Symmetric vs. Asymmetric Encryption

Posted on October 23, 2018 by Administrator Posted in A Level Concepts, Computer Networks, Computer Science, Computing Concepts, Cryptography

Cryptography is the art of encoding and decoding secret messages. Cryptographic techniques have been used for thousands of years, well before the introduction of computers, and the techniques have evolved since. (e.g. See how the Caesar Cipher was used by the roman empire 2000 years ago).

More recently, with the introduction of electronics and later on computer science, it has been possible to implement more advanced encryption techniques based on complex mathematical calculations. (e.g. See Alan Turing’s work on breaking codes encrypted by the Germans using the Enigma Machine during World War 2).

Symmetric Encryption

At this stage, encryption techniques were based on symmetric encryption algorithms. With such algorithms a single secret key is needed to both encrypt and decrypt a message. The secret key is possessed by both parties involved in the communication, the sender and the receiver.

Symmetric Encryption: The same cryptographic key is used both to encrypt and decrypt messages.

The following algorithms use Symmetric Encryption: RC4, AES, DES, 3DES, QUA.

Symmetric keys are usually 128 or 256 bits long. The larger the key size, the harder the key is to crack. For example, a 128-bit key has around 340,000,000,000,000,000,000,000,000,000,000,000,000 encryption code possibilities. This means that a brute force attack (trying every possible key until you find the right one) is no longer a realistic approach to crack such a key.

Asymmetric Encryption

In today’s digital world, there has been a need to develop a different approach to encryption, called asymmetric encryption. With this approach a pair of linked keys is used and consists of a public key, used to encrypt data and a private key used to decrypt data. Both keys are different (but related). The public key, is available to everyone who wishes to send a message. On the other hand, the private key is kept at a secure place by the owner of the public key.

Asymmetric Encryption: A public key is used to encrypt plaintext into ciphertext whereas a private key is used to decrypt a ciphertext.

As they involve a pair of keys, asymmetric algorithms tend to be more complex to implement (and slightly slower to execute) than symmetric algorithms. The following algorithms use Asymmetric Encryption: RSA, Diffie-Hellman, ECC, El Gamal, DSA.

Asymmetric keys are typically 1024 or 2048 bits long which leads to 2¹⁰²⁴ or 2²⁰⁴⁸ encryption codes. (We did not even try to write these numbers down as they would contain several hundreds digits!)

HTTPS and the SSL Handshake

On the internet, a lot of websites are now using the HTTPS protocol. This means that the communication between the web browser and the web server is encrypted in both directions (data being uploaded, such as your credit card number when you pay online, as well as data that is downloaded: the HTML code, the images and video clips, etc. that appear on a webpage).

The HTPPS protocol uses SSL (Secure Sockets Layer), a standard security technology to create an encrypted link between a server and a client.

The following steps describe the process of creating a secure connection between a web browser and a web server. It is called the SSL handshake and uses both symmetric encryption and asymmetric encryption:

To recap, the 5 steps of a SSL handshake are:

Browser sends an https://www… request.
Web Server sends a digital certificate with its asymmetric Public Key.
Browser generates a symmetric session key, encrypts it using the public key and sends it to the server.
Server decrypts the encrypted session key using its asymmetric private key to get the symmetric session key.
Server and Browser now encrypt and decrypt all transmitted data using the symmetric session key. The communication channel is secure as only the web browser and the server know the symmetric session key. The session key is only used for that session. If the browser was to connect to the same server at another time, a new session key would be created following the 5 steps of the SSL handshake.

Symmetric vs. Asymmetric Encryption

Check our online symmetric and asymmetric encryption tools:

Symmetric EncryptionAsymmetric Encryption

Tagged with: cryptography, encryption

Epoch/Unix Timestamp Converter

Posted on October 19, 2018 by Administrator Posted in Computer Science, Computing Concepts, Python - Advanced, Python Challenges, Solved Challenges

The Unix epoch (or Unix time or POSIX time or Unix timestamp) is the number of seconds that have elapsed since January 1, 1970 (midnight GMT).

This explains how date & time values are actually stored on computers: using an integer value representing the number of seconds since 01/01/1970 00:00:00 GMT. Note that a negative value would represent a date prior to 01/01/1970.

