Choosing a key - the key has a special property which identifies its uniqueness from the 129 digit sequence. The public key must be the product of two different prime numbers,
p and q. So it would look like "KR= pq".
With the idea of using two prime numbers of roughly equal size two each other to multiply, it produces a number twice as long. For the example of the 129 digit p and q must be
between 64 or 65 digits long to produce the public key required. As well as being long enough and prime numbers, they must also be 2 greater than a multiple of 3. For example,
having p as 5 and q as 11 - both being 2 greater than 3 and 9 (multiples of 3), they create the public key of 55.
Encrypting a message - for the example, 6-bit blocks of ASCII are used to encrypt a piece of clear text. The following will show how to encrypt the amount taken in a credit card
transaction.
****$0.02
In binary this is how it is expressed:
0010 1010 0010 1010 0010 1010 0010 1010 0010 0100 0011 0000 0010 1110 0011 0000 0011 0010
Further to this they then get grouped into 6-bit blocks as follows:
0010 10/10 0010\ 1010 00/10 1010\ 0010 10/10 0010\ 0100 00/11 0000\ 0010 11/10 0011\ 0000 00/11 0010\
In number form the binary digits look like this:
T = 10, /34\, 40, /42\, 10, /34\, 16, /48\, 11, /35\, 0, /50\
The cube of these are:
T3 = 1000, /39304\, 64000, /74088\, 1000, /39304\, 4096, /110592\, 1331, /42875\, 0, /125000\
The important role comes in when they are divided by the key KR = 55
1000 =55 . 18 + 10
39304 = 55 . 714 + 34
64000 = 55 . 1163 + 35
74088 = 55 . 1347 + 3
1000 = 55 . 18 + 10
39304 = 55 . 714 + 34
4096 = 55 . 74 + 26
110592 = 55 . 2010 + 42
1331 = 55 . 24 + 11
42875 = 55 . 779 + 30
0
125000 = 55 . 2272 + 40
So these remainders are converted to the cipher text of:
C = 10, /34\, 35, /3\, 10, /34\, 26, /42\, 11, /30\, 0, /40\
The above is the encrypted message to be sent!
Decryption method - this is the important part where the receiver must now reconstruct the message to clear text. First we must implement this equation to p and q:
S = (1/3)(2(p-1)(q-1) +1)
So this is what it would look like for the example method:
S = (1/3) (2 . 4 . 10 +1) = 81/3 = 27
Remembering the requirement of "2 greater than a multiple of 3" when choosing p and q.
So a convenient and easy method is remembering that the cipher text numbers C are each raised to the s power - Cs - C27, further divided by the key KR - leaving the remainder to be clear text.
This is the equation to remember for this:
Cs = KR . c + T
Encryption techniques - Public key encryption is known as a strong encryption. This assures the communicating parties that they can safely protect the identity of their messages without outside
users reading it.
There are ways in which the "bad guys" will be able to encrypt their messages through buying their own software for encryption. So there are two techniques to discover these ´illegal encryptions´.
Trapdoor - when the cipher text is sent, the clear text could also be sent to law enforcement or security officials, where they would work to secretly configure to message that is trying to be sent across.
However for these to happen, court approved warrants need to be obtained, providing reasons and evidence for why it should be done.
The second technique is Key escrow. If the key is known, it makes the code easy to break into. So a key escrow system with encryption software to register the key along with a third party would hold the prime numbers. So if law enforcement teams needed a reason for a court approved warrant, the key escrow agent could provide the two necessary primes.
The bigger the key the harder it is to crack the code, so RSA scheme is still secure. The difficulty of factoring increases dramatically too when the key length grows.
To really be able to crack the code, you would have to figure out what ´s´ is. Constructing ´s´ is easy if the two primes p and q are known.
Snyder, L. (2008). Shhh, It´s a Secret. In: Fluency With Information Technology: skills, concepts & capabilities. 3rd ed. United States of America: Pearson Education. p361-367.
A majority of the businesses today rely on the use of computers for their daily routines. Archives kept at off-sites need to be kept so if a disaster occurs, the disaster doesn´t attack the backup also. So mostly, a system recovery team is in place to ´clean up´ after a disaster. Along with system redundancy where multiple computers perform the same work so if one fails a ´hot spare´ is functioning.
The idea of recovering information after a disaster needs to be understood for backups to be of any use. First we must begin with keeping a full backup where a copy of everything is kept on the system from a specific time and date. After this, partial backups are created of any changes that have taken place since the last full backup. The frequency of partial backups depends on the cost and grief of losing the information since the previous partial backup was performed. More frequent backups will cost more for a business but will prevent major losses if a disaster was to occur. In the unfortunate event of a disaster to occur, recovery can begin by installing the last full backup copy where the system can then be recreated through bringing up the saved partial backups in order - the closest procedure to "full recovery" as possible.
Backups aren´t just limited for business use. All schools and colleges must have efficient backup systems for staff and students, as loss of information for them just like businesses, is crucial. For personal computers at home, a backup of information is the user´s responsibility. For a worthy backup, understanding what needs to be backed up and how it´s going to be done are the most important factors. Software can be purchased where users can automatically have frequent incremental backups performed which saves time. Or users can manually backup files and directories to an appropriate CD or disk. Certain files on your system will not be needed if a disaster was to attack, such as your Web Cache which is not necessary.
Other benefits of carrying out regular backups of information are that if any important information is deleted by accident it can be restored. Backups can be used as evidence for any reasons such as crimes or inappropriate behaviour, such as CCTV footage of a crime committed 2 or 3 months previously. An example of an immediate backup is sending out an email to another user. Once it has been sent, a copy of the email is kept for the sender and another sent out to the recipient. Then it becomes impossible for the sender to delete as it elsewhere on another system.
Snyder, L. (2008). Shhh, It´s a Secret. In: Fluency With Information Technology: skills, concepts & capabilities. 3rd ed. United States of America: Pearson Education. p367-369.
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