1. 引言
SHA-256（安全哈希算法，FIPS 182-2）是密码学哈希函数，其摘要长度为256位。SHA-256为keyless哈希函数，即为MDC（Manipulation Detection Code）。【MAC消息认证码有key，不是keyless的。】
SHA-256哈希函数可定义为：
public static BigInteger hash(byte[] M)
其中：
- 输入：消息 M M M为任意长度的字节数组。
- 输出：在 [ 0 , 2 256 ) [0,2^{256}) [0,2256)范围的正整数，为消息 M M M的哈希值。
相关的测试用例有：【其中hash值以十六进制表示】
消息按block处理：
- 每个block长度为512 = 16 x 32 位
- 每个block需要64轮
2. 基本运算
SHA-256中的基本运算有：
- 布尔运算：AND表示为 ∧ \wedge ∧，XOR表示为 ⊕ \oplus ⊕，OR表示为 ∨ \vee ∨。
- Bitwise complement（按位补码），表示为： ˉ \bar{} ˉ。
- 证明加法对 2 32 2^{32} 232求模运算，表示为 A + B A+B A+B。
以上运算均是基于32位 words的（每个word对应32位）。binary words解析为以2为基的整数：
- R o t R ( A , n ) RotR(A,n) RotR(A,n)：表示将binary word A A A 循环右移 n n n位。
- S h R ( A , n ) ShR(A,n) ShR(A,n)：表示将binary word A A A 右移 n n n位。
- A ∣ ∣ B A||B A∣∣B：表示将binary word A A A 和 binary word B B B 拼接在一起。
3. 函数和常量
SHA-256中使用的函数有：
- C h ( X , Y , Z ) = ( X ∧ Y ) ⊕ ( X ˉ ∧ Z ) Ch(X, Y, Z) = (X\wedge Y)\oplus(\bar{X}\wedge Z) Ch(X,Y,Z)=(X∧Y)⊕(Xˉ∧Z)
- M a j ( X , Y , Z ) = ( X ∧ Y ) ⊕ ( X ∧ Z ) ⊕ ( Y ∧ Z ) Maj(X,Y,Z)= (X\wedge Y)\oplus(X\wedge Z)\oplus(Y\wedge Z) Maj(X,Y,Z)=(X∧Y)⊕(X∧Z)⊕(Y∧Z)
- ∑ 0 ( X ) = R o t R ( X , 2 ) ⊕ R o t R ( X , 13 ) ⊕ R o t R ( X , 22 ) \sum_0(X)=RotR(X,2)\oplus RotR(X,13)\oplus RotR(X,22) ∑0(X)=RotR(X,2)⊕RotR(X,13)⊕RotR(X,22)
- ∑ 1 ( X ) = R o t R ( X , 6 ) ⊕ R o t R ( X , 11 ) ⊕ R o t R ( X , 25 ) \sum_1(X)=RotR(X,6)\oplus RotR(X,11)\oplus RotR(X,25) ∑1(X)=RotR(X,6)⊕RotR(X,11)⊕RotR(X,25)
- σ 0 ( X ) = R o t R ( X , 7 ) ⊕ R o t R ( X , 18 ) ⊕ S h R ( X , 3 ) \sigma_0(X)=RotR(X,7)\oplus RotR(X,18)\oplus ShR(X,3) σ0(X)=RotR(X,7)⊕RotR(X,18)⊕ShR(X,3)
- σ 1 ( X ) = R o t R ( X , 17 ) ⊕ R o t R ( X , 19 ) ⊕ S h R ( X , 10 ) \sigma_1(X)=RotR(X,17)\oplus RotR(X,19)\oplus ShR(X,10) σ1(X)=RotR(X,17)⊕RotR(X,19)⊕ShR(X,10)
SHA-256中每个block需要64轮，每一轮对应的64个constant words K 0 , K 1 , ⋯ , K 64 K_0,K_1,\cdots, K_{64} K0,K1,⋯,K64为：
0x428a2f98 0x71374491 0xb5c0fbcf 0xe9b5dba5 0x3956c25b 0x59f111f1 0x923f82a4 0xab1c5ed5
0xd807aa98 0x12835b01 0x243185be 0x550c7dc3 0x72be5d74 0x80deb1fe 0x9bdc06a7 0xc19bf174
0xe49b69c1 0xefbe4786 0x0fc19dc6 0x240ca1cc 0x2de92c6f 0x4a7484aa 0x5cb0a9dc 0x76f988da
0x983e5152 0xa831c66d 0xb00327c8 0xbf597fc7 0xc6e00bf3 0xd5a79147 0x06ca6351 0x14292967
0x27b70a85 0x2e1b2138 0x4d2c6dfc 0x53380d13 0x650a7354 0x766a0abb 0x81c2c92e 0x92722c85
0xa2bfe8a1 0xa81a664b 0xc24b8b70 0xc76c51a3 0xd192e819 0xd6990624 0xf40e3585 0x106aa070
0x19a4c116 0x1e376c08 0x2748774c 0x34b0bcb5 0x391c0cb3 0x4ed8aa4a 0x5b9cca4f 0x682e6ff3
0x748f82ee 0x78a5636f 0x84c87814 0x8cc70208 0x90befffa 0xa4506ceb 0xbef9a3f7 0xc67178f2