For instance, the current date & time is:

Human Readable Date to Epoch Date Converter

Your first challenge is to write a script, using a programming language of your choice, to convert a date entered in a human readable format e.g. DD/MM/YYYY HH:MM:SS as an input and output the date using the Epoch/Unix Timestamp.

To do so you will need to calculate the number of seconds elapsed between the date given and 01/01/1970 00:00:00.

To simplify your calculations you can make the following assumptions:

There are 365.25 days in a year.
There are 30.44 days in a month (on average).
There are 24 hours in a day.
There are 60 minutes in an hour.
There are 60 seconds in a minute.

You can test you script with today’s date and compare the output of your program with the Epoch date that appears at the top of this blog post.

Epoch Date to Human Readable Date Converter

Your second challenge is to work out and output an actual date in the DD/MM/YYYY HH:MM:SS format from an Epoch timestamp.

Testing

Here are some key dates for you to test your scripts:

Epoch/Unix Timestamp	Date	Event
410270400	1 January 1983	ARPANET adopted TCP/IP on January 1, 1983, and from there researchers began to assemble the “network of networks” that became the modern Internet. The online world then took on a more recognizable form in 1990, when computer scientist Tim Berners-Lee invented the World Wide Web.
479736000	15 March 1985	The first domain name registered was Symbolics.com. It was registered March 15, 1985, to Symbolics Inc., a computer systems company in Cambridge, Massachussetts.
773409600	05 July 1994	Amazon was founded in the garage of Bezos’ rented home in Bellevue, Washington. In July 1995, the company began service as an online bookstore.
904910400	4 September 1998	The search engine Google was invented by computer scientists Larry Page and Sergey Brin. It was named after a googol (the name for the number 1 followed by 100 zeros) found in the book “Mathematics and the Imagination” by Edward Kasner and James Newman.
1075896000	4 February 2004	The social network Facebook was launched on February 4, 2004, by Mark Zuckerberg, along with fellow Harvard College students and roommates Eduardo Saverin, Andrew McCollum, Dustin Moskovitz and Chris Hughes

Using the time library

Note that, in Python, the time library already includes a few functions to manipulate Unix Epoch timestamps. You can for example use this library to convert a Unix Epoch Timestamp into a human readable format, using the following code:

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Hashing Algorithms for Integrity Validation

Posted on October 18, 2018 by Administrator Posted in A Level Concepts, Algorithms, Computer Science, Computing Concepts, Cryptography

The enigma machine was used during World War II to encrypt secret messages.

Imagine working for the British Secret Services during World War 2 or during the cold war. As part of your role, you would be expected to exchange secret messages with your allies.

Your messages would most likely be encrypted using various encryption techniques.

The issue is that, occasionally, you may receive messages but may not be 100% sure that these messages are genuine messages or not. It could be that your enemies are sending messages pretending to be one of your allies. They may use the same encryption techniques to lure you. Also, your enemies may have intercepted some of your messages and altered them to confuse you.

This is the reason why secret services had to come with a solution when sending and receiving messages to validate the integrity of a message: So, when a message is received, the recipient should be 100% confident that:

the message has been issued by the right person,
the message has not been tampered with before reaching its destination.

In the 1950’s the first hashing algorithms used to validate the integrity of a message were introduced. They were using the idea of using a complex mathematical calculations on the content of a message (the key) to generate a hash called a checksum that would be appended at the end of the message to be sent.

Let’s consider the following secret message:

Let’s consider a very basic hashing algorithm that takes this message as an input and returns the hash as being the number of characters of this message.

checksum = hash(message) = LENGTH(message)

When applying our hashing algorithm to our secret message we get a checksum of 23.

We will now append this checksum at the end of the message before sending it. Our new message is now:

The recipient of this message will run the same hashing algorithm with the content of the message. They will then compare the resulting checksum with the checksum that has been received. If the two checksums are equal, they can be fairly confident that the message is genuine.

If an enemy intercepts the message and tries to alter it, they will not know how the checksum was calculated. Hence they may change the content of the message but will not be able to recalculate the right checksum. (Provided that your hashing algorithm is not as obvious as calculating the number of characters in the message: This would be a very easy algorithm to guess and recreate).

