DES密钥长度48位 des 密钥长度

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mob64ca140caeb2 2024-04-06 09:54:03

文章标签 DES密钥长度48位密码学 python IP 加密算法 文章分类 架构后端开发

DES

DES简介

数据加密标准（英语：Data Encryption Standard，缩写为DES）是⼀一种对称密钥加密分组密码算法，1976 年年被美国联邦政府的国家标准局确定为联邦资料处理标准（FIPS），随后在国际上广泛流传开来。DES 是⼀一种典型的分组加密⽅方案，分组长度为64 比特，密钥表面上是64 比特，然而只有其中的56 比特被实际用于算法，其余8 比特可以被用于奇偶校验，并在算法中被丢弃。因此，DES 的有效密钥长度仅为56比特。

算法原理

DES利用56比特串长度的密钥K来加密长度为64位的明文，得到长度为64位的
密文。加密算法分为三个阶段实现：

给定明文X，通过一个固定的初始置换IP排列X中的位，得到X₀。 $DES密钥长度48位 des 密钥长度_DES密钥长度48位$ 。其中L₀由X₀的前32位组成，R₀由后32位组成。
计算函数F的16次迭代，根据下述规则计算 $DES密钥长度48位 des 密钥长度_python_02$ : $DES密钥长度48位 des 密钥长度_加密算法_03$ 。其中K_i为48位子密钥。K_i可由56位密钥计算得出。
对 $DES密钥长度48位 des 密钥长度_密码学_04$ 使用逆置换IP^-1得到密文Y： $DES密钥长度48位 des 密钥长度_IP_05$ 。

由于DES算法具有可逆性和对合性，因此DES的加密算法与解密算法可以共用同一结构。不同的是，解密算法的1~16轮的子密钥应为加密算法的16~1轮的子密钥（即倒序）。

下面对函数F以及子密钥的产生的原理进行阐述。

（1）函数F

函数F中首先对R_i-1进行了扩展置换E使之长度变为48位，然后与本轮的48位子密钥异或，作为8个S盒的输入。每个S盒以6位为输入，以4位为输出。S盒的2~7位为代替表的列数，1和8位组成的数作为代替表行数。8个S盒的输出重新组合为32位的数，进行P置换。置换后的结果与L_i-1异或，即R_i。

（2）密钥编排算法

每轮的子密钥由密钥编排算法给出。64位的密钥经过置换选择1（PC-1）得到56位的密钥（8的整数倍位为奇偶校验位）。同时将这56位的密钥分为两部分 $DES密钥长度48位 des 密钥长度_密码学_06$ （C₀由前28位组成，D₀由后28位组成）。每轮的子密钥都通过循环左移和置换选择2得到。假设第i-1轮有 $DES密钥长度48位 des 密钥长度_DES密钥长度48位_07$ ，则第i轮的子密钥可表示为： $DES密钥长度48位 des 密钥长度_DES密钥长度48位_08$ ，其中M为循环左移，P为置换选择2。

算法流程

算法流程大致如下：

根据密钥编排算法由给定的64位密钥计算出16轮的子密钥
如果是加密，则按次序存入列表；如果是解密，按逆序存入列表
对明文进行初始置换IP，并将结果分为两部分L₀R₀
for i from 0 to 16，进行以下循环：
$DES密钥长度48位 des 密钥长度_IP_09$
对 $DES密钥长度48位 des 密钥长度_密码学_10$ 进行逆初始置换IP^-1，得到密文

算法的伪代码如下：

# DES主体函数
def DES(p, key, mode):
	key_list = KeyCreater(key)
	p = IP_Trans(p)
	divide p into L and R
	for i from 0 to 16:
		L, R = R, L ^ Function(R,key)
	merge R and L into p
	p = IP_I_Trans(p)
	return p
	
