The starting point talking about encryption is to understand
\nwhat the point of it is; what it’s supposed to do, what problems it’s supposed to avoid.<\/p>\n
Encryption is fundamentally about communication: you’ve got two parties who want to communicate, but don’t want anyone else to be able to listen in.<\/p>\n
They way that you do that is by sharing a secret. You use that secret to somehow modify the information that you’re going to send, so that it can’t be read by someone who doesn’t have the secret. People often think of encryption as a way of using a password to hide information, but a password is just one of many kinds of secrets that you can use. The secret that you share with your counterpart can be a password, a number, a textbook, or just about anything else you can imagine.<\/p>\n
<\/p>\n
For example, one very hard to break encryption is based on you and your counterpart having identical copies of a textbook. Then for each word in your message, One of the simplest forms of encryption is something called a simple To see how substitution ciphers work, we’ll look at a simple example. To keep things simpule, we’ll only look at letters; we’ll leave spaces and punctuation unchanged, and upper\/lower case unchanged. The substitution map is as follows:<\/p>\n Using this, we can encrypt things. We take each letter of the message For example, “Mark has a big nose” would be encrypted as “Xgiw jgu g qby pluz”.<\/p>\n Implementing a cipher like this borders on trivial. Here’s a way of doing it in python, with a sample cipher and invocation demo:<\/p>\n That’s it, and the largest part of that is really dealing with maintaining upper and lower case through the encryption.<\/p>\n Obviously, this isn’t a great way of encrypting things. Why?<\/p>\n By maintaining case, punctuation, and word boundaries, you make it really<\/em> easy to identify some likely mappings. For example, if you see a single uppercase letter anywhere other than the beginning of a sentence, you can be almost certain that it’s “I”. If you see a singe character that appears on its own in lowercase, it’s Just to give you a sense of how easy this is: just look at the encryption of “Mark has a big nose”: “”Xgiw jgu g qby pluz”. The “g” is obviously an A. So we immediately Improving on this, while keeping the same basic concept is pretty easy. For example, one common technique is to have each letter that you encode also<\/em> alter the translation in some way. Ultimately, that’s the basis for how the infamous “Enigma” encryption machine used by the Nazi’s during World War 2 worked. Next post, I’ll show you a basic example of this technique, using something called a rotating cipher.<\/p>\n","protected":false},"excerpt":{"rendered":" The starting point talking about encryption is to understand what the point of it is; what it’s supposed to do, what problems it’s supposed to avoid. Encryption is fundamentally about communication: you’ve got two parties who want to communicate, but don’t want anyone else to be able to listen in. They way that you do […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[84],"tags":[],"class_list":["post-668","post","type-post","status-publish","format-standard","hentry","category-encryption"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-aM","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/668","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=668"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/668\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=668"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nyou find that word in your textbook. You encode the word as page#, paragraph#, word#. The encrypted message is then a sequence of triplets of numbers. Without knowing what book you used, if you do a good job with this kind of system,
\nyou can make it pretty much impossible to decode your message without knowing
\nwhat book you used. But this illustrates an important point: in encryption, you need to have a clear understanding of exactly what<\/em> the shared secret is, and
