Hash function, what is it?

Greetings to the dear reader!

Today I would like to talk about what a hash function is, touch on its main properties, give examples of use and in general outline the modern SHA-3 hashing algorithm, which was published as the US Federal Information Processing Standard in 2015.

General information

A cryptographic hash function is a mathematical algorithm that maps arbitrary-sized data into a fixed-size bitmap.

, -, «-» «», «».

- :

) - ̆, -

b) -

c) ̆ , -

d) ̆ -

e) ,

- SHA3-256.

256 , 256 , .

, 64 . , 256 .

: " , , 256 ?"

: 256 !

, 256 - $2 ^ {256}$ , $2 ^ {256}$ .

, , :

$2 ^ {256} \ approx 1.158 \ times 10 ^ {77}$

, , !

.

- .

̆ - ̆:

Pre-image resistance

h, m , h = hash (m)

Second pre-image resistance

m_1 , ̆ ,

hash (m_1) = hash (m_2)

Collision resistance

m_1 ,

hash (m_1) = hash (m_2)

m_1 -

.

Collision resistance. , , ̆ . , - ̆̆ , , . , ̆ - ̆ , , . - ̆ , , ̆.

, -̆ ̆ , ̆ .

Pre-image resistance. . - , , , . , . .

Second pre-image resistance. . , - . , , , , . , , , hash (m_1) = h, m_2 , hash (m_2) = h

, . -, , .

, , .

, , , .

, - , .

-

-:

•

- ̆, , , - ̆.

•

. , . , . -, .

•

, , . . , -.

:

, . , , . , ( ). , , , . , -, .

SHA-3.

SHA-3

(NIST) 2007—2012 -, SHA-1 SHA-2.

, :

•

•

,

•

, ISA

5 :

• BLAKE

• Grøstl

• JH

• Keccak

• Skein

SHA-3 Keccak.

Keccak .

Keccak

- ̆ Keccak ̆ , ̆ «» , Z «» .

Keccak Keccak-f, Keccak-f [b] , $b \ in \ {25, 50, 100, 200, 400, 800, 1600 \}$

Keccak-f ̆ , . n_r n_r = 12 + 2l, 2l = b / 25

SHA-3 Keccak-f[1600], n_r = 24

Keccak-f [1600]

, .

1600 , , .

, , SHA3-256 r = 1088, c = 512

SHA-3 S $5 \ times 5$ w = 64 , $5 \ times 5 \ times 64 = 1600$ . Keccak , 2.

- :

• M P ̆ r

• P n $r: P_0, P_1,…, P_ {n-1}$

• «»: ̆ $P_ {i}$ (b = r+c) 2 , , 2 $P_ {i + 1}$ . 0.

• «»: , - -, . «» , .

, :

SHA-3 10...1: 1, 0 r - 1 1.

r - 1 , ̆ r - 1 . , r - 1 .

M r, , ̆ ̆ , r - 2 . , , , - .

, - ̆, , .

12 + 2l :

$\ theta$
$\ rho$
$\ pi$
$\ chi$
$\ iota$

, , , ,

:

$5 \ times 5 \ times 64$ , a [x] [y] [z]

A [x] [y] [z]

ROT (a, d) , :

$ROT (a [x] [y] [z], d) = a [x] [y] [z + d \: \: mod \: w]$

ROT (a, d) - , $z + d \: \: mod \: w$ ,

- (64 )

, .

$\ theta$

$\ theta$ : a [x] [y] [z] $a [x-1] [\ cdot] [z]$ $a [x + 1] [\ cdot] [z-1]$

:

:

$\ rho$

$\ rho$ ( z).

:

$\ pi$

$\ pi$ :

$\ chi$

$\ chi$ Keccak-f

:

$\ iota$

$\ iota$ . Keccak-f , , . .

RC [i] w = 64

:

r [x, y] :

, -

SHA-3 Keccak, Secure Hash Algorithm

I hope everything was clear and interesting

Thank you all for your attention!

All Articles