这些常量是对自然数中前64个素数(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97…)的立方根的小数部分取前32bit而来。
4. 填充
假设消息长度可 以64位整数表示，为确保消息长度为512位的整数倍，需做如下填充：
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- 1）附加bit 1。
- 2）附加 k k k个bit 0， k k k取值为使得 l + 1 + k ≡ 448 m o d 512 l+1+k\equiv 448 \mod 512 l+1+k≡448mod512的最小正整数，其中 l l l为初始消息位长度。
- 3）初始消息长度 l < 2 64 l<2^{64} l<264以正好64位big-endian表示，将这64位附加到2）之后。
消息通常需要填充。即使消息初始长度已是512的整数倍，也需要填充。
5. block分解
SHA-256中每个block M ∈ { 0 , 1 } 512 M\in\{0,1\}^{512} M∈{ 0,1}512，对应64个words（每个word为32位）的构建方式为：
- 前16个words为：将 M M M按512位block切分为16个32位words：
M = W 1 ∣ ∣ W 2 ∣ ∣ ⋯ ∣ ∣ W 15 ∣ ∣ W 16 M=W_1||W_2||\cdots||W_{15}||W_{16} M=W1∣∣W2∣∣⋯∣∣W15∣∣W16 - 剩下48个words按如下公式构建：
W i = σ 1 ( W i − 2 ) + W i − 7 + σ 0 ( W i − 15 ) + W i − 16 , 17 ≤ i ≤ 64 W_i=\sigma_1(W_{i-2})+W_{i-7}+\sigma_0(W_{i-15})+W_{i-16},17\leq i \leq 64 Wi=σ1(Wi−2)+Wi−7+σ0(Wi−15)+Wi−16,17≤i≤64
6. 哈希计算（压缩函数）
哈希计算，本质为SHA256压缩函数：
- consumes the previous 32-byte digest and a 64-byte block of the padded input。
SHA-256哈希计算步骤为：
-
1）设置8个固定的32bit变量 I V IV IV作为SHA-256哈希计算初始值：
H 1 ( 0 ) = 0 x 6 a 09 e 667 H 2 ( 0 ) = 0 x b b 67 a e 85 H 3 ( 0 ) = 0 x 3 c 6 e f 372 H 4 ( 0 ) = 0 x a 54 f f 53 a H_1^{(0)}=0x6a09e667\ \ H_2^{(0)}=0xbb67ae85 \ \ H_3^{(0)}=0x3c6ef372 \ \ H_4^{(0)}=0xa54ff53a H1(0)=0x6a09e667 H2(0)=0xbb67ae85 H3(0)=0x3c6ef372 H4(0)=0xa54ff53a
H 5 ( 0 ) = 0 x 510 e 527 f H 6 ( 0 ) = 0 x 9 b 05688 c H 7 ( 0 ) = 0 x 1 f 83 d 9 a b H 8 ( 0 ) = 0 x 5 b e 0 c d 19 H_5^{(0)}=0x510e527f\ \ H_6^{(0)}=0x9b05688c \ \ H_7^{(0)}=0x1f83d9ab \ \ H_8^{(0)}=0x5be0cd19 H5(0)=0x510e527f H6(0)=0x9b05688c H7(0)=0x1f83d9ab H8(0)=0x5be0cd19
这些初始值是对自然数中前8个素数（2,3,5,7,11,13,17,19）的平方根的小数部分取前32bit而来。如， 2 = 0.414213562373095048 \sqrt{2}=0.414213562373095048 2=0.414213562373095048，而 0.414213562373095048 ≈ 6 × 1 6 − 1 + a × 1 6 − 2 + 0 × 1 6 − 3 ⋯ 0.414213562373095048\approx 6\times 16^{-1}+a\times 16^{-2}+0\times 16^{-3}\cdots 0.414213562373095048≈6×16−1+a×16−2+0×16−3⋯，于是素数 2 2 2的平方根的小数部分取前32bit就对应为0x6a09e667。 -
2）对于每个blocks M ( 1 ) , M ( 2 ) , ⋯ , M ( N ) M^{(1)},M^{(2)},\cdots,M^{(N)} M(1),M(2),⋯,M(N)，均按如下方式处理：
For t = 1 to N \text{For } t=1 \text{ to } N For t=1 to N- 2.1）根据上面“5. block分解”，为 M ( t ) M^{(t)} M(t)构建64个words W i W_i Wi。
- 2.2）设置： ( a , b , c , d , e , f , g , h ) = ( H 1 ( t − 1 ) , H 2 ( t − 1 ) , H 3 ( t − 1 ) , H 4 ( t − 1 ) , H 5 ( t − 1 ) , H 6 ( t − 1 ) , H 7 ( t − 1 ) , H 8 ( t − 1 ) ) (a,b,c,d,e,f,g,h)=(H_1^{(t-1)},H_2^{(t-1)},H_3^{(t-1)},H_4^{(t-1)},H_5^{(t-1)},H_6^{(t-1)},H_7^{(t-1)},H_8^{(t-1)}) (a,b,c,d,e,f,g,h)=(H1(t−1),H2(t−1),H3(t−1),H4(t−1),H5(t−1),H6(t−1),H7(t−1),H8(t−1))
