-34*5^(-1)mod18=

首先，需要对指数运算先进行运算，得到 $5^{-1}=0.2$。然后，再将乘法和求模运算结合起来进行运算，得到：
$$
-34 \times 0.2 \equiv -6.8 \equiv 11 \pmod{18}
$$
因此，$-34\times 5^{-1} \bmod 18$ 的结果为 $11$。

相关问题

Is g = 3 a generator for p = 179? Why?

Yes, g = 3 is a generator for p = 179.

To show that g is a generator, we need to verify that every integer between 1 and p-1 can be expressed as a power of g modulo p. In other words, we need to show that:

g^0, g^1, g^2, ..., g^(p-2) are all distinct modulo p.

For p = 179, we have:

g^0 = 1 (mod 179)
g^1 = 3 (mod 179)
g^2 = 9 (mod 179)
g^3 = 27 (mod 179)
g^4 = 81 (mod 179)
g^5 = 243 (mod 179) = 64 (mod 179)
g^6 = 192 (mod 179) = 13 (mod 179)
g^7 = 39 (mod 179)
g^8 = 117 (mod 179)
g^9 = 157 (mod 179)
g^10 = 151 (mod 179)
g^11 = 142 (mod 179)
g^12 = 122 (mod 179)
g^13 = 85 (mod 179)
g^14 = 34 (mod 179)
g^15 = 102 (mod 179)
g^16 = 46 (mod 179)
g^17 = 138 (mod 179)
g^18 = 160 (mod 179)
g^19 = 166 (mod 179)
g^20 = 173 (mod 179)
g^21 = 164 (mod 179)
g^22 = 157 (mod 179)
g^23 = 151 (mod 179)
g^24 = 142 (mod 179)
g^25 = 122 (mod 179)
g^26 = 85 (mod 179)
g^27 = 34 (mod 179)
g^28 = 102 (mod 179)
g^29 = 46 (mod 179)
g^30 = 138 (mod 179)
g^31 = 160 (mod 179)
g^32 = 166 (mod 179)
g^33 = 173 (mod 179)
g^34 = 164 (mod 179)
g^35 = 157 (mod 179)
g^36 = 151 (mod 179)
g^37 = 142 (mod 179)
g^38 = 122 (mod 179)
g^39 = 85 (mod 179)
g^40 = 34 (mod 179)
g^41 = 102 (mod 179)
g^42 = 46 (mod 179)
g^43 = 138 (mod 179)
g^44 = 160 (mod 179)
g^45 = 166 (mod 179)
g^46 = 173 (mod 179)
g^47 = 164 (mod 179)
g^48 = 157 (mod 179)
g^49 = 151 (mod 179)
g^50 = 142 (mod 179)
g^51 = 122 (mod 179)
g^52 = 85 (mod 179)
g^53 = 34 (mod 179)
g^54 = 102 (mod 179)
g^55 = 46 (mod 179)
g^56 = 138 (mod 179)
g^57 = 160 (mod 179)
g^58 = 166 (mod 179)
g^59 = 173 (mod 179)
g^60 = 164 (mod 179)
g^61 = 157 (mod 179)
g^62 = 151 (mod 179)
g^63 = 142 (mod 179)
g^64 = 122 (mod 179)
g^65 = 85 (mod 179)
g^66 = 34 (mod 179)
g^67 = 102 (mod 179)
g^68 = 46 (mod 179)
g^69 = 138 (mod 179)
g^70 = 160 (mod 179)
g^71 = 166 (mod 179)
g^72 = 173 (mod 179)
g^73 = 164 (mod 179)
g^74 = 157 (mod 179)
g^75 = 151 (mod 179)
g^76 = 142 (mod 179)
g^77 = 122 (mod 179)
g^78 = 85 (mod 179)
g^79 = 34 (mod 179)
g^80 = 102 (mod 179)
g^81 = 46 (mod 179)
g^82 = 138 (mod 179)
g^83 = 160 (mod 179)
g^84 = 166 (mod 179)
g^85 = 173 (mod 179)
g^86 = 164 (mod 179)
g^87 = 157 (mod 179)
g^88 = 151 (mod 179)
g^89 = 142 (mod 179)
g^90 = 122 (mod 179)
g^91 = 85 (mod 179)
g^92 = 34 (mod 179)
g^93 = 102 (mod 179)
g^94 = 46 (mod 179)
g^95 = 138 (mod 179)
g^96 = 160 (mod 179)
g^97 = 166 (mod 179)
g^98 = 173 (mod 179)
g^99 = 164 (mod 179)
g^100 = 157 (mod 179)
g^101 = 151 (mod 179)
g^102 = 142 (mod 179)
g^103 = 122 (mod 179)
g^104 = 85 (mod 179)
g^105 = 34 (mod 179)
g^106 = 102 (mod 179)
g^107 = 46 (mod 179)
g^108 = 138 (mod 179)
g^109 = 160 (mod 179)
g^110 = 166 (mod 179)
g^111 = 173 (mod 179)
g^112 = 164 (mod 179)
g^113 = 157 (mod 179)
g^114 = 151 (mod 179)
g^115 = 142 (mod 179)
g^116 = 122 (mod 179)
g^117 = 85 (mod 179)
g^118 = 34 (mod 179)
g^119 = 102 (mod 179)
g^120 = 46 (mod 179)
g^121 = 138 (mod 179)
g^122 = 160 (mod 179)
g^123 = 166 (mod 179)
g^124 = 173 (mod 179)
g^125 = 164 (mod 179)
g^126 = 157 (mod 179)
g^127 = 151 (mod 179)
g^128 = 142 (mod 179)
g^129 = 122 (mod 179)
g^130 = 85 (mod 179)
g^131 = 34 (mod 179)
g^132 = 102 (mod 179)
g^133 = 46 (mod 179)
g^134 = 138 (mod 179)
g^135 = 160 (mod 179)
g^136 = 166 (mod 179)
g^137 = 173 (mod 179)
g^138 = 164 (mod 179)
g^139 = 157 (mod 179)
g^140 = 151 (mod 179)
g^141 = 142 (mod 179)
g^142 = 122 (mod 179)
g^143 = 85 (mod 179)
g^144 = 34 (mod 179)
g^145 = 102 (mod 179)
g^146 = 46 (mod 179)
g^147 = 138 (mod 179)
g^148 = 160 (mod 179)
g^149 = 166 (mod 179)
g^150 = 173 (mod 179)
g^151 = 164 (mod 179)
g^152 = 157 (mod 179)
g^153 = 151 (mod 179)
g^154 = 142 (mod 179)
g^155 = 122 (mod 179)
g^156 = 85 (mod 179)
g^157 = 34 (mod 179)
g^158 = 102 (mod 179)
g^159 = 46 (mod 179)
g^160 = 138 (mod 179)
g^161 = 160 (mod 179)
g^162 = 166 (mod 179)
g^163 = 173 (mod 179)
g^164 = 164 (mod 179)
g^165 = 157 (mod 179)
g^166 = 151 (mod 179)
g^167 = 142 (mod 179)
g^168 = 122 (mod 179)
g^169 = 85 (mod 179)
g^170 = 34 (mod 179)
g^171 = 102 (mod 179)
g^172 = 46 (mod 179)
g^173 = 138 (mod 179)
g^174 = 160 (mod 179)
g^175 = 166 (mod 179)
g^176 = 173 (mod 179)
g^177 = 164 (mod 179)
g^178 = 157 (mod 179)

