SHA256标准详解：安全哈希算法的权威介绍

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SHA256标准，正式名称为Secure Hash Signature Standard (SHS) (FIPSPUB180-2)，是联邦信息处理标准(FIPS)系列的一部分，由美国国家标准与技术研究院(NIST)发布。该标准发布于2002年8月1日，旨在为电子数据（消息）提供一种安全的、压缩的表示形式，以确保数据完整性、认证和一致性。 SHA256属于计算机安全标准类别，特别关注于密码学领域，它是在1996年《信息技术管理改革法》(Public Law 104-106)和1987年的《计算机安全法》(Public Law 100-235)的法律框架下制定的。这一标准规定了四种安全哈希算法：SHA-1、SHA-256、SHA-384和SHA-512。SHA-256是最常用的，其输出的哈希值长度为256位，能够处理任意长度小于2^64比特的消息。 SHA-256的主要功能是将输入数据通过一系列复杂的数学运算转化为一个固定长度的输出，这个过程是单向的，即无法从哈希值反推回原始数据，这在数字签名、消息认证码(MAC)、散列函数以及防篡改应用中具有重要作用。使用SHA-256时，其安全性基于密码学原理，如预定义的固定算法、碰撞抵抗性和第二预映射阻力等，以确保即使面对强大的计算能力，也难以找到两个不同的输入产生相同的哈希值。 SHA-256标准的发布标志着对旧版哈希算法的升级，随着技术的发展，NIST不断更新标准以应对新出现的安全威胁。2004年2月25日，FIPS Publication 180-2被最新版本所取代，对于当前的SHA256及其相关规范，应参考NIST官方网站的最新修订版，地址为：http://csrc.nist.gov/publications/PubsFIPS.html#fips180-4。 SHA-256的广泛采用源于其平衡的性能、安全性和实用性，不仅在网络安全协议、软件开发、数字证书等领域广泛应用，也在区块链技术中扮演了关键角色，例如比特币的交易验证就依赖于SHA-256的哈希计算来保护交易记录的完整性和不可篡改性。SHA256标准是现代信息安全基础设施中不可或缺的一部分。

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This operation is used by the SHA-256, SHA-384, and SHA-512 algorithms.

5. The rotate left (circular left shift) operation, ROTL

(x), where x is a w-bit word and n

is an integer with 0

≤

n < w, is defined by

ROTL

(x) = (x << n)

∨

(x >> w - n).

Thus, ROTL

(x) is equivalent to a circular shift (rotation) of x by n positions to the

left.

This operation is used only in the SHA-1 algorithm. Note that in Ref. [180-1] this

operation was referred to as “S

(X)”; however, the notation has been modified for

clarity and consistency with the notation used for operations in the other secure hash

algorithms.

6. Note the following equivalence relationships, where w is fixed in each relationship:

ROTL

(x)

≈

ROTR

w-n

(x)

ROTR

(x)

≈

ROTL

w-n

(x).

4. FUNCTIONS AND CONSTANTS

4.1 Functions

This section defines the functions that are used by each of the algorithms. Although the SHA-

256, SHA-384, and SHA-512 algorithms all use similar functions, their descriptions are

separated into sections for SHA-256 (Sec. 4.1.2) and for SHA-384 and SHA-512 (Sec. 4.1.3),

since the input and output for these functions are words of different sizes. Each of the algorithms

include Ch(x, y, z) and Maj(x, y, z) functions; the exclusive-OR operation (

⊕

) in these functions

may be replaced by a bitwise OR operation (∨) and produce identical results.

4.1.1 SHA-1 Functions

SHA-1 uses a sequence of logical functions, f

, f

,…, f

. Each function f

, where 0

≤

t < 79,

operates on three 32-bit words, x, y, and z, and produces a 32-bit word as output. The function f

(x, y, z) is defined as follows:

Ch(x, y, z) = (x

∧

⊕

( x

∧

z) 0

≤

Parity(x, y, z) = x

⊕

z 20

≤

(x, y, z) = (4.1)

Maj(x, y, z) = (x

∧

⊕

∧

⊕

∧

z) 40

≤

Parity(x, y, z) = x

⊕

z 60

≤

79.

