dChan - Q Origins Project Archive

What is Bounded Quantum Polynomial time?

What algorithms run in its efficiency?

Has its equivalency to P been explored in the past (circa mid-nineties)?

Are there mathematical structures which can be constructed which calculate all values at once, thus running a quantum algorithm on a classical computer?

Do the patterns in the Mandelbrot set PROVE they exist?

It is also involved in the RSA cryptosystem (ie multiplicative inverses are used in the decryption step).

(C)

https://tls.mbed.org/aes-source-code

For those who can program in C, this is good to read. It has many code comments.

And for those interested in Elliptical Curve Cryptography, this explains the full implementation, no oversimplications.

https://www.johannes-bauer.com/compsci/ecc/

AES: Advanced Encryption Standard - a Conceptual Review

https://youtube.com/watch?v=liKXtikP9F0

Data rearranged in so many ways using so many variables and functions nobody would ever try to reverse it. And how could they–since it's like garbling a message in an extremely sophisticated way 16*4 (and a few more constants) times.

How

Could

They.

Anonymous ID: ce30f1 Nov. 25, 2018, 10:11 p.m. No.4033456 🗄️.is 🔗kun >>3463

#include <stdint.h>#define ROTL8(x,shift) ((uint8_t) ((x) << (shift)) | ((x) >(8 - (shift))))void initialize_aes_sbox(uint8_t sbox[256]) { uint8_t p = 1, q = 1; / loop invariant: p * q == 1 in the Galois field / do { / multiply p by 3 / p = p ^ (p << 1) ^ (p & 0x80 ? 0x1B : 0); / divide q by 3 (equals multiplication by 0xf6) / q ^= q << 1; q ^= q << 2; q ^= q << 4; q ^= q & 0x80 ? 0x09 : 0; / compute the affine transformation / uint8_t xformed = q ^ ROTL8(q, 1) ^ ROTL8(q, 2) ^ ROTL8(q, 3) ^ ROTL8(q, 4); sbox[p] = xformed ^ 0x63; } while (p != 1); / 0 is a special case since it has no inverse / sbox[0] = 0x63;}

Anonymous ID: ce30f1 Nov. 25, 2018, 10:12 p.m. No.4033463 🗄️.is 🔗kun >>5189

>>4033456

This is where a briefing on modular arithmetic comes in handy. Galois fields are simply mathematical spaces where every operation is run modulo a certain number (mostly primes in the case of ECC).

Let's look at a few videos before we go through code in a language that is easier for everybody to understand than C (such as Java or C#)

AES Rijndael Cipher explained as a Flash animation (remember to pause)

https://www.youtube.com/watch?v=gP4PqVGudtg

Lecture 8: Advanced Encryption Standard (AES) by Christof Paar

https://www.youtube.com/watch?v=NHuibtoL_qk

I will post code for the encryption of a simple message, then for a file, (probably explaining some mathematical concepts along the way.) We will look at the decryption process, then we will outline how a method to decrypt without the cipher key would behave. We will study how our government placed a backdoor in the elliptical curve random number generator. We will get to current cryptanalysis efforts on block ciphers and the flaws in their approach.

We'll explore the idea that true, unbreakable mathematical security requires the key to be the same size as the plaintext (which is how One-Time-Pads work), and that because AES does not do this (that would be highly impractical), the patterns of the cipher key must exist in the cipher text.