- 2.3）做64轮如下运算：
For i = 1 to 64 \text{For } i=1 \text{ to } 64 For i=1 to 64
T 1 = h + ∑ 1 ( e ) + C h ( e , f , g ) + K i \ \ \ \ T_1=h+\sum_1(e)+Ch(e,f,g)+K_i T1=h+∑1(e)+Ch(e,f,g)+Ki
T 2 = ∑ 0 ( a ) + M a j ( a , b , c ) \ \ \ \ T_2=\sum_0(a)+Maj(a,b,c) T2=∑0(a)+Maj(a,b,c)
h = g \ \ \ \ h=g h=g
g = f \ \ \ \ g=f g=f
f = e \ \ \ \ f=e f=e
e = d + T 1 \ \ \ \ e=d+T_1 e=d+T1
d = c \ \ \ \ d=c d=c
c = b \ \ \ \ c=b c=b
b = a \ \ \ \ b=a b=a
a = T 1 + T 2 \ \ \ \ a=T_1+T_2 a=T1+T2
End for i \text{End for } i End for i - 2.4）计算 H j ( t ) H_j^{(t)} Hj(t)的新值：【 j j j 的取值为1~8 】
H 1 ( t ) = H 1 ( t − 1 ) + a H_1^{(t)}=H_1^{(t-1)}+a H1(t)=H1(t−1)+a
H 2 ( t ) = H 2 ( t − 1 ) + b H_2^{(t)}=H_2^{(t-1)}+b H2(t)=H2(t−1)+b
H 3 ( t ) = H 3 ( t − 1 ) + c H_3^{(t)}=H_3^{(t-1)}+c H3(t)=H3(t−1)+c
H 4 ( t ) = H 4 ( t − 1 ) + d H_4^{(t)}=H_4^{(t-1)}+d H4(t)=H4(t−1)+d
H 5 ( t ) = H 5 ( t − 1 ) + e H_5^{(t)}=H_5^{(t-1)}+e H5(t)=H5(t−1)+e
H 6 ( t ) = H 6 ( t − 1 ) + f H_6^{(t)}=H_6^{(t-1)}+f H6(t)=H6(t−1)+f
H 7 ( t ) = H 7 ( t − 1 ) + g H_7^{(t)}=H_7^{(t-1)}+g H7(t)=H7(t−1)+g
H 8 ( t ) = H 8 ( t − 1 ) + h H_8^{(t)}=H_8^{(t-1)}+h H8(t)=H8(t−1)+h
End for t \text{End for } t End for t
-
3）当处理完最后一个block之后，将 H j ( N ) H_j^{(N)} Hj(N)变量拼接在一起，即为消息的哈希值：
H = H 1 ( N ) ∣ ∣ H 2 ( N ) ∣ ∣ H 3 ( N ) ∣ ∣ H 4 ( N ) ∣ ∣ H 5 ( N ) ∣ ∣ H 6 ( N ) ∣ ∣ H 7 ( N ) ∣ ∣ H 8 ( N ) H=H_1^{(N)}||H_2^{(N)}||H_3^{(N)}||H_4^{(N)}||H_5^{(N)}||H_6^{(N)}||H_7^{(N)}||H_8^{(N)} H=H1(N)∣∣H2(N)∣∣H3(N)∣∣H4(N)∣∣H5(N)∣∣H6(N)∣∣H7(N)∣∣H8(N)
7. SHA-256示例
以对“hello world”进行SHA-256计算为例：
-
1）STEP 1：预处理。预处理后的长度为512bit的整数倍。
- 1.1）将“hello world”转换为二进制表示为：【即消息原始长度为88bit】
01101000 01100101 01101100 01101100 01101111 00100000 01110111 01101111 01110010 01101100 01100100 - 1.2）附加单个bit 1：
01101000 01100101 01101100 01101100 01101111 00100000 01110111 01101111 01110010 01101100 01100100 1 - 1.3）附加 k k k个bit 0， k k k取值为使得 l + 1 + k ≡ 448 m o d 512 l+1+k\equiv 448 \mod 512 l+1+k≡448mod512的最小正整数，其中 l l l为初始消息位长度。
01101000 01100101 01101100 01101100 01101111 00100000 01110111 01101111 01110010 01101100 01100100 10000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 - 1.4）初始消息长度 l < 2 64 l<2^{64} l<264以正好64位big-endian表示，将这64位附加到1.3）之后。此处“hello world”二进制表示长度为 l = 88 = 1011000 l=88=1011000 l=88=1011000。
至此，后续STEP的输入即为512bit的整数倍。01101000 01100101 01101100 01101100 01101111 00100000 01110111 01101111 01110010 01101100 01100100 10000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 01011000
