Bell's Theorem - Bell Inequality

Classical computing:

For binary bits measurements: 

a0b0 + a0b1 + a1b0 - a1b1 <=2

In quantum mechanics 

For using qubits, it can violate the the inequlity:

At Bell state / entanglement 

The average of four measures can be over 2 sqrt(2) = 2.828..., exceed two! This can be proofed in the lab setting:

Experiment to show the violation of Bell Inequality

AES Algorithm

A quantum-safe symmetric key encryption, and fast due to the block cipher techniques used. 

• Convert to State Array
• Transformations (and inverses)
• AddRoundKey
• SubBytes
• ShiltRows
• MixColumns
• Key Expansion

1. Convert to state array

2a. AddRoundKey

2b. SubBytes (S-box)

for index 55, the s-box value is fc

2c. ShiftRows

2d. MixColumns

3. Key Expansion (new round key)

#AES round key (128 bits)

current round key = w0, w1, w2, w3 (column, vertical)

w0=column 1, w1 = c.2, w2 = c.3, w3 = c.4

g(w3) calculation:

   1) shift left, 2) apply s-box,

   3) add round constant (01,00,00,00)

new roundkey: w4, w5, w6, w7

   w4 = w0 xor g(w3), w5 = w4 xor w1,

   w6 = w5 xor w2,    w7 = w6 xor w3 

 

Example

Calculation of round key (round 1)

w3 = 01 02 14 13, shift left = 02 14 13 01, after s-box 77 fa 7b 7c, after + 1000h = 76 fa 7b 7c.

so g(w3) = 76 fa 7b 7c, then w4 = wo xor g(w3) = 74, fb 6a 7c (column one of round 1 key)

 

Algorithm

10 round = 128-bit keys

12 round = 196-bit keys

14 round = 256-bit keys 

AES-256 is considered to be quantum resistant. 

References:

1. Rijndael-Inspector - Rijndael_Animation_v4-eng.exe|swf - A flash application

2. AES-example.pdf

3. Zhou-Xuan-fulltext.pdf (Univ. of Manchester)