A message which has been tampered with by an enemy may look like this:

A message which has been tampered with.

When the recipient receives this message, they will apply the same hashing algorithm and get a checksum of 24. When comparing this with the checksum of the received message they will realise that both checksums do not match and hence will be able to identify that the message is invalid: It has either been produced by someone who does not know the hashing algorithm in use, or it has been tampered with before reaching its recipient. In both case the recipient will have to discard this message as it is not reliable.

Hashing Algorithms for Integrity Validation

To summarise what we have learned so far, the idea of a hashing algorithm used for integrity validation is to provide some assurance that a transferred message or file has arrived intact, that it has not been altered on its way to the recipient.

Note that alterations can be caused intentionally by a third party (e.g. a hacker) or can be the consequence of an unintentional “glitch” in the communication. (e.g. poor quality of communication link such as wifi interference, collisons of data packets on a TCP/IP network, human or sensor error when inputting a message or scanning a barcode, etc.)

Nowadays hashing algorithms used for integrity validation are widely used in a range of contexts such as:

Barcodes and ISBN book numbers use a similar approach called check digit.
The CSV number of a credit card is also a form of checksum used to validate credit cards.
The TCP/IP protocols (HTTP, FTP, SMTP, etc.) all use a checksum on all data packets being sent over the Internet, to ensure that the recipient can validate the integrity of the data packets being received.
Digital certificates and software licences also use a checksum to minimise the risk of fraudulent digital certificates and software license keys.
exe files of popular software include a checksum. This is to prevent malicious websites trying to get you to download software where the content of the exe file has been altered to add a virus or a trojan horse.

The hash of a hashing algorithm used for integrity validation is often called a checksum and is appended at the end of the data to be transferred.

Sometimes the hash is called a check digit if it only consists of one digit. This is the case for barcodes, ISBN numbers and credit card numbers where the last digit of the code is a check digit, the result of a complex calculation using all the other digits of the code.

You can check the following links to investigate the use of check digits on a barcode or on a credit card (using the Luhn Algorithm to validate a credit card number).

Hashing Algorithms for Storing Sensitive Data

Posted on October 17, 2018 by Administrator Posted in A Level Concepts, Algorithms, Computer Science, Computing Concepts, Cryptography

More and more online systems such as e-commerce websites, online banking apps, or social networks need to access some sensitive data about you including your password, your credit card details and more recently, some biometric data (e.g. for fingerprint authentication process).

The servers that store your personal data are at risk of being hacked and though the organisations who run these online services invest a lot of money in ensuring their servers are secure (firewalls, encryption of data, etc.) there is always a risk of a hacker accessing the data stored on their servers. This is why organisations prefer not to store very sensitive data directly (passwords, credit card numbers and biometric data). Instead these organisation use complex hashing algorithms to store hash values of your most sensitive data.

Hashing Algorithm

A hashing algorithm is a complex mathematical calculation that takes an input called the key (e.g. your credit card number or your password) to generate a hash value. The hash value often consists of a string of characters of a fixed size (e.g. 32 alpha-numeric characters).

The hashing algorithm will always produce the same hash for a given key. The hash value will be fairly unique (different for each key, though on rare occasions two different keys can produce the same hash, this is called a collision).

When a user enter their password, for instance to login, the same hashing algorithm is used to recreate the hash value. This hash value can then be compared to the hash stored on the server for this user. If they are the same we can assume that the password entered by the user is correct.

This works exactly the same with credit card numbers. When asked to pay online, the user enters their credit card number. The hashing algorithm is applied to the key (credit card number) to produce a hash value which can be compared with the hash value stored on the system for that user. If the two hash values are identical, we can assume that the credit card number entered is correct.

A one-way process

Hash functions are one-way functions which means that with the key you can calculate the hash value, however with a hash value you cannot determine the key.

This is an essential characteristic of hashing algorithms which ensures that even if a hacker manages to access the organisation’s database, they will not be able to easily work out your password or credit card numbers from the hash values stored on the database.