- 1.1）将“hello world”转换为二进制表示为：【即消息原始长度为88bit】
-
2）STEP 2：初始化哈希值。
h0 := 0x6a09e667 h1 := 0xbb67ae85 h2 := 0x3c6ef372 h3 := 0xa54ff53a h4 := 0x510e527f h5 := 0x9b05688c h6 := 0x1f83d9ab h7 := 0x5be0cd19 -
3）STEP 3：初始化Round常量。
0x428a2f98 0x71374491 0xb5c0fbcf 0xe9b5dba5 0x3956c25b 0x59f111f1 0x923f82a4 0xab1c5ed5 0xd807aa98 0x12835b01 0x243185be 0x550c7dc3 0x72be5d74 0x80deb1fe 0x9bdc06a7 0xc19bf174 0xe49b69c1 0xefbe4786 0x0fc19dc6 0x240ca1cc 0x2de92c6f 0x4a7484aa 0x5cb0a9dc 0x76f988da 0x983e5152 0xa831c66d 0xb00327c8 0xbf597fc7 0xc6e00bf3 0xd5a79147 0x06ca6351 0x14292967 0x27b70a85 0x2e1b2138 0x4d2c6dfc 0x53380d13 0x650a7354 0x766a0abb 0x81c2c92e 0x92722c85 0xa2bfe8a1 0xa81a664b 0xc24b8b70 0xc76c51a3 0xd192e819 0xd6990624 0xf40e3585 0x106aa070 0x19a4c116 0x1e376c08 0x2748774c 0x34b0bcb5 0x391c0cb3 0x4ed8aa4a 0x5b9cca4f 0x682e6ff3 0x748f82ee 0x78a5636f 0x84c87814 0x8cc70208 0x90befffa 0xa4506ceb 0xbef9a3f7 0xc67178f2 -
4）STEP 4：Block Loop（或又名Chunk Loop）。将输入拆分为以512 bit为单位的block。由于本例中“hello world”太短，对应为1个block。 对每个block，做如下STEP操作。
-
5）STEP 5：block分解。
- 5.1） 前16个words为：将 M M M按512位block切分为16个32位words：
01101000011001010110110001101100 01101111001000000111011101101111 01110010011011000110010010000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000001011000 - 5.2）剩下48个words按如下公式构建：
W i = σ 1 ( W i − 2 ) + W i − 7 + σ 0 ( W i − 15 ) + W i − 16 , 17 ≤ i ≤ 64 W_i=\sigma_1(W_{i-2})+W_{i-7}+\sigma_0(W_{i-15})+W_{i-16},17\leq i \leq 64 Wi=σ1(Wi−2)+Wi−7+σ0(Wi−15)+Wi−16,17≤i≤6401101000011001010110110001101100 01101111001000000111011101101111 01110010011011000110010010000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000001011000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 ... ... 00000000000000000000000000000000 00000000000000000000000000000000
最终整个64个words（ W W W）为：
01101000011001010110110001101100 01101111001000000111011101101111 01110010011011000110010010000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000001011000 00110111010001110000001000110111 10000110110100001100000000110001 11010011101111010001000100001011 01111000001111110100011110000010 00101010100100000111110011101101 01001011001011110111110011001001 00110001111000011001010001011101 10001001001101100100100101100100 01111111011110100000011011011010 11000001011110011010100100111010 10111011111010001111011001010101 00001100000110101110001111100110 10110000111111100000110101111101 01011111011011100101010110010011 00000000100010011001101101010010 