📶 🏿 👨‍👩‍👧‍👧 RC6. From simple to complex ⛹🏼 👨🏿‍🤝‍👨🏻 👨🏿

In this article, you will learn

Who is your block cipher.
What principles did the creators of the algorithm adhere to?
How does the key preparation process look like?
Work algorithm.
And what does RC5 have to do with it?

Introduction to RC6.

RC6 ( Rivest's Cipher 6 ) is a symmetric block cipher based on the Festel network , developed by Ronald Rivest in 1998.

First, let's figure out the terminology:

What does symmetrical mean?

There are two types of cipher ~~people~~ :

Symmetrical (what we need)
Asymmetric (some other time, bro)

In symmetric encryption, the same key is used to encrypt and decrypt data . It must be kept secret . Those. neither the sender nor the recipient should show it to anyone. Otherwise, your data can be intercepted / changed or even worse.

Symmetric encryption algorithms:

AES (Advanced Encryption Standard)

3DES (Triple Data Encryption Algorithm)

RC4, RC5, RC6 (Rivest cipher)

: . , , .

:

RSA (Rivest-Shamir-Adleman)

DSA (Digital Signature Algorithm), DSS (Digital Signature Standard)

Diffie-Hellman

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2 ( xor) .
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() . K_i ~ - - ( ).

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RC6 . , , . :

, , w ~ - . , RC6 . 4 A, B, C, D w ~ - . w = 32 . $4 \ times 32 = 128$ .

, . :

. . (.. 4 ).
. ( ). $0 \ leq r \ leq 255$ .
.
: .

, RC6 / w / r / b .

$P_w \ leftarrow Odd ((e-2) 2 ^ w) \\ Q_w \ leftarrow Odd ((\ phi-1) 2 ^ w)$

e = 2.71828 ... (), $\ phi = 1.61803 ...$ ( ). $Odd (\ cdot) ~ -$ .

, w = 32 , :

$P32 = 10110111111000010101010101011 = b7e15163 \\ Q32 = 10011110001101110110110111001 = 9e3779b9$

. :

1 .

K [0 ... b-1] L [0 ... s-1] , c = b / u , u = w / 8- . w / 8 , :

#  x<<<y -    

c = [max(b, 1) / u]
for b - 1 downto 0 do
	L[i/u] = (L[i/u]<<<8) + K[i]

2 .

. , :

S[0] = P_w

for i = 1 to 2r + 3 do
	S[i] = S[i - 1] + Q_w

3 .

, , :

# :    b ,   
#			 	L[0,...,c-1]
#				  r

# : w-   S[0,...,2r+3]
  
A = B = i = j = 0

v = 3 * max(c, 2r + 4)
for s = 1 to v do
{
	A = S[i] = (S[i] + A + B)<<<3
  B = L[j] = (L[j] + A + B)<<<(A + B)
  i = (i + 1)mod(2r + 4)
  j = (j + 1)mod(c)
}

, RC6. , , RC5. , RC6:

RC5

RC5 , 1994 . RC6 , . .

, :

RC5 . .. () , .
RC5 , .
RC5 . , 64- , RC5 .
RC5 . .. , .
RC5 . .
RC5 . .
RC5 .
, RC5 .

RC5 , RC6. . C RC5:

A = A + S[0]
B = B + S[1]
for i = 1 to r do 
  A = ((A xor B)<<<B) + S[2i]
  B = ((B xor A)<<<A) + S[2i + 1]

, RC5 .

RC5 RC6

RC5 :

, RC6.

-( ) RC5:

for i = 1 to r do 
{
  A = ((A xor B)<<<B) + S[2i]
  (A, B) = (B, A)
}

RC5. A B, C D:

for i = 1 to r do 
{
  A = ((A xor B)<<<B) + S[2i]
  C = ((C xor D)<<<D) + S[2i + 1]
  (A, B) = (B, A)
  (C, D) = (D, C)
}

, A B C D, (A, B, C, D) = (B, C, D, A). AB CD:

for i = 1 to r do 
{
  A = ((A xor B)<<<B) + S[2i]
  C = ((C xor D)<<<D) + S[2i + 1]
  (A, B, C, D) = (B, A, D, C)
}

AB CD :

for i = 1 to r do 
{
  A = ((A xor B)<<<D) + S[2i]
  C = ((C xor D)<<<B) + S[2i + 1]
  (A, B, C, D) = (B, A, D, C)
}

, B D, , . , , .

f (x) = x (2x + 1) (mod ~ 2 ^ w) , :

for i = 1 to r do
{
	t = (B * (2B + 1))<<<5
  u = (D * (2D + 1))<<<5
  A = ((A xor t)<<<u) + S[2i]
  C = ((C xor u)<<<t) + S[2i + 1]
  (A, B, C, D) = (B, C, D, A)
}

, , ( , pre- post-whitening):

B = B + S[0]
D = D + S[1]
for i = 1 to r do
{
	t = (B * (2B + 1))<<<5
  u = (D * (2D + 1))<<<5
  A = ((A xor t)<<<u) + S[2i]
  C = ((C xor u)<<<t) + S[2i + 1]
  (A, B, C, D) = (B, C, D, A)
}
A = A + S[2r + 2]
C = C + S[2r + 3]

, , , :

, RC6 w ~ - A, B, C, D. , . A, D. :

# :    4- w-  A, B, C, D
#				  r
#				w-   S[0,...,2r+3]

# : ,   A, B, C, D

B = B + S[0]
D = D + S[1]
for i = 1 to r do
{
	t = (B * (2B + 1))<<<lg(w)
  u = (D * (2D + 1))<<<lg(w)
  A = ((A xor t)<<<u) + S[2i]
  C = ((C xor u)<<<t) + S[2i + 1]
  (A, B, C, D) = (B, C, D, A)
}
A = A + S[2r + 2]
C = C + S[2r + 3]

# (A, B, C, D) = (B, C, D, A)    .

RC6 :

# :    4- w-  A, B, C, D
#				  r
#				w-   S[0,...,2r+3]

# :  ,   A, B, C, D

C = C - S[2r + 3]
A = A - S[2r +2]

for i = r downto 1 do
{
	(A, B, C, D) = (D, A, B, C)
  u = (D * (2D + 1))<<<lg(w)
  t = (B * (2B + 1)) << lg(w)
  C = ((C - S[2i + 1)>>>t) xor u
  A = ((A - S[2i])>>>u) xor t
}
D = D - S[1]
B = B - S[0]