{"id":31081,"date":"2017-04-10T10:08:55","date_gmt":"2017-04-10T14:08:55","guid":{"rendered":"http:\/\/www.opensource.im\/?p=31081"},"modified":"2017-04-10T10:08:55","modified_gmt":"2017-04-10T14:08:55","slug":"encryption-ucsd-mathematics","status":"publish","type":"post","link":"https:\/\/euvolution.com\/open-source-convergence\/encryption\/encryption-ucsd-mathematics.php","title":{"rendered":"Encryption &#8211; UCSD Mathematics"},"content":{"rendered":"<p><p>    Encryption is a method of hiding data so that it cannot be read    by anyone who does not know the key. The key is used to lock    and unlock data. To encrypt a data one would perform some    mathematical functions on the data and the result of these    functions would produce some output that makes the data look    like garbage to anyone who doesn't know how to reverse the    operations. Encryption can be used to encrypt files that the    owner feels are too sensitive for anyone else to read. And now,    with the rise of the Internet, encryption is used to encrypt    data, like a credit card number, and then send it across the    net. This way no one can read intercept and read the data while    it is traveling through the web. The recipient of the data does    have to know how to decrypt the information or else the data    will look like garbage to the recipient too.  <\/p>\n<p>    There are two categories of encryption, private key and public    key. The major difference is who knows the key. Encryption is    an entirely mathematical process applied to the world of    computers. The only thing an encryption program will do is take    in data, perform some predefined mathematical operations on the    data, and then output the result. Decryption is the process of    taking the encrypted data, that now looks like garbage, and    reverse the mathematical functions so that the result is the    same data that originally existed before the encryption    process. The \"key\" is the set of mathematical operations and    values that are used to encrypt and decrypt the data.    Encryption and decryption algorithms describe the mathematical    operations while key describes the exact process which includes    the algorithms and any other random initial values that are    used in the algorithms. Lets first look at private key    encryption and how it works.  <\/p>\n<p>    PRIVATE KEY ENCRYPTION  <\/p>\n<p>    What private key means is that the same method is used to    encrypt and decrypt. If someone knows what method was used to    encrypt the message then that person can decrypt the message.    Thus, the key must be kept private. Only the person sending the    data and the person receiving the data should know the key.    Private key cryptography, also known as symmetric cryptography    since the encryption and decryption processes are just    opposites, is an encryption method where the encryption    algorithm is known before hand by the sender and the recipient.    Accordingly, the two users must communicate beforehand and    agree on the algorithm and the key so that the recipient can    decode the message. A very simple example of private key    cryptology is to take the text that is to be sent across the    Internet and use the next letter in the alphabet in place of    the original letter. Then send the scrambled text across the    Internet. The person receiving the text would have to know how    the message he receives is scrambled so that he can unscramble    it. Thus, the \"key\" being used in this example is, 'use the    next letter in the alphabet.'  <\/p>\n<p>    With this key the text, \"hi rob\" would become, \"ij spc\". Since    the recipient of the message knows the key, that person will    take the message he received and take the previous letter in    the alphabet. The person would receive the message, \"ij spc,\"    and using the previous letter that person would recover, \"hi    rob.\" This example is much simpler than the private key    encryption algorithms used today, but it illustrates the fact    that in private key encryption the encryption and decryption    processes are just the reverse of each other  <\/p>\n<p>    Private key encryption has the benefits of being very fast in    that the computer programs that will perform the encryption and    decryption will finish executing in a very short amount of    time. The more complex the key the longer the process takes.    However, even the most complex private keys algorithms can    encrypt and decrypt data faster than that of public key    cryptology. A disadvantage to private key cryptography is that    the key must be communicated before hand. You would have to    tell me exactly how you were going to encrypt the messages that    you will send to me so that I could recover the original    message later.. You could not encrypt this information as I    wouldn't know the key yet. In a large organization or over the    Internet it is easy for these keys to become compromised    because they have communicated, without using encryption,    before the actual encryption takes place.  <\/p>\n<p>    PUBLIC KEY ENCRYPTION  <\/p>\n<p>    Public key cryptography (asymmetric) was created to eliminate    the shortcomings of private key cryptography. The biggest    advantage of public key cryptography is that no prior    communication needs to take place between the recipient and the    sender.  <\/p>\n<p>    Public key cryptography works like this, everyone has two keys,    a public key, which the entire world has access to, and a    private key, which only the owner knows. Note that the private    key referred to here is completely different than the private    key used in private key cryptography. For lack of a better name    the secret key in public key cryptography is called a private    key. These two \"keys\" are much different form the \"keys\" used    in private key cryptography. In fact both keys used in public    key cryptography are just very large integers, on the order of    300 digits long. With public key cryptography there is only one    algorithm that is in use, that algorithm is know as the RSA    algorithm. The RSA algorithm is the only algorithm that will be    used to encrypt and decrypt data.  <\/p>\n<p>    The algorithm works by taking in some data, and then using one    of the keys which is a large number, and using the key to    perform modulo and exponential functions on the data. The    result is a message so scrambled that no amount of statistical    analysis could break the code. The beauty of RSA is that a    message encrypted with a public key can be decrypted with the    corresponding private key and a message encrypted with a    private key can be decrypted with the corresponding public key.    For this reason RSA is know as asymmetric cryptography,    different algorithms are used to decrypt and encrypt data. The    algorithm is actually just a very complex mathematical    identity. Thus, person X can encrypt a message with person Ys    public key and only person Y can decrypt the message using his    private key, this is the process used to encrypt e-mail. More    importantly, if I had a public and private key, and only I know    my public key, I could encrypt a message using my private key    and everyone could decrypt the message using my public key. If    my public key successfully decrypts the message you can be sure    that I sent it because the message could have only been created    with my private key. The reason it could have only been created    with my private key is that my public key was used to decrypt    the message. By decrypting the message with my public key you    know only my private key created it. This works as long as only    I have access to my private key. The process described here is    known as a digital signature because by creating a message that    only I could have created I am effectively signing the message.  <\/p>\n<p>    Like private key cryptography the encryption and decryption    process must reverse each others actions, but the difference    lies in that there are two different numbers and two different    algorithms used. One number is the public key and the other    number is the private key. These numbers are used in the two    different algorithms one to encrypt a message and one to    decrypt a message. The important aspect of RSA and public key    cryptography is that no prior communication has to take place    before a message is sent. If you receive a message encrypted    with RSA and your public key you have all the information you    need to decrypt the message. RSA does have some disadvantages    however, since the numbers used are so large the amount of time    it takes to encrypt or decrypt is a lot longer than private key    cryptography.  <\/p>\n<p>    What you should understand now is that there are two methods of    encryption, private key and public key, each with its own    advantages and disadvantages. You should also understand the    concept of a digital signature as this will be used later to    prove identity.  <\/p>\n<p>    To go back to main page click here or    to proceed to the page describing digital certificates,    click here  <\/p>\n<p><!-- Auto Generated --><\/p>\n<p>Read the original here:<br \/>\n<a target=\"_blank\" href=\"http:\/\/math.ucsd.edu\/~crypto\/students\/crypt.html\" title=\"Encryption - UCSD Mathematics\">Encryption - UCSD Mathematics<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p> Encryption is a method of hiding data so that it cannot be read by anyone who does not know the key. The key is used to lock and unlock data. To encrypt a data one would perform some mathematical functions on the data and the result of these functions would produce some output that makes the data look like garbage to anyone who doesn't know how to reverse the operations<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[45],"tags":[],"class_list":["post-31081","post","type-post","status-publish","format-standard","hentry","category-encryption"],"_links":{"self":[{"href":"https:\/\/euvolution.com\/open-source-convergence\/wp-json\/wp\/v2\/posts\/31081"}],"collection":[{"href":"https:\/\/euvolution.com\/open-source-convergence\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/euvolution.com\/open-source-convergence\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/euvolution.com\/open-source-convergence\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/euvolution.com\/open-source-convergence\/wp-json\/wp\/v2\/comments?post=31081"}],"version-history":[{"count":0,"href":"https:\/\/euvolution.com\/open-source-convergence\/wp-json\/wp\/v2\/posts\/31081\/revisions"}],"wp:attachment":[{"href":"https:\/\/euvolution.com\/open-source-convergence\/wp-json\/wp\/v2\/media?parent=31081"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/euvolution.com\/open-source-convergence\/wp-json\/wp\/v2\/categories?post=31081"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/euvolution.com\/open-source-convergence\/wp-json\/wp\/v2\/tags?post=31081"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}