Popular Hashing Algorithms

If you want to find out more about some of the most popular hashing algorithms you can investigate the following hash functions:

Hashing Algorithms for Memory Addressing

Posted on October 17, 2018 by Administrator Posted in A Level Concepts, Algorithms, Computer Science, Computing Concepts

In this blog post, we will investigate the use of hashing algorithms to quickly locate a record in a large database.

Let’s consider the database of members of a social network such as Instagram, Twitter or Facebook.

Every time the user uses the website or their smartphone app to access the social network, the server retrieves the user’s login name and password. It then has to find the record matching the given username to access their data and verify their password.

Large social networks have millions of members. Locating a single record in a table that contains millions of records can be time consuming especially if you perform a linear search to locate the record. (Linear Big O Notation). Alternative algorithms such as a binary search can speed up the process (Logarithmic Big O Notation), however a binary search only works when the data is sorted in alphabetical order. This is unlikely to be the case for a social network members table as members will have joined the network at different dates, hence the data will not be sorted in alphabetical order of their usernames. The assumption is that the records are stored in chronological order (based on the date they first signed in).

Using a Hashing Algorithm

To solve this problem, social networks use hashing algorithms when storing and accessing data in a large database.

A hashing algorithm is a complex mathematical calculation that takes an input (a.k.a. the key) (in this case the username of the member) and returns a value called a hash value or hash. When used for memory addressing the hash value generated is the memory location of where the record is stored.

Let’s consider a very basic hashing algorithm used to identify the memory location of a new member who has just signed up.

Our hashing algorithm will add up all the ASCII values of each character of their username. We will assume our database will contain around 50 memory locations. So our hashing algorithm will use the remainder of dividing the total ASCII value by 50 to get a unique number between 0 and 50.

For instance, for a user called James Bond whose username is “Bond”, the resulting hash value would be:

hashKey("Bond") =  (ASCII("B") + ASCII("o") + ASCII ("n") + ASCII("d")) MOD 50
                =  (  66       +     111    +     110     +     100   ) MOD 50
                =  387 MOD 50
                =  37

The details can be stored on location 37 of the members table (hash table) provided below.

Every time the user James Bond accesses the social network, he will provide his username. As part of the login process, the server will use the hashing algorithm on this username to quickly calculate the memory location of where James Bond’s record is stored. This is a very efficient approach to access the data. (Constant Big O notation).

Collisions

The hash values generated by a hashing algorithm should be fairly unique. However there will be occasions where two input values return the same hash value. For instance, let’s consider what would happen if a new user, Austin Powers signs in and their username is aPowers:

hashkey("aPowers") =  (ASCII("a") + ASCII("P") + ASCII ("o") + ASCII("w") + ASCII("e") + ASCII("r") + ASCII("s")) MOD 50
                   =  (  97       +     80     +     111     +     119    +    101     +     114    +   115     ) MOD 50
                   =  737 MOD 50
                   =  37

This hash is the same as the hash generated for James Bond’s username. This create a collision. In this case, instead of overwritting the content of memory location 37 (already used by James Bond) the algorithm will jump to location 37 and carry on a linear search from there to find the next empty memory location. This could be memory location 38 if it’s empty, 39 if not, and so on till an empty location is found.

This will slightly slow down the process when trying to locate Austin Powers’ record but would still be far more efficient than without using a hashing algorithm.

Complex hashing algorithms are designed the minimize the risk of collisions: The effectiveness of a hashing algorithm is based on the total number of unique values the algorithm will generate to minimize the risks of collisions.

Hashing Algorithm in Action!

We have implemented our basic hashing algorithm as described above.

Your task is to use it to generate the hash values for these new members of our social network.
Using these hash values, you will then be able to add their information on the members hash table (see “Members Table” tab below). You will notice that a few members have already been stored in this table.

Warning: On occasion the generated hash may generate a collision with an existing member. In this case you you will have to use the next available location to store the members detail in the members table.

The new members to add are:

Jason Bourne, username: jBourne
Johny English, username: English
Lara Croft, username: lCroft

Also, a few users are logging in. Can you use the hashing algorithm to quickly locate their records in the members hash table and access their details.