# 密钥生成函数
# PC_1, KeyMove, PC_2分别为置换选择1，循环左移，置换选择2
def KeyCreater(key, mode):
	key = PC_1(key)
	divide key into C and D
	for i from 0 to 16:
		C, D = KeyMove(C, D, i)
		merge C and D into key
		key = PC_2(key)
		add key to list
	if (mode == "decrypt"):
		reverse list
	return list
	
# F函数
# E_Trans, S_box, P_Trans分别为扩展置换E，S盒代替，P置换
def Function(R, key):
	R = E_Trans(R)
	s_in = R ^ key
	s_out = S_box(s_in)
	R = P_Trans(s_out)
	
# 置换函数和代换函数在此不做赘述

函数调用关系大致如下图（该图由Understand分析代码结构得到）：（int、range等六边形边框的函数为Python的内置函数，可忽略）

DES密钥长度48位 des 密钥长度_DES密钥长度48位_11

程序代码

import os

IP = [
    58, 50, 42, 34, 26, 18, 10, 2,
    60, 52, 44, 36, 28, 20, 12, 4,
    62, 54, 46, 38, 30, 22, 14, 6,
    64, 56, 48, 40, 32, 24, 16, 8,
    57, 49, 41, 33, 25, 17, 9, 1,
    59, 51, 43, 35, 27, 19, 11, 3,
    61, 53, 45, 37, 29, 21, 13, 5,
    63, 55, 47, 39, 31, 23, 15, 7
]

IP_I = [
    40, 8, 48, 16, 56, 24, 64, 32,
    39, 7, 47, 15, 55, 23, 63, 31,
    38, 6, 46, 14, 54, 22, 62, 30,
    37, 5, 45, 13, 53, 21, 61, 29,
    36, 4, 44, 12, 52, 20, 60, 28,
    35, 3, 43, 11, 51, 19, 59, 27,
    34, 2, 42, 10, 50, 18, 58, 26,
    33, 1, 41, 9, 49, 17, 57, 25
]