00000111111100011100101010010100 00111011010111111110010111010110 01101000011001010110001011100110 11001000010011100000101010011110 00000110101011111001101100100101 10010010111011110110010011010111 01100011111110010101111001011010 11100011000101100110011111010111 10000100001110111101111000010110 11101110111011001010100001011011 10100000010011111111001000100001 11111001000110001010110110111000 00010100101010001001001000011001 00010000100001000101001100011101 01100000100100111110000011001101 10000011000000110101111111101001 11010101101011100111100100111000 00111001001111110000010110101101 11111011010010110001101111101111 11101011011101011111111100101001 01101010001101101001010100110100 00100010111111001001110011011000 10101001011101000000110100101011 01100000110011110011100010000101 11000100101011001001100000111010 00010001010000101111110110101101 10110000101100000001110111011001 10011000111100001100001101101111 01110010000101111011100000011110 10100010110101000110011110011010 00000001000011111001100101111011 11111100000101110100111100001010 11000010110000101110101100010110 - 5.1） 前16个words为：将 M M M按512位block切分为16个32位words：
-
6）STEP 6：压缩。按上面“6. 哈希计算”做64轮运算之后，有：
a = 4F434152 = 01001111010000110100000101010010 b = D7E58F83 = 11010111111001011000111110000011 c = 68BF5F65 = 01101000101111110101111101100101 d = 352DB6C0 = 00110101001011011011011011000000 e = 73769D64 = 01110011011101101001110101100100 f = DF4E1862 = 11011111010011100001100001100010 g = 71051E01 = 01110001000001010001111000000001 h = 870F00D0 = 10000111000011110000000011010000 -
7）STEP 7：修正final值。按上面“6. 哈希计算”中“2.4）计算 H j ( t ) H_j^{(t)} Hj(t)的新值”，有：
h0 = h0 + a = 10111001010011010010011110111001 h1 = h1 + b = 10010011010011010011111000001000 h2 = h2 + c = 10100101001011100101001011010111 h3 = h3 + d = 11011010011111011010101111111010 h4 = h4 + e = 11000100100001001110111111100011 h5 = h5 + f = 01111010010100111000000011101110 h6 = h6 + g = 10010000100010001111011110101100 h7 = h7 + h = 11100010111011111100110111101001 -
8）STEP 8：拼接最终哈希值：
digest = h0 append h1 append h2 append h3 append h4 append h5 append h6 append h7 = B94D27B9934D3E08A52E52D7DA7DABFAC484EFE37A5380EE9088F7ACE2EFCDE9
SHA-256伪代码为：
Note 1: All variables are 32 bit unsigned integers and addition is calculated modulo 232
Note 2: For each round, there is one round constant k[i] and one entry in the message schedule array w[i], 0 ≤ i ≤ 63
Note 3: The compression function uses 8 working variables, a through h
