Cryptography

My journey learning cryptography. I am using CommonLoungue to learn cryptography. The course is free.

A lot of the notes below are copied and pasted from the material provided by CommonLoungue. For more detailed information please refer to their material

Intro

Cryptography deals with a set of methods which enable us to store and transmit information while safeguarding it from intruders.

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Branches of Cryptography

• Cryptology - is an umbrella term for the fields of cryptography and cryptanalysis

• Cryptography - is the area of cryptology related to the creation of new codes and ciphers.

• Cryptanalysis - is the art and science of breaking ciphers.

• Steganography - is the science of hiding information "in plain sight".

Goals of Cryptography

• Confidentiality - means that cryptographic algorithms attempt to keep the contents of a message secret.

• Integrity - means that a cryptographic algorithm verifies that a message was not modified in transit.

• Authentication - means that a cryptographic algorithm verifies that a message is sent by the entity that claims to have sent the message

• Non-repudiation - means that the sender can not deny sending a message

Kerckhoff's Principle

A cryptosystem should be secure even if everything about the system, except the key, is public knowledge.

Cryptosystems Components and Design objectives

A cryptosystem is a pair of algorithms: one for the encryption of data and another for decryption. Often these algorithms use a unique key which should be kept secret, in which case the process for generating and sharing the key is also considered part of the cryptosystem.

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Cryptography terms

• Plaintext - The original message in its original legible form

• Ciphertext - Encrypted text that will appear to be a random string

• Encryption - The process of converting data into its cryptic form that prevents unauthorized access

• Decryption - The process of converting encrypted data back into its original form for use

• Symmetric Key Cryptosystems - Cryptosystems that use the same key for encryption as well as decryption. Examples include:

  • Cipher - A system of encryption that maps each character to a substitute

  • Code - A system of encryption that maps each word or feature to a substitute

  • Shift Cipher - A cipher that replaces each character with another chosen by moving forwards through the alphabet by some fixed shift factor

• Asymmetric or Public Key Cryptosystems - Cryptosystems that use public-private key pairs.

• Digital Signatures - A digital code which is attached to an electronically transmitted document to verify its contents and the sender's identity.

Number Theory Terms

• Modulo - The remainder operator (e.g. 17 modulo 5 is 2, i.e. 17 when divided by 5 leaves a remainder of 2). This is often shortened to mod, we write 17 ≡ 2 (mod 5), read as "17 is congruent to 2, modulo 5".

• Coprime - In number theory two values are said to be coprime or relatively prime if they do not share any common prime factors. That’s to say that their greatest common divisor (GCD) or highest common factor is 1.

Design Objectives and Goals

The design objectives of a cryptosystem can be summarized by Kerckhoff’s Priniciple

Symmetric Cryptosystems

These use the same key for encryption and decryption.

Asymmetric Cryptosystems

These are cryptosystems where the encryption key differs from the decryption key.

The Caesar Cipher

• In the Caesar cipher, each letter of a message is replaced by the letter three steps to the right of it in the alphabet. For example, A is replaced by D, B by E, etc. The shift "wraps" around the alphabet so that X is replaced by A, Y is replaced by B, and Z is replaced by C.

• To decode a message encrypted with a Caesar cipher, it is necessary to shift each letter in the ciphertext left by three steps to reach the original plaintext letter, so A becomes X, D becomes A, etc.

Example

plaintext - 'KENGO'
'K' - 'N'
'E' - 'H'
'N' - 'Q'
'G' - 'J'
'O' - 'R'
ciphertext - 'NHQJR'

The Vigenère’s Cipher

Vigenère’s cipher was invented in the 16th century and was considered secure until well into the twentieth century despite attacks being developed in the 19th century by the British mathematician Charles Babbage and the German cryptographer Friedrich Kasiski.

The successful use of Vigenère’s cipher is dependent on the same key being known by the sender of the encrypted message and the receiver. This is why the key is often known as a shared secret.