S_BOX = [
    [
        [14, 4, 13, 1, 2, 15, 11, 8, 3, 10, 6, 12, 5, 9, 0, 7],
        [0, 15, 7, 4, 14, 2, 13, 1, 10, 6, 12, 11, 9, 5, 3, 8],
        [4, 1, 14, 8, 13, 6, 2, 11, 15, 12, 9, 7, 3, 10, 5, 0],
        [15, 12, 8, 2, 4, 9, 1, 7, 5, 11, 3, 14, 10, 0, 6, 13]
    ],
    [
        [15, 1, 8, 14, 6, 11, 3, 4, 9, 7, 2, 13, 12, 0, 5, 10],
        [3, 13, 4, 7, 15, 2, 8, 14, 12, 0, 1, 10, 6, 9, 11, 5],
        [0, 14, 7, 11, 10, 4, 13, 1, 5, 8, 12, 6, 9, 3, 2, 15],
        [13, 8, 10, 1, 3, 15, 4, 2, 11, 6, 7, 12, 0, 5, 14, 9]
    ],
    [
        [10, 0, 9, 14, 6, 3, 15, 5, 1, 13, 12, 7, 11, 4, 2, 8],
        [13, 7, 0, 9, 3, 4, 6, 10, 2, 8, 5, 14, 12, 11, 15, 1],
        [13, 6, 4, 9, 8, 15, 3, 0, 11, 1, 2, 12, 5, 10, 14, 7],
        [1, 10, 13, 0, 6, 9, 8, 7, 4, 15, 14, 3, 11, 5, 2, 12]
    ],
    [
        [7, 13, 14, 3, 0, 6, 9, 10, 1, 2, 8, 5, 11, 12, 4, 15],
        [13, 8, 11, 5, 6, 15, 0, 3, 4, 7, 2, 12, 1, 10, 14, 9],
        [10, 6, 9, 0, 12, 11, 7, 13, 15, 1, 3, 14, 5, 2, 8, 4],
        [3, 15, 0, 6, 10, 1, 13, 8, 9, 4, 5, 11, 12, 7, 2, 14]
    ],
    [
        [2, 12, 4, 1, 7, 10, 11, 6, 8, 5, 3, 15, 13, 0, 14, 9],
        [14, 11, 2, 12, 4, 7, 13, 1, 5, 0, 15, 10, 3, 9, 8, 6],
        [4, 2, 1, 11, 10, 13, 7, 8, 15, 9, 12, 5, 6, 3, 0, 14],
        [11, 8, 12, 7, 1, 14, 2, 13, 6, 15, 0, 9, 10, 4, 5, 3]
    ],
    [
        [12, 1, 10, 15, 9, 2, 6, 8, 0, 13, 3, 4, 14, 7, 5, 11],
        [10, 15, 4, 2, 7, 12, 9, 5, 6, 1, 13, 14, 0, 11, 3, 8],
        [9, 14, 15, 5, 2, 8, 12, 3, 7, 0, 4, 10, 1, 13, 11, 6],
        [4, 3, 2, 12, 9, 5, 15, 10, 11, 14, 1, 7, 6, 0, 8, 13]
    ],
    [
        [4, 11, 2, 14, 15, 0, 8, 13, 3, 12, 9, 7, 5, 10, 6, 1],
        [13, 0, 11, 7, 4, 9, 1, 10, 14, 3, 5, 12, 2, 15, 8, 6],
        [1, 4, 11, 13, 12, 3, 7, 14, 10, 15, 6, 8, 0, 5, 9, 2],
        [6, 11, 13, 8, 1, 4, 10, 7, 9, 5, 0, 15, 14, 2, 3, 12]
    ],
    [
        [13, 2, 8, 4, 6, 15, 11, 1, 10, 9, 3, 14, 5, 0, 12, 7],
        [1, 15, 13, 8, 10, 3, 7, 4, 12, 5, 6, 11, 0, 14, 9, 2],
        [7, 11, 4, 1, 9, 12, 14, 2, 0, 6, 10, 13, 15, 3, 5, 8],
        [2, 1, 14, 7, 4, 10, 8, 13, 15, 12, 9, 0, 3, 5, 6, 11]
    ]
]

E_TRANS = [
    32, 1, 2, 3, 4, 5,
    4, 5, 6, 7, 8, 9,
    8, 9, 10, 11, 12, 13,
    12, 13, 14, 15, 16, 17,
    16, 17, 18, 19, 20, 21,
    20, 21, 22, 23, 24, 25,
    24, 25, 26, 27, 28, 29,
    28, 29, 30, 31, 32, 1
]

P_TRANS = [
    16, 7, 20, 21, 29, 12, 28, 17,
    1, 15, 23, 26, 5, 18, 31, 10,
    2, 8, 24, 14, 32, 27, 3, 9,
    19, 13, 30, 6, 22, 11, 4, 25
]

KEY_MOVE = [1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1]

KEY_TRANS_1 = [
    57, 49, 41, 33, 25, 17, 9,
    1, 58, 50, 42, 34, 26, 18,
    10, 2, 59, 51, 43, 35, 27,
    19, 11, 3, 60, 52, 44, 36,
    63, 55, 47, 39, 31, 23, 15,
    7, 62, 54, 46, 38, 30, 22,
    14, 6, 61, 53, 45, 37, 29,
    21, 13, 5, 28, 20, 12, 4,
]

KEY_TRANS_2 = [
    14, 17, 11, 24, 1, 5, 3, 28,
    15, 6, 21, 10, 23, 19, 12, 4,
    26, 8, 16, 7, 27, 20, 13, 2,
    41, 52, 31, 37, 47, 55, 30, 40,
    51, 45, 33, 48, 44, 49, 39, 56,
    34, 53, 46, 42, 50, 36, 29, 32
]