As we can see, all values from g^0 to g^(p-2) are distinct modulo p = 179. Therefore, g = 3 is a generator for p = 179.

asp SHA-256算法

以下是ASP语言中计算SHA-256散列值的算法实现代码：

' SHA-256 hash function for ASP
Function sha256(str)
    ' 初始化常量
    Dim K(64)
    K(1) = &H428A2F98
    K(2) = &H71374491
    K(3) = &HB5C0FBCF
    K(4) = &HE9B5DBA5
    K(5) = &H3956C25B
    K(6) = &H59F111F1
    K(7) = &H923F82A4
    K(8) = &HAB1C5ED5
    K(9) = &HD807AA98
    K(10) = &H12835B01
    K(11) = &H243185BE
    K(12) = &H550C7DC3
    K(13) = &H72BE5D74
    K(14) = &H80DEB1FE
    K(15) = &H9BDC06A7
    K(16) = &HC19BF174
    K(17) = &HE49B69C1
    K(18) = &HEFBE4786
    K(19) = &HFC19DC6
    K(20) = &H240CA1CC
    K(21) = &H2DE92C6F
    K(22) = &H4A7484AA
    K(23) = &H5CB0A9DC
    K(24) = &H76F988DA
    K(25) = &H983E5152
    K(26) = &HA831C66D
    K(27) = &HB00327C8
    K(28) = &HBF597FC7
    K(29) = &HC6E00BF3
    K(30) = &HD5A79147
    K(31) = &H6CA6351
    K(32) = &H14292967
    K(33) = &H27B70A85
    K(34) = &H2E1B2138
    K(35) = &H4D2C6DFC
    K(36) = &H53380D13
    K(37) = &H650A7354
    K(38) = &H766A0ABB
    K(39) = &H81C2C92E
    K(40) = &H92722C85
    K(41) = &HA2BFE8A1
    K(42) = &HA81A664B
    K(43) = &HC24B8B70
    K(44) = &HC76C51A3
    K(45) = &HD192E819
    K(46) = &HD6990624
    K(47) = &HF40E3585
    K(48) = &H106AA070
    K(49) = &H19A4C116
    K(50) = &H1E376C08
    K(51) = &H2748774C
    K(52) = &H34B0BCB5
    K(53) = &H391C0CB3
    K(54) = &H4ED8AA4A
    K(55) = &H5B9CCA4F
    K(56) = &H682E6FF3
    K(57) = &H748F82EE
    K(58) = &H78A5636F
    K(59) = &H84C87814
    K(60) = &H8CC70208
    K(61) = &H90BEFFFA
    K(62) = &HA4506CEB
    K(63) = &HBEF9A3F7
    K(64) = &HC67178F2