4.1.2 SHA-256 Functions

SHA-256 uses six logical functions, where each function operates on 32-bit words, which are

represented as x, y, and z. The result of each function is a new 32-bit word.

(

)

(

∧

)

⊕

(

∧

)

(4.2)

Maj

(

)

(

∧

)

⊕

(

∧

)

⊕

(

∧

)

(4.3)

{256}

∑

(x) = ROTR

(x)

⊕

ROTR

(x)

⊕

ROTR

(x) (4.4)

{256}

∑

(x) = ROTR

(x)

⊕

ROTR

(x)

⊕

ROTR

(x) (4.5)

{256}

( )s

x = ROTR

(x)

⊕

ROTR

(x)

⊕

SHR

(x) (4.6)

{256}

( ) SHR

(x)s

x = ROTR

(x)

⊕

ROTR

(x)

⊕

(4.7)

4.1.3 SHA-384 and SHA-512 Functions

SHA-384 and SHA-512 each use six logical functions, where each function operates on 64-bit

words, which are represented as x, y, and z. The result of each function is a new 64-bit word.

(

)

(

∧

)

⊕

(

∧

)

(4.8)

Maj

(

)

(

∧

)

⊕

(

∧

)

⊕

(

∧

)

(4.9)

{512}

∑

(x) = ROTR

(x)

⊕

ROTR

(x)

⊕

ROTR

(x) (4.10)

{512}

∑

(x) = ROTR

(x)

⊕

ROTR

(x)

⊕

ROTR

(x) (4.11)

{512}

( )s

x = ROTR

(x)

⊕

ROTR

(x)

⊕

SHR

(x) (4.12)

{512}

( )s

x = ROTR

(x)

⊕

ROTR

(x)

⊕

SHR

(x) (4.13)

4.2 Constants

4.2.1 SHA-1 Constants

SHA-1 uses a sequence of eighty constant 32-bit words, K

, K

,…, K

, which are given by

5a827999 0

≤

6ed9eba1 20

≤

= (4.14)

8f1bbcdc 40

≤

ca62c1d6 60

≤

79.

4.2.2 SHA-256 Constants

{256} {256} {256}

SHA-256 uses a sequence of sixty-four constant 32-bit words, K , K ,K, K . These

0 1 63

words represent the first thirty-two bits of the fractional parts of the cube roots of the first sixty-

four prime numbers. In hex, these constant words are (from left to right)

428a2f98 71374491 b5c0fbcf e9b5dba5 3956c25b 59f111f1 923f82a4 ab1c5ed5

d807aa98 12835b01 243185be 550c7dc3 72be5d74 80deb1fe 9bdc06a7 c19bf174

e49b69c1 efbe4786 0fc19dc6 240ca1cc 2de92c6f 4a7484aa 5cb0a9dc 76f988da

983e5152 a831c66d b00327c8 bf597fc7 c6e00bf3 d5a79147 06ca6351 14292967

27b70a85 2e1b2138 4d2c6dfc 53380d13 650a7354 766a0abb 81c2c92e 92722c85

a2bfe8a1 a81a664b c24b8b70 c76c51a3 d192e819 d6990624 f40e3585 106aa070

19a4c116 1e376c08 2748774c 34b0bcb5 391c0cb3 4ed8aa4a 5b9cca4f 682e6ff3

748f82ee 78a5636f 84c87814 8cc70208 90befffa a4506ceb bef9a3f7 c67178f2.

4.2.3 SHA-384 and SHA-512 Constants

SHA-384 and SHA-512 use the same sequence of eighty constant 64-bit words,

{512} {512} {512}

, K

,K, K

. These words represent the first sixty-four bits of the fractional parts of

the cube roots of the first eighty prime numbers. In hex, these constant words are (from left to

right)

428a2f98d728ae22 7137449123ef65cd b5c0fbcfec4d3b2f e9b5dba58189dbbc

3956c25bf348b538 59f111f1b605d019 923f82a4af194f9b ab1c5ed5da6d8118

d807aa98a3030242 12835b0145706fbe 243185be4ee4b28c 550c7dc3d5ffb4e2

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