Autosave: 2024-12-20 13:12:10

neuron/dc239556-fd21-4147-b56e-3d8b474984ad/a4601796_trapdoor_functions.md

@@ -0,0 +1,40 @@
+---
+tags: [cryptography]
+created: Friday, December 20, 2024
+---
+
+# a4601796_trapdoor_functions
+
+How does [public key cryptography](./bbdcb54f_public_key_cryptography.md)
+achieve the feat of making the encyrpted data only decipherable in one
+direction. In other words how come the same data can be encrypted with one key
+but only decryptable by another?
+
+It is acheived by the use of **trapdoor functions**. These are functions that
+are easy to compute in one direction but extremely difficult to reverse. But
+they also contain trapdoors which, if known, make the functions trivially easy
+to compute in both directions.
+
+The public key holder can compute the encryption but only the private key holder
+has the trapdoor that makes reversing the encryption trivial.
+
+As an example we can look at a common method for generating trapdoor functions
+using prime numbers.
+
+First we need to convert the message into numerical form. One way would be to
+convert the characters to their ASCII numbers. These numbers then become input
+into the mathematical encryption function.
+
+Next we would pick two very large prime numbers. Using RSA-like encryption they
+would be need to be 2048+ bits in length. For the example we will use 17 and 23.
+
+For simplicity let's say that our message is one character equivalent to `5` in
+ASCII. We multiply our two primes to get 391 (17 x 23 = 391) and then find the
+remainder of: our message cubed and divided by the prime sum. This is `125`
+(`5^3 / 391`) which is now our encrypted message which we send.
+
+Unless you know the two primes which were used, it is extremely difficult and
+time consuming to reverse the calculation and find the factors that would get
+you back to the starting point (remember the numbers will be much larger in
+reality). The owner of the private key knows these primes however, so can do
+this.

neuron/dc239556-fd21-4147-b56e-3d8b474984ad/bbdcb54f_public_key_cryptography.md

@@ -0,0 +1,31 @@
+---
+tags: [encryption]
+created: Friday, December 20, 2024
+---
+
+# bbdcb54f_public_key_cryptography
+
+_A_ wants to send a message to _B_. A wants to ensure that only _B_ can read the
+message and that it is not intercepted or altered during transmission to _B_.
+
+Think of _B_ as being in possession of a letterbox. The letterbox contains
+messages that only he can read. Anyone can put letters in it for _B_ to read but
+_B_ alone can read them.
+
+This is achieved by encyrpting the messages with two keys: a public key and a
+private key. The public key can be shared with others and anyone in possession
+of the public key can encrypt a message for _B_. Once encrypted, only _B_ can
+decrypt it using his private key. Once receiving the message, B uses his private
+secret key - that he doesn't share with anyone else - to decrypt. This is the
+equivalent to opening up the letterbox and taking out the letters.
+
+Another useful analogy is to think of invisible ink. Anyone can write a letter
+using the invisible ink but only the recipient has the liquid that can render it
+visible again. Anyone intercepting the message (without the liquid) will see
+nothing, equivalent to the encrypted data.
+
+This is asymmetric encryption because the two communicating parties do not have
+equal access to the messages exchanged. _A_ can only send messages - he can't
+decrypt them, only _B_ can. So _A_ is unequal relative to _B_. With symmetric
+encryption _A_ and _B_ would both share a single private key which they would
+each use to encrypt and decrypt their messages.

neuron/dc239556-fd21-4147-b56e-3d8b474984ad/index.md

@@ -13,12 +13,14 @@ computer science.
 
 ![not-by-ai-badge](static/not-by-ai-alternative--light.svg)
  
-**Build ID:** a04df86f-a05c-47a7-b4e9-17284e6b14a3
+**Build ID:** dc239556-fd21-4147-b56e-3d8b474984ad
 
-**Published:** Fri 20 Dec 2024 11:32:52
+**Published:** Fri 20 Dec 2024 13:12:09
 
 ### Recent edits 
 
+- [[a4601796_trapdoor_functions]] 
+- [[bbdcb54f_public_key_cryptography]] 
 - [[Dynamic_and_static_websites]] 
 - [[User_agent]] 
 - [[Architecture_of_the_World_Wide_Web]] 
@@ -29,11 +31,9 @@ computer science.
 - [[fbbfbc32-political-accommodation-inveigelment-surveillance-capitalism]] 
 - [[a247fa9b_surveillance_capitalism_not_necessary]] 
 - [[AWS_SNS]] 
-- [[AWS_SQS]] 
-- [[AWS_SQS_SDK]] 
 
