Tiny Bytes: RSA
tldr RSA works by exploiting the fact we can’t easily factor 2 large prime numbers and group theory to make a trapdoor permutation, aka a function that turns x into y but y can’t easily be turned into x without a secret. However, implementing RSA gets tricky because there’s lots of subtle attacks.MathRSA takes advantage of the group Z^*_{n} (multiplicative group of integers modulo n). This is the non-negative integers less than n that have an inverse modulo n. 1 x 1 mod n = 1. 0 x int = 0 so ...
Tiny Bytes: Chilling
Hi, Just chilling tonight. Aiming to finish up chapter tomorrow. Night, Lucas
Tiny Bytes: Quickie
Hi, Did much more writing on RSA. Will finish soon. Bye, Lucas
Tiny Bytes: RSA
tldr RSA works by exploiting the fact we can’t easily factor 2 large prime numbers and group theory to make a trapdoor permutation, aka a function that turns x into y but y can’t easily be turned into x without a secret. However, implementing RSA gets tricky because there’s lots of subtle attacks.MathRSA takes advantage of the group Z^*_{n} (multiplicative group of integers modulo n). This is the non-negative integers less than n that have an inverse modulo n. 1 x 1 mod n = 1. 0 x int = 0 so ...
Tiny Bytes: Chilling
Hi, Just chilling tonight. Aiming to finish up chapter tomorrow. Night, Lucas
Tiny Bytes: Quickie
Hi, Did much more writing on RSA. Will finish soon. Bye, Lucas
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It’s day 2 y’all,
Given that part of the reason I started this is to practice explaining technical concepts, I thought, let’s do something like that today. Now it needs to be something I already understand pretty well. Cryptographic key management is on the mind, so Imma do a post on cryptographic keys: what they are, how they work, and why they are pretty neat.
After writing this, I realized I should probably define security and privacy because they are at the heart of the value of keys. While I can and will write long descriptions of security and privacy, let’s break them down into single sentences:
**Security: **My information is secure if I can do what I want with it and others can’t.
Privacy: My information is private if only I know what my information is.
They are very similar, and often good security gives me good privacy. For example, I send Alice a package that only Alice can open. I have security because I know no one can steal what’s inside and I have privacy because I know no one knows what is inside. If someone can destroy the package without opening it, my security is hurt but my privacy is maintained. On the flip side, if someone can use an x-ray to see what’s in the box, my security in unaffected but what I am sending is no longer private.
In a nutshell, cryptographic keys allow me to protect my information, communicate without someone listening in, and identify who I am. In essence, keys improve my security and privacy in the digital world.
I can protect my own data by turning it into a random blob that only I can turn back into my data. I can do the same to prevent someone from listening to me chat with Bob by turning my texts into random blobs that only Bob can turn back. I can prove to Bob that my texts are from me by sending Bob a particular blob that only I could have created.
Keys work through the following functions:
Generate: Create the key(s).
**Encrypt: (**Use a key to) Turn data into random data.
Decrypt: (Use a key to) Turn random data into original data.
Sign: (Use a key to) Sign a piece of data to show it was from me.
Verify: (Use a key to) Prove the signature came from me.
It’s worth mentioning that there are loads of ways to generate keys, each affecting the specific encryption/decryption/signing/verifying schemes. The most common methods create either a single key or a secret/public key pair. In the single key case, it’s used for every algorithm and is kept hidden from anyone who you don’t want access to your data. In the key pair case, a secret key is kept hidden and used to decrypt/sign, while the public key is known by everyone and is used to encrypt/verify.
Of course, you could go crazy with these schemes; for example, you could make it take 100 keys to encrypt data and only 2 to decrypt.
Cryptographic keys are instrumental to securely interacting with the web. They unlock interesting applications because of the security they add. They can SIGnal who people are and allow them into their accounts. Right now, on Mirror, I signed in using my wallet to prove my identity so that I can realize I’m running out of time and write bad and even cryptic puns.
That derailed fast. But remember, cryptographic keys are superbly cool and enable people to safely interact on the web. If they aren’t managed well, and someone learns your keys, all that goes out the window.
Bye,
Lucas
It’s day 2 y’all,
Given that part of the reason I started this is to practice explaining technical concepts, I thought, let’s do something like that today. Now it needs to be something I already understand pretty well. Cryptographic key management is on the mind, so Imma do a post on cryptographic keys: what they are, how they work, and why they are pretty neat.
After writing this, I realized I should probably define security and privacy because they are at the heart of the value of keys. While I can and will write long descriptions of security and privacy, let’s break them down into single sentences:
**Security: **My information is secure if I can do what I want with it and others can’t.
Privacy: My information is private if only I know what my information is.
They are very similar, and often good security gives me good privacy. For example, I send Alice a package that only Alice can open. I have security because I know no one can steal what’s inside and I have privacy because I know no one knows what is inside. If someone can destroy the package without opening it, my security is hurt but my privacy is maintained. On the flip side, if someone can use an x-ray to see what’s in the box, my security in unaffected but what I am sending is no longer private.
In a nutshell, cryptographic keys allow me to protect my information, communicate without someone listening in, and identify who I am. In essence, keys improve my security and privacy in the digital world.
I can protect my own data by turning it into a random blob that only I can turn back into my data. I can do the same to prevent someone from listening to me chat with Bob by turning my texts into random blobs that only Bob can turn back. I can prove to Bob that my texts are from me by sending Bob a particular blob that only I could have created.
Keys work through the following functions:
Generate: Create the key(s).
**Encrypt: (**Use a key to) Turn data into random data.
Decrypt: (Use a key to) Turn random data into original data.
Sign: (Use a key to) Sign a piece of data to show it was from me.
Verify: (Use a key to) Prove the signature came from me.
It’s worth mentioning that there are loads of ways to generate keys, each affecting the specific encryption/decryption/signing/verifying schemes. The most common methods create either a single key or a secret/public key pair. In the single key case, it’s used for every algorithm and is kept hidden from anyone who you don’t want access to your data. In the key pair case, a secret key is kept hidden and used to decrypt/sign, while the public key is known by everyone and is used to encrypt/verify.
Of course, you could go crazy with these schemes; for example, you could make it take 100 keys to encrypt data and only 2 to decrypt.
Cryptographic keys are instrumental to securely interacting with the web. They unlock interesting applications because of the security they add. They can SIGnal who people are and allow them into their accounts. Right now, on Mirror, I signed in using my wallet to prove my identity so that I can realize I’m running out of time and write bad and even cryptic puns.
That derailed fast. But remember, cryptographic keys are superbly cool and enable people to safely interact on the web. If they aren’t managed well, and someone learns your keys, all that goes out the window.
Bye,
Lucas
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