field of cryptography, Alberti's merits were the 25-page “Treatise on Ciphers” - he published the first book in Europe devoted to cryptanalysis, and invented a device that implements a polyalphabetic substitution cipher, called the “Alberti disk”.

Slide #9: William Friedman

American cryptographer, one of the founders of modern scientific cryptography. During World War I, Friedman served in the American Cryptographic Service, including as a codebreaker. In addition to his cryptanalytic work, Friedman taught a course in cryptography for army officers. By 1918, he had prepared a series of eight lectures for listeners. In total, Friedman wrote 3 textbooks on military cryptography and a number of scientific works on the analysis of codes and ciphers, and he also developed 9 cipher machines. Friedman demonstrated the effectiveness of probability-theoretic methods in solving cryptographic problems. He took part in the development and evaluation of the strength of a number of American encryptors. Before and during World War II, he made significant progress in deciphering Japanese messages.

Slide No. 10: Types of ciphers

Thus, the main types of ciphers are:

• monoalphabetic substitution
• polyalphabetic substitution

Slide 11: Mono-alphabetic substitution

Mono-alphabetic substitution is an encryption system that uses a single cipher alphabet to hide the letters of a clear message.

In Europe by the beginning of the 15th century. Mono-alphabetic ciphers were most often used as a method of masking information. In mono-alphabetic substitution, special characters or numbers can also be used as equivalents. In a mono-alphabetic cipher, a letter can not only be replaced by a letter; in it, a letter can be represented by several equivalents.

Slide 12:

Shift Cipher (Caesar Cipher)

One of the earliest and simplest varieties of cipher that uses letter substitution is the Caesar substitution cipher. This cipher is named after Gaius Julius Caesar, who used it to encrypt messages during his successful military campaigns in Gaul (an area covering modern France, Belgium, parts of the Netherlands, Germany, Switzerland and Italy).

Plain text alphabet: A B C D E E F G H I J K L M N O P R S T U V H C CH W SQ Y Y Y Y

Cipher alphabet: G D E E F G H I J K L M N O P R S T U V

Slide 13: Multi-alphabetic replacement

Multi-alphabetic substitution is a method of generating a cipher using several substitution alphabets.

This technique allows cryptographers to hide the words and sentences of their original message among the meanings of several levels of letters.

Slide 14:

This table was one of the first geometric figures used to accommodate alphabets, numbers and symbols for the purpose of encryption, and an important step forward, since it showed all its cipher alphabets at the same time.

Trithemius called his method the "square board" because the 24 letters of the alphabet were arranged in a square containing 24 lines. Part of this table is shown here.

The table is obtained by shifting the normal alphabet in each subsequent line one position to the left. Letters i And j, as well as And And v, were considered identical. This operation could rightfully be called the very first serial key, whereby each alphabet is used in turn before any of them appears again.

The cryptographic advantages of polyalphabetic ciphers and sequential keys contributed to the widespread adoption of this encryption method.

Slide 15:

Since 1991 Institute of Cryptography, Communications and Informatics of the FSB Academy

The Russian Federation holds annual Olympiads in cryptography and

mathematics for schoolchildren in Moscow and the Moscow region. We present to your attention one of the tasks of the Olympiad:

An encrypted message is given:

Find the original message if you know that the transformation cipher was as follows. Let the roots of the trinomial - . To the serial number of each letter in the standard Russian alphabet (33 letters), the value of the polynomial, calculated either at or at (in an order unknown to us), was added, and then the resulting number was replaced by the corresponding letter.

Slide 16: The solution of the problem.

It's easy to see that .

Hence the roots of the polynomial

We get

Answer: KEEP IT UP

Slide 17. THANK YOU FOR YOUR ATTENTION!

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"fundamentals of cryptography"

Cryptography (from ancient Greek κρυπτός - hidden and γράφω - I write) - the science of privacy practices (impossibility for outsiders to read information) and authenticity (integrity and authenticity of authorship, as well as the impossibility of renouncing authorship) information.

The cipher of the wanderer

Lycurgus - King of Sparta

from the genus Eurypontidae,

ruling

in 220 - 212 BC uh .

Caesar Cipher

Gaius Julius Caesar

(100 - 4 4 BC e.) -

ancient Roman

state and

political figure,

dictator . , commander,

writer.

Francois Viet

Francois Viet (1540 – 1603) -

French mathematician

founder

symbolic algebra.

John Wallis

1616 – 1703 yy .