The users are:

jBauer
eHunt
Holmes

Hashing AlgorithmMembers Table / Hash Table

Memory Location	Username	Firstname	Lastname
0
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
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50

Recursive vs. Iterative Palindrome Check

Posted on October 16, 2018 by Administrator Posted in Algorithms, Computer Science, Python - Advanced, Python Challenges, Solved Challenges

A word, phrase, or sequence that reads the same backwards as forwards, e.g. madam.

For this challenge we will investigate two algorithms used to find out if a word is a palindrome or not. The first algorithm will use an iterative approach, the second algorithm will use a recursive approach.

Iterative Approach

An iterative approach is based around the use of a loop which can be:

A count-controlled loop (e.g. FOR loop)
A condition-controlled loop (e.g. WHILE loop or REPEAT UNTIL loop)

For our iterative palindrome check algorithm, we will use a loop to check all the letters in the first half of the word and compare them with the letters in the second half of the word (in reverse order). If they all match then the word is a palindrome.

Recursive Apporach

A recursive function is a function that:

Includes a call to itself,
Has a stopping condition to stop the recursion.

For our recursive palindrome check algorithm, we will use a function that:

Checks that the word is at least two characters long:

If the word is less than two characters then the function will stop the recursion (stopping condition) and Return True as the word is a palindrome.
If the word is two or more characters long, the function will check that the first and last letter of the word are the same:

If they are the same, the function will extract the word in the middle (remove the first and the last letter) and call itself with this new shortest word.
If they are different, then the word is not a palindrome. The function will stop the recursion here (stopping condition) and return False.

You can visualise/trace this recursive function on recursionvisualizer.com

Your Task

Complete the following factorial challenge using both an iterative approach and a recursive approach.

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: iteration, recursion

Blackbeard’s Hidden Treasures

Posted on October 14, 2018 by Administrator Posted in A Level Quiz, Coding Quiz, Computer Science, Computing Concepts, GCSE Concepts, GCSE Quiz, Quizzes, Solved Challenges

The period of the late 17th and early 18th centuries is known as the Golden Age of Piracy. During this period the most notorious and the most feared of all pirates was Blackbeard. There are many legends based around Blackbeard’s piracy acts in the Caribbean sea and in the Pacific Ocean but the most captivating legend is based around Blackbeard’s great buried treasure, which has yet to be found.

A small treasure chest, full of parchments has recently been found by a team of historians who were researching the Golden Age of piracy at The Codrington Library, Oxford UK. The parchments were hidden within the inside cover of an ancient book about Myths and Legends of the Golden Age of Piracy.

It would seem that Blackbeard may not have buried his treasure in one single location but may instead have split his treasure and buried it using twelve different locations.

Your task is to use the 12 parchments, as well as the treasure map provided below to locate all the content of Blackbeard’s treasure.

Blackbeard’s TreasuresOpen in New Window

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Blackbeard’s Treasure Map

Posted on October 10, 2018 by Administrator Posted in A Level Concepts, A Level Quiz, Coding Quiz, Computer Science, GCSE Concepts, GCSE Quiz, Python - Intermediate, Python Challenges, Solved Challenges

We have all heard of the famous English pirate called Blackbeard who sailed the seven seas during the XVIII century. Through his numerous acts of piracy, Blackbeard accumulated a huge collection of riches including golden coins, jewels, golden plates and precious stones. Blackbeard was wise enough not to carry his treasure on his vessel. Instead he buried his treasure in a secret location, somewhere in the middle of the Pacific Ocean.

Recently, a team of SCUBA divers found a message in a bottle while SCUBA diving near Coral Bay, Western Australia. Inside this old bottle of rhum, they found two pieces of parchment believed to have belonged to Blackbeard.

The first piece of parchment is a map. Looking at the shapes of the three islands on the map, the SCUBA divers have been able to identify the location of these islands somewhere a few miles off the coast of Australia. They strongly believe that this map will help them find the exact location of Blackbeard’s treasure.

The second parchment is believed to be the key to help locate the position of the treasure on the map.

Treasure Hunt

Your task is to write a computer program, using the programming language of your choice, in order to find the row number and the column number to solve the following equation:

Row x Column = 1889121
Looking at the map, we can deduce that the row number could be any number between 2440 and 2470 and that the column number could be any number between 750 and 770.