\ntake care to protect it. (During World War 2, the allies only managed to break
\nthe Enigma encryption system after they got an actual Enigma encryption machine: the structure of the machine is a critical part of the secret of Enigma encryption. With
\nthe machine, and a few other tricks to figure out the rest of the secret, Enigma
\nwas cracked. Without the machine, it wouldn’t have been.)<\/p>\n
\nsubstitution cipher. The idea of that is that you have a mapping from one set of symbols to another. If you know the mapping, you can encode and decode messages. The secret that you’re sharing with the person you’re communicating with is the character mapping. If someone can either get, or figure out that mapping, then
\nyou no longer have a secret. As I’ll explain later, the problem with this kind
\nof encryption is that it’s pretty easy to figure out the secret, and thus break
\nthe encryption.<\/p>\n\n
\n Character<\/th>\n A<\/td>\n B<\/td>\n C<\/td>\n D<\/td>\n E<\/td>\n F<\/td>\n G<\/td>\n H<\/td>\n I<\/td>\n J<\/td>\n K<\/td>\n L<\/td>\n M<\/td>\n<\/tr>\n \n Coding<\/th>\n G<\/td>\n Q<\/td>\n F<\/td>\n C<\/td>\n Z<\/td>\n L<\/td>\n Y<\/td>\n J<\/td>\n B<\/td>\n E<\/td>\n W<\/td>\n R<\/td>\n X<\/td>\n<\/tr>\n \n Character<\/th>\n N<\/td>\n O<\/td>\n P<\/td>\n Q<\/td>\n R<\/td>\n S<\/td>\n T<\/td>\n U<\/td>\n V<\/td>\n W<\/td>\n X<\/td>\n Y<\/td>\n Z<\/td>\n<\/tr>\n \n Coding<\/th>\n P<\/td>\n L<\/td>\n D<\/td>\n S<\/td>\n I<\/td>\n U<\/td>\n H<\/td>\n V<\/td>\n A<\/td>\n K<\/td>\n O<\/td>\n T<\/td>\n N<\/td>\n<\/tr>\n<\/th>\n<\/table>\n
\nwe want to send, and look it up in the character row of the table, and replace it
\nwith the corresponding letter in the coding row. To decrypt, we do the opposite: look up the letter in the encrypted message in the coding row, and replace it with the corresponding letter in the character row.<\/p>\n\nclass Cipher(object):\ndef __init__(self, mapping):\nself._mapping = mapping\nself._reverse = {}\n# set up the reverse mapping for decryption.\nfor k in mapping:\nself._reverse[mapping[k]] = k\ndef encrypt(self, message):\n\"\"\"Take a message string, and encrypt it according to the\ncipher mapping\"\"\"\"\nresult = \"\"\nfor c in message:\nif c.islower():\ncu = c.upper()\nelse:\ncu = c\nif self._mapping.has_key(cu):\nm = self._mapping[cu]\nelse:\nm = cu\nif c.isupper():\nresult += m\nelse:\nresult += m.lower()\nreturn result\ndef decrypt(self, message):\nresult = \"\"\nfor c in message:\nif c.islower():\ncu = c.upper()\nelse:\ncu = c\nif self._reverse.has_key(cu):\nm = self._reverse[cu]\nelse:\nm = cu\nif c.isupper():\nresult += m\nelse:\nresult += m.lower()\nreturn result\ncipher = Cipher({ 'A': 'G', 'B': 'Q', 'C': 'F', 'D': 'C', 'E': 'Z',\n'F': 'L', 'G': 'Y', 'H': 'J', 'I': 'B', 'J': 'E',\n'K': 'W', 'L': 'R', 'M': 'X', 'N': 'P', 'O': 'L',\n'P': 'D', 'Q': 'S', 'R': 'I', 'S': 'U', 'T': 'H',\n'U': 'V', 'V': 'A', 'W': 'K', 'X': 'O', 'Y': 'T',\n'Z': 'N', })\nen = cipher.encrypt(\"Mark has a Big nose\")\nde = cipher.decrypt(en)\nprint \"Encrypted = %s\" % en\nprint \"Decrypted = %s\" % de\n<\/pre>\n
\nquite probably “a”. Frequent three letter words will be either “and” or “the”, and “the” will frequently appear at the beginning of sentences. Even if you include mappings for all of the punctuation and space, and you don’t distinguish case, it’s still easy to decrypt.
\nWith a fixed mapping like this, by using frequency tables for the characters and character groups, you’ll be able to pretty quickly
\nfigure it out. This is easy enough to crack that there’s actually a popular daily newspaper puzzle called “CryptoQuote” that presents an encrypted quote every day for readers to decode.<\/p>\n
\nget “xAiw jAu A qby pluz”. A three letter word with “a” as the middle is probably
\n“has”, so we can guess that “h” is translated to “j”, and “s” is translated to “u”. So
\nwe get “xAiw HAS A qbz plSe”. In 10 seconds, you’ve got a third of the message decoded – and that’s for a message that’s only 5 words\/20 letters long!<\/p>\n