English

mathematician, one of the predecessors

mathematical analysis

Leon Batista Alberti

1402 – 1470 yy .

Italian architect, sculptor, art theorist, painter and musician

William Friedman

18 9 1 G ., Chisinau – 1969 G ., Washington

American cryptographer, called the "father of American cryptology"

• monoalphabetic substitution
• polyalphabetic substitution

Mono-alphabetic substitution

Mono-alphabetic substitution is an encryption system in which a single alphabet cipher is used to hide the letters of a plaintext message.

• Plain text alphabet: A B C D E E F G H I J K L M N O P R S T U V H C CH W SQ Y Y Y Y
• Cipher alphabet: G D E E F G H I J K L M N O P R S T U V

Polyalphabetic replacement

Polyalphabetic substitution is a method of generating a cipher using multiple substitution alphabets.

The solution of the problem:

Letter sh.s.

Number

Number

Letter o.s

Literature

1. Arshinov M.N. Sadovsky L.E. Codes and mathematics. - M.: Nauka, 1983. – 216 p.

2. Babash A.V., Shankin G.P. History of cryptography. Part 1. – M.: Helios ARV, 2002. – 240 p.

3. Babash A.V., Shankin G.P. Cryptography. / Edited by V.P. Sherstyuk, E.A. Primenko.

– M.: SOLON-R, 2007. – 512 p.

4. Barichev S.G., Goncharov V.V., Serov R.E. Fundamentals of modern cryptography. – M.: Hotline-Telecom, 2001. – 120 p.

5. Introduction to cryptography / Ed. ed. V.V. Yashchenko. - M.: MTsNMO: “CheRo”, 1999. – 317 p.

6. Werner M. Basics of coding. Textbook for universities. – M.: Tekhnosphere, 2006. – 288 p.

7. Gerasimenko V.A., Malyuk A.A. Fundamentals of information security. - M.: MEPhI, 1997. – 537 p.

8. Gribunin V.G., Okov I.N., Turintsev I.V. Digital steganography. – M.: SOLON-Press, 2002. – 272 p.

9. Domashev A.V. and others. Programming information security algorithms. Tutorial. – M.: Knowledge Publishing House, 2002. – 416 p.

10. Zhelnikov V. Cryptography from papyrus to computer. - M.: ABF, 1997. - 336 p.

11. Coutinho S. Introduction to number theory. Algorithm RSA. – M.: Postmarket, 2001. – 328 p.

12. Konakhovich G.F. Computer steganography: theory and practice. – M.: MK-Press, 2006.

– 221 p.

13. Moldovyan A.A., Moldovyan N.A., Sovetov B.Ya. Cryptography. - Series “Textbooks for universities. Special literature". - St. Petersburg: Lan Publishing House, 2000. – 224 p.

14. Nechaev V.I. Elements of cryptography (Fundamentals of information security theory): Textbook for un-tov and ped. universities / Ed. V.A. Sadovnichego - M.: Higher. school, 1999 – 109 p.

15. Novikov F.A. Discrete mathematics for programmers - St. Petersburg: Peter, 2001. - 304 p.

16. Peterson W., Weldon E. Error-Correcting Codes: Transl. from English - M.: Mir, 1986. - 594 p.

17. Romanets Yu.V., Timofeev P.A., Shangin V.F. Information protection in computer systems and networks / Ed. V.F. Shangina. - M.: Radio and communication, 1999. - 328 p.

18. Salomaa A. Public key cryptography. - M.: Mir, 1996 - 304 p.

19. Smart N. Cryptography. – M.: Tekhnosphere, 2006. – 528 p.

“... the history of cryptography... is the history of humanity”

V.G. Belinsky

“We interrogate the past so that it explains our present and hints about our future.”

Ways to protect secret messages

Physical

Cryptographic

Steganographic

Physical protection

Protection of material media Selecting a communication channel that is difficult to intercept

Special courier

Cable communication lines

Special types of radio broadcasts

and so on.

Steganography

Described in the works of the ancient Greek historian Herodotus

The required message was written on the slave's head, which was shaved bald. When the slave's hair grew long enough, he was sent to the recipient, who again shaved the slave's head and read the message received.

Writing with sympathetic ink on items of clothing, handkerchiefs and so on.

Book of Changes

IN Symbolism was widely developed in ancient China.

IN The book of changes is based on 8 trigrams, each of which consists of three parallel lines, solid (light intensity - Yang) and intermittent (the power of darkness - Yin), denoting sky, earth, fire, water, air, mountain, thunder.