 
-### All notes (507) 
+### All notes (509) 
 
 - [[0716531c_rewilding_the_internet]] 
 - [[241fe1a3_the_Web_versus_modem_BBSs]] 
@@ -523,7 +523,9 @@ computer science.
 - [[Zero_property_of_multiplication]] 
 - [[Zip_function_in_Python]] 
 - [[a247fa9b_surveillance_capitalism_not_necessary]] 
+- [[a4601796_trapdoor_functions]] 
 - [[a771a6d9_attributes_of_internet_enclosure]] 
+- [[bbdcb54f_public_key_cryptography]] 
 - [[c301a0b3-1d8_Mosaic_Netscape_and_Browser_Wars]] 
 - [[c8173d17_TIMPs]] 
 - [[cfbef1c4_web_precursors]] 

zk/a4601796_trapdoor_functions.md

@@ -0,0 +1,40 @@
+---
+tags: [cryptography]
+created: Friday, December 20, 2024
+---
+
+# a4601796_trapdoor_functions
+
+How does [public key cryptography](./bbdcb54f_public_key_cryptography.md)
+achieve the feat of making the encyrpted data only decipherable in one
+direction. In other words how come the same data can be encrypted with one key
+but only decryptable by another?
+
+It is acheived by the use of **trapdoor functions**. These are functions that
+are easy to compute in one direction but extremely difficult to reverse. But
+they also contain trapdoors which, if known, make the functions trivially easy
+to compute in both directions.
+
+The public key holder can compute the encryption but only the private key holder
+has the trapdoor that makes reversing the encryption trivial.
+
+As an example we can look at a common method for generating trapdoor functions
+using prime numbers.
+
+First we need to convert the message into numerical form. One way would be to
+convert the characters to their ASCII numbers. These numbers then become input
+into the mathematical encryption function.
+
+Next we would pick two very large prime numbers. Using RSA-like encryption they
+would be need to be 2048+ bits in length. For the example we will use 17 and 23.
+
+For simplicity let's say that our message is one character equivalent to `5` in
+ASCII. We multiply our two primes to get 391 (17 x 23 = 391) and then find the
+remainder of: our message cubed and divided by the prime sum. This is `125`
+(`5^3 / 391`) which is now our encrypted message which we send.
+
+Unless you know the two primes which were used, it is extremely difficult and
+time consuming to reverse the calculation and find the factors that would get
+you back to the starting point (remember the numbers will be much larger in
+reality). The owner of the private key knows these primes however, so can do
+this.

zk/bbdcb54f_public_key_cryptography.md

@@ -0,0 +1,31 @@
+---
+tags: [encryption]
+created: Friday, December 20, 2024
+---
+
+# bbdcb54f_public_key_cryptography
+
+_A_ wants to send a message to _B_. A wants to ensure that only _B_ can read the
+message and that it is not intercepted or altered during transmission to _B_.
+
+Think of _B_ as being in possession of a letterbox. The letterbox contains
+messages that only he can read. Anyone can put letters in it for _B_ to read but
+_B_ alone can read them.
+
+This is achieved by encyrpting the messages with two keys: a public key and a
+private key. The public key can be shared with others and anyone in possession
+of the public key can encrypt a message for _B_. Once encrypted, only _B_ can
+decrypt it using his private key. Once receiving the message, B uses his private
+secret key - that he doesn't share with anyone else - to decrypt. This is the
+equivalent to opening up the letterbox and taking out the letters.
+
+Another useful analogy is to think of invisible ink. Anyone can write a letter
+using the invisible ink but only the recipient has the liquid that can render it
+visible again. Anyone intercepting the message (without the liquid) will see
+nothing, equivalent to the encrypted data.
+
+This is asymmetric encryption because the two communicating parties do not have
+equal access to the messages exchanged. _A_ can only send messages - he can't
+decrypt them, only _B_ can. So _A_ is unequal relative to _B_. With symmetric
+encryption _A_ and _B_ would both share a single private key which they would
+each use to encrypt and decrypt their messages.