Encryption

• Choose a key length and then a set of characters to match the key length

• Conver the plaintect and key to integers. You can base this on alphabetic positions e.g A=0, B=1, ..., Z=25.

• Repeat the key, if necessary, until it's the length of the plaintext

• Add the values of the of the key to the values of the plaintext and take the modulus of the sums. In this case mod 26

• Convert the values back to characters.

Plaintext - THISISATEST
Key - VECTOR

Plaintext:  THISISATEST → 19 07 08 18 08 18 00 19 04 18 19
Key:        VECTORVECTO → 21 04 02 19 14 17 21 04 02 19 14
                          ————————————————————————————————
            +             40 11 10 37 22 35 21 23 06 37 33
            (mod 26)      14 11 10 11 22 09 21 23 06 11 07
Ciphertext:               O  L  K  L  W  J  V  X  G  L  H

Ciphertext - OLKLWJVXGLH

Decryption

• Choose a key length and then a set of characters to match the key length

• Conver the cipher text and key to integers. You can base this on alphabetic positions e.g A=0, B=1, ..., Z=25.

• Repeat the key, if necessary, until it's the length of the plaintext

• Subtract the values of the key from the cipher text, add 26 and then take the modulus e.g mod 26

• Convert the values back to characters

Ciphertext - OLKLWJVXGLH
Key - VECTOR

Ciphertext:  OLKNWLVXGNH → 14 11 10 11 22 09 21 23 06 11 07
Key:         VECTORVECTO → 21 04 02 19 14 17 21 04 02 19 14
                           ————————————————————————————————
             -             -7 07 08 -8 08 -8 00 19 04 -8 -7
             (add 26)      19 33 34 18 34 18 26 45 30 18 19
                           ————————————————————————————————
             (mod 26)      19 07 08 18 08 18 00 19 04 18 19
Plaintext:                 T  H  I  S  I  S  A  T  E  S  T

Plaintext - THISISATEST

Playfair Cipher

The Playfair cipher uses a 5x5 matrix of letters for encryption and decryption. The secrets in the Playfair cipher are a keyword and the method by which the 5x5 matrix is filled.

Playfair Encryption

To encrypt a message with the Playfair cipher, it must be broken into sets of two letters or digrams. For each of these digrams, the following rules are applied.

• If both letters are the same or only one letter remains (at the end of the message or a sentence within it), replace the second letter with an X and move to the next step.

• If both letters are in the same row of the matrix, replace each with the letter to its right (wrapping around to the beginning of the row if necessary) and move on to the next digram

• If both letters are in the same column of the matrix, replace each with the letter below (wrapping around to the top of the column if necessary) and move on to the next digram

• If neither of the previous two rules are true, create a rectangle on the grid with the two letters at its corners. Replace each letter of the digram with the letter on the corner of the rectangle that is on the same row.

Playfair Decryption

To decrypt with the Playfair cipher, the same matrix is used. In decryption, the reverse of the encryption operations are performed. These are as follows:

• If both letters are in the same row of the matrix, replace each with the letter to its left (wrapping around to the beginning of the row if necessary) and move on to step 4

• If both letters are in the same column of the matrix, replace each with the letter above (wrapping around to the top of the column if necessary) and move on to step 4

• If neither of the previous two rules are true, create a rectangle on the grid with the two letters at its corners. Replace each letter of the digram with the letter on the corner of the rectangle that is on the same row.

• If the second letter is an X, evaluate whether or not it makes sense to be an X based on context. If not, replace it with the first letter or drop it (if the last letter of the message)

Implementation

I will be implementing the algorithms in JavaScript.

Getting started

• Clone the repo

• cd Cryptography

• Run npm install

• Now run npm start and follow the prompts

• Also run npm test to run the tests

Contributing

• Fork the repo

• Make the changes and write tests that pass

• Document your changes at the bottom of the README

• Create a pull request and add your name to the authors list

Authors

• Kengo Wada