Note 4: Big-endian convention is used when expressing the constants in this pseudocode,
and when parsing message block data from bytes to words, for example,
the first word of the input message "abc" after padding is 0x61626380
Initialize hash values:
(first 32 bits of the fractional parts of the square roots of the first 8 primes 2..19):
h0 := 0x6a09e667
h1 := 0xbb67ae85
h2 := 0x3c6ef372
h3 := 0xa54ff53a
h4 := 0x510e527f
h5 := 0x9b05688c
h6 := 0x1f83d9ab
h7 := 0x5be0cd19
Initialize array of round constants:
(first 32 bits of the fractional parts of the cube roots of the first 64 primes 2..311):
k[0..63] :=
0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2
Pre-processing (Padding):
begin with the original message of length L bits
append a single '1' bit
append K '0' bits, where K is the minimum number >= 0 such that L + 1 + K + 64 is a multiple of 512
append L as a 64-bit big-endian integer, making the total post-processed length a multiple of 512 bits
Process the message in successive 512-bit chunks:
break message into 512-bit chunks
for each chunk
create a 64-entry message schedule array w[0..63] of 32-bit words
(The initial values in w[0..63] don't matter, so many implementations zero them here)
copy chunk into first 16 words w[0..15] of the message schedule array
Extend the first 16 words into the remaining 48 words w[16..63] of the message schedule array:
for i from 16 to 63
s0 := (w[i-15] rightrotate 7) xor (w[i-15] rightrotate 18) xor (w[i-15] rightshift 3)
s1 := (w[i- 2] rightrotate 17) xor (w[i- 2] rightrotate 19) xor (w[i- 2] rightshift 10)
w[i] := w[i-16] + s0 + w[i-7] + s1
Initialize working variables to current hash value:
a := h0
b := h1
c := h2
d := h3
e := h4
f := h5
g := h6
h := h7
Compression function main loop:
for i from 0 to 63
S1 := (e rightrotate 6) xor (e rightrotate 11) xor (e rightrotate 25)
ch := (e and f) xor ((not e) and g)
temp1 := h + S1 + ch + k[i] + w[i]
S0 := (a rightrotate 2) xor (a rightrotate 13) xor (a rightrotate 22)
maj := (a and b) xor (a and c) xor (b and c)
temp2 := S0 + maj
h := g
g := f
f := e
e := d + temp1
d := c
c := b
b := a
a := temp1 + temp2
Add the compressed chunk to the current hash value:
h0 := h0 + a
h1 := h1 + b
h2 := h2 + c
h3 := h3 + d
h4 := h4 + e
h5 := h5 + f
h6 := h6 + g
h7 := h7 + h
Produce the final hash value (big-endian):
digest := hash := h0 append h1 append h2 append h3 append h4 append h5 append h6 append h7
参考资料
[1] The cryptographic hash function SHA-256
[2] WHAT IS SHA-256?
[3] Descriptions of SHA-256, SHA-384, and SHA-512