Your computer program will enable you to pinpoint the exact location of Blackbeard’s treasure on this map!

Once you have found your row and column numbers type them below to check if you have located the treasure!

Row:
Column:

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

The Pigpen Cipher

Posted on October 10, 2018 by Administrator Posted in Computer Science, Cryptography, HTML, CSS & JavaScript, JavaScript

The Pigpen cipher (a.k.a. tic-tac-toe cipher) is a geometric substitution cipher, which exchanges letters for symbols which are fragments of a grid.

Secret Message

Using the key provided on the right, can you decode the following secret message?

Pigpen Cipher Encoder

You can use our online Pigpen Cipher Encoder to encode your own secret messages.

See the Pen pigpen cipher – encoder by 101 Computing (@101Computing) on CodePen.

Press the “Edit on CodePen” button at the top of this codepen to open in full screen mode

Tagged with: cryptography, encryption

The Rail Fence Cipher

Posted on October 8, 2018 by Administrator Posted in Computer Science, Cryptography, Python - Intermediate, Python Challenges, Solved Challenges

The rail fence cipher (sometimes called zigzag cipher) is a transposition cipher that jumbles up the order of the letters of a message using a basic algorithm.

The rail fence cipher works by writing your message on alternate lines across the page, and then reading off each line in turn.

For example, let’s consider the plaintext “This is a secret message”.

To encode this message we will first write over two lines (the “rails of the fence”) as follows:

Note that all white spaces have been removed from the plain text.

The ciphertext is then read off by writing the top row first, followed by the bottom row:

Your Challenge

For this challenge, you will have to write two python programs, one to encrypt a message (plaintext to ciphertext), one to decrypt an encoded message (ciphertext to plaintext). To help you with this challenge we have created the flowcharts of both the encoder and the decoder algorithms.

Encoder AlgorithmDecoder Algorithm

Rail Fence Cipher – Encoder

Rail Fence Cipher – Encoder Algorithm

Python Code

Rail Fence Cipher – Decoder

The Rail Fence Cipher – Decoder Algorithm

Python Code

Break the code!

Use your python script to decipher the following encoded message:

CYTGAHITEROWIIGROVNCDSRPORPYSHATFRTNOSLIGOE

Extension Task

More complex Rail Fence Ciphers have more “rails”. For instance instead of writing the code over two lines (“rails”) you can write over three or four or more lines. The number of lines used in a Rail Fence Cipher is called the key.

Key = 3

A Rail Fence Cipher with 3 “rails” (Key = 3)

Key = 4

A Rail Fence Cipher with 4 “rails” (Key = 4)

Investigate how you could adapt both your encoding and decoding python programmes to enable to encrypt and decrypt messages with different keys.

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: cryptography, encryption

Learning Zone ✕

Theory Concepts

Interactive Quizzes

GCSE Computer Science (UK)

A-Level Computer Science (UK)

Coding Challenges ✕

Python Challenges

HTML / CSS & JavaScript

LMC

SQL

Block Programming

Interactive Coding Puzzles

Online Interactive Tools ✕

Coding Tools

Design Tools

Logic Gates Circuits

Cryptography Corner

Member's Area ✕

Register/Sign Up

Get In Touch

Books Corner

Symmetric Encryption

Asymmetric Encryption

HTTPS and the SSL Handshake

Symmetric vs. Asymmetric Encryption

Human Readable Date to Epoch Date Converter

Epoch Date to Human Readable Date Converter

Testing

Using the time library

Solution...

Hashing Algorithms for Integrity Validation

Hashing Algorithm

A one-way process

Popular Hashing Algorithms

Using a Hashing Algorithm

Collisions

Hashing Algorithm in Action!

Iterative Approach

Recursive Apporach

Your Task

Solution...

Solution...

Treasure Hunt

Solution...

Secret Message

Pigpen Cipher Encoder

Your Challenge

Rail Fence Cipher – Encoder

Python Code

Rail Fence Cipher – Decoder

Python Code

Break the code!

Extension Task

Key = 3

Key = 4

Solution...

Recent Posts

Our Latest Book