def DES(p, key, mode):
    p_IP, p_IP_I = 0, 0
    # e_trans
    p_IP = IP_Trans(p)
    print("IP(p): " + hex(p_IP))
    # divide p into L and R
    L, R = p_IP >> 32, p_IP & (int("0xffffffff", 16))
    print("L0: " + hex(L))
    print("R0: " + hex(R))
    # create key_list
    key_list = Key_Creater(key, mode)[:]
    # feistel strcture
    for i in range(16):
        L, R = R, Function(R, key_list[i]) ^ L
        print("Round {}: L={}, R={}".format(
            i + 1,
            hex(L).replace("0x", "").zfill(8),
            hex(R).replace("0x", "").zfill(8)))
    p = (R << 32) + L
    p_IP_I = IP_I_Trans(p)
    print("IP_I(p): ", hex(p_IP_I).zfill(16))
    return hex(p_IP_I).replace("0x", "").zfill(16)


def Key_Creater(key, mode):
    key_list, key_in = [], 0
    key_in = PC_1(key)
    # divide key_in into C and D
    C, D = key_in >> 28, key_in & (int("0xfffffff", 16))
    for i in range(16):
        # left move
        C, D = KeyMove(C, D, i)
        key, key_out = (C << 28) + D, 0
        # key_trans_2
        key_out = PC_2(key)
        key_list.append(key_out)
    if mode == 2:
        key_list.reverse()
    return key_list


def IP_Trans(p):
    p_IP = 0
    # e_trans
    for i in range(64):
        p_IP <<= 1
        if p & (1 << (64 - IP[i])) != 0:
            p_IP += 1
    return p_IP


def IP_I_Trans(p):
    p_IP_I = 0
    for i in range(64):
        p_IP_I <<= 1
        if p & (1 << (64 - IP_I[i])) != 0:
            p_IP_I += 1
    return p_IP_I


def E_Trans(R):
    R_E = 0
    # e_trans
    for i in range(48):
        R_E <<= 1
        if R & (1 << (32 - E_TRANS[i])) != 0:
            R_E += 1
    return R_E


def P_Trans(s_out):
    R_P = 0
    for i in range(32):
        R_P <<= 1
        if s_out & (1 << (32 - P_TRANS[i])) != 0:
            R_P += 1
    return R_P


def S_box(s_in):
    extract, s_out = int("0b111111", 2), 0
    # s_box
    for i in range(8):
        s_out <<= 4
        # get 6 bits input
        s = (s_in >> ((7 - i) * 6)) & extract
        # select is used to determine which list will be chose
        select = ((s >> 5) << 1) + (s & 1)
        index = (s & int("0b011110", 2)) >> 1
        s_out += S_BOX[i][select][index]
    return s_out


def PC_1(key):
    key_in = 0
    # key_trans_1
    for i in range(56):
        key_in <<= 1
        if key & (1 << (64 - KEY_TRANS_1[i])) != 0:
            key_in += 1
    return key_in


def PC_2(key):
    key_out = 0
    for k in range(48):
        key_out <<= 1
        if key & (1 << (56 - KEY_TRANS_2[k])) != 0:
            key_out += 1
    return key_out


def KeyMove(C, D, i):
    for j in range(KEY_MOVE[i]):
        C = ((C << 1) & int("0xfffffff", 16)) + (C >> 27)
        D = ((D << 1) & int("0xfffffff", 16)) + (D >> 27)
    return C, D


def Function(R, key):
    R_E, R_P = 0, 0
    # e_trans
    R_E = E_Trans(R)
    # s_in is a 48-bit input, extract is used to divide s_in into 8 4-bit pieces
    s_in, extract, s_out = R_E ^ key, int("0b111111", 2), 0
    # s_box
    s_out = S_box(s_in)
    # p_trans
    R_P = P_Trans(s_out)
    return R_P


if __name__ == "__main__":
    mode = int(input("mode: [1]crypt [2]decrypt "))
    p = int(input("input text: "), 16)
    key = int(input("input key: "), 16)
    print("\nciphertext is: " + DES(p, key, mode))
    os.system("pause")

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