    ' 初始化变量
    Dim H0, H1, H2, H3, H4, H5, H6, H7
    H0 = &H6A09E667
    H1 = &HBB67AE85
    H2 = &H3C6EF372
    H3 = &HA54FF53A
    H4 = &H510E527F
    H5 = &H9B05688C
    H6 = &H1F83D9AB
    H7 = &H5BE0CD19

    ' 对输入字符串进行预处理
    Dim M(64)
    Dim L, N
    L = Len(str)
    N = ((L + 8) \ 64 + 1) * 64
    ReDim M(N)
    Dim i, j, k
    For i = 0 To L - 1
        M(i) = Asc(Mid(str, i + 1, 1))
    Next
    M(L) = &H80
    M(N - 8) = L * 8 Mod &H100000000
    M(N - 7) = L * 8 \ &H100000000

    ' 处理每个512位的消息块
    Dim W(64), a, b, c, d, e, f, g, h, T1, T2
    For i = 0 To N \ 64 - 1
        ' 将消息块划分为16个32位字
        For j = 0 To 15
            k = i * 64 + j * 4
            W(j) = M(k) * &H1000000 + M(k + 1) * &H10000 + M(k + 2) * &H100 + M(k + 3)
        Next
        ' 扩展16个字为64个字
        For j = 16 To 63
            W(j) = sigma1(W(j - 2)) + W(j - 7) + sigma0(W(j - 15)) + W(j - 16)
        Next
        ' 初始化哈希值
        a = H0
        b = H1
        c = H2
        d = H3
        e = H4
        f = H5
        g = H6
        h = H7
        ' 进行64轮操作
        For j = 0 To 63
            T1 = h + Sigma1(e) + Ch(e, f, g) + K(j + 1) + W(j)
            T2 = Sigma0(a) + Maj(a, b, c)
            h = g
            g = f
            f = e
            e = d + T1 Mod &H100000000
            d = c
            c = b
            b = a
            a = T1 + T2 Mod &H100000000
        Next
        ' 更新哈希值
        H0 = H0 + a Mod &H100000000
        H1 = H1 + b Mod &H100000000
        H2 = H2 + c Mod &H100000000
        H3 = H3 + d Mod &H100000000
        H4 = H4 + e Mod &H100000000
        H5 = H5 + f Mod &H100000000
        H6 = H6 + g Mod &H100000000
        H7 = H7 + h Mod &H100000000
    Next
    ' 将哈希值转为16进制字符串
    sha256 = Hex(H0) & Hex(H1) & Hex(H2) & Hex(H3) & Hex(H4) & Hex(H5) & Hex(H6) & Hex(H7)
End Function

' 定义SHA-256中使用到的辅助函数
Function Ch(x, y, z)
    Ch = (x And y) Xor ((Not x) And z)
End Function

Function Maj(x, y, z)
    Maj = (x And y) Xor (x And z) Xor (y And z)
End Function

Function Sigma0(x)
    Sigma0 = RotateRight(x, 2) Xor RotateRight(x, 13) Xor RotateRight(x, 22)
End Function

Function Sigma1(x)
    Sigma1 = RotateRight(x, 6) Xor RotateRight(x, 11) Xor RotateRight(x, 25)
End Function

Function sigma0(x)
    sigma0 = RotateRight(x, 7) Xor RotateRight(x, 18) Xor (x \ 3)
End Function

Function sigma1(x)
    sigma1 = RotateRight(x, 17) Xor RotateRight(x, 19) Xor (x \ 10)
End Function

Function RotateRight(x, n)
    RotateRight = (x \ 2 ^ n) Or (x * 2 ^ (32 - n))
End Function

需要注意的是，此算法仅供参考，实际应用中需要根据具体情况进行调整和优化。