2025黄河流域密码部分解

题目好，人菜

2025黄河流域

crypto

三明治

中间m未知，想到是coppersmith来解，框架我提供，ai来写具体代码

# sagemath
from Crypto.Util.number import *
n = 130210658110511504736422597261591182174531847806532340762131145212035478695205314931974421838392310731226415266775095601890938846830080329061111533796518633011922277343217149648494987341818402753017296362015915834670450122261511337212801488239810623226740266516836721952886027130703886460578247562781194524199
c = 58274335440051115211211273605191310114692293785750437685473044454042062899661976407492451518086227780147882738264722645944582899451063113444881286175099872016956825274378613983870549046907444680021237171113596116147511706486372974792692071549068969896395366667516390709069131700584308236332248449116109156503
e = 0x3

pad1_len = len(pad1)  # 12字节
pad2_len = len(pad2)  # 15字节
flag_len = 39         # 字节

# 计算m的高位和低位
m_high = bytes_to_long(pad1) << (8 * (flag_len + pad2_len))  # 高位部分左移(39+15)*8位
m_low = bytes_to_long(pad2)  # 低位部分
shift = 8 * pad2_len  # 中间部分需要左移的位数

# 构造多项式环
P.<x> = PolynomialRing(Zmod(n))

# 定义多项式：m_high + x * 2^shift + m_low 的e次方减去c
f = (m_high + x * (2^shift) + m_low)^e - c

# 将多项式转换为首一多项式
f = f.monic()

# 使用small_roots方法求解，X为中间部分的最大可能值（39字节）
X = 2^(8 * flag_len)  # 2^(312)
roots = f.small_roots(X=X, beta=0.499, epsilon=0.01)

if roots:
    x0 = roots[0]
    flag = long_to_bytes(int(x0))
    print(flag.decode())
else:
    print("未找到解，可能需要调整参数。")

lattice

iv是16个字节

一个字节是8位二进制

那么需要128位二进制

解hint的

import numpy as np
from itertools import product

# 题目提供的参数
q = 127
n = 3
N = 16  # 根据1.1*3*log(127)计算得到
P = [[87, -27, -52, -29], [57, -41, -24, -60], [76, -17, -55, -37], [75, -46, -33, -21], [121, -55, -33, -34], [47, -4, -34, -45], [112, -33, -44, -16], [74, -44, -5, -25], [20, -21, -16, -49], [89, -21, -54, -24], [18, -23, -53, -1], [35, -40, -4, -29], [105, -54, -2, -8], [44, -24, -43, -36], [111, -15, -15, -54]]
C = [[24, 75, 81, 85], [24, 14, 85, 102], [115, 1, 5, 21], [58, 118, 104, 77], [65, 42, 101, 103], [33, 38, 50, 67], [7, 81, 38, 58], [117, 101, 54, 11], [44, 29, 81, 8], [59, 114, 70, 121], [62, 13, 9, 105], [11, 43, 97, 23], [39, 82, 75, 97], [122, 113, 14, 30], [70, 102, 116, 5], [58, 44, 61, 20], [73, 119, 59, 28], [119, 68, 57, 122], [61, 91, 83, 44], [103, 29, 1, 73], [47, 60, 120, 125], [17, 126, 14, 21], [104, 8, 78, 123], [72, 121, 54, 74], [48, 104, 49, 66], [72, 56, 27, 69], [34, 110, 41, 54], [33, 54, 74, 44], [70, 65, 11, 113], [122, 3, 69, 35], [58, 7, 39, 64], [59, 106, 49, 66], [77, 92, 87, 92], [95, 21, 96, 83], [67, 55, 30, 73], [99, 54, 18, 90], [101, 102, 126, 107], [81, 46, 104, 83], [38, 24, 94, 60], [114, 105, 76, 97], [22, 115, 20, 67], [40, 72, 110, 65], [111, 92, 106, 117], [5, 123, 21, 96], [41, 14, 23, 114], [113, 75, 43, 65], [56, 3, 61, 48], [40, 101, 16, 114], [42, 84, 95, 13], [36, 110, 91, 107], [4, 13, 60, 74], [24, 80, 125, 76], [123, 26, 27, 119], [31, 87, 6, 123], [61, 106, 73, 120], [66, 10, 36, 65], [91, 38, 46, 9], [121, 20, 106, 48], [123, 21, 78, 27], [22, 74, 55, 110], [47, 49, 118, 76], [30, 10, 16, 118], [43, 19, 52, 61], [100, 9, 37, 35], [20, 102, 111, 94], [116, 63, 55, 43], [13, 110, 42, 14], [46, 65, 71, 28], [82, 5, 76, 74], [86, 34, 117, 84], [28, 44, 82, 50], [76, 79, 77, 11], [68, 39, 51, 89], [83, 93, 95, 2], [54, 108, 101, 82], [99, 90, 122, 37], [16, 92, 79, 12], [67, 86, 24, 36], [80, 94, 106, 59], [50, 56, 95, 98], [33, 68, 89, 40], [74, 124, 14, 82], [88, 93, 54, 93], [51, 17, 124, 31], [17, 17, 45, 35], [113, 71, 76, 44], [48, 6, 120, 4], [36, 91, 108, 11], [2, 41, 58, 72], [42, 59, 51, 81], [73, 22, 79, 27], [85, 35, 29, 98], [76, 76, 37, 22], [82, 29, 42, 27], [75, 114, 37, 106], [40, 69, 53, 73], [39, 44, 33, 121], [94, 85, 92, 54], [91, 77, 124, 46], [108, 31, 101, 84], [35, 33, 97, 45], [99, 32, 17, 14], [1, 66, 11, 35], [78, 100, 95, 81], [73, 49, 14, 37], [70, 9, 107, 2], [84, 98, 92, 62], [123, 87, 87, 110], [3, 81, 111, 28], [20, 2, 91, 37], [93, 101, 77, 93], [27, 16, 31, 105], [95, 81, 87, 17], [10, 103, 21, 102], [81, 57, 118, 82], [15, 92, 60, 71], [16, 84, 126, 49], [35, 26, 2, 120], [70, 86, 45, 9], [29, 8, 40, 66], [99, 77, 14, 9], [12, 70, 50, 52], [21, 21, 85, 54], [91, 94, 100, 85], [9, 42, 47, 14], [117, 55, 17, 99], [53, 45, 4, 72], [49, 10, 27, 121], [108, 61, 73, 42], [121, 42, 41, 71], [49, 63, 50, 117], [5, 78, 24, 101], [0, 117, 21, 46], [90, 43, 47, 32], [74, 85, 118, 84], [13, 73, 18, 66], [95, 24, 120, 18], [94, 21, 111, 34], [66, 68, 80, 21], [102, 49, 57, 55], [25, 85, 107, 98], [8, 18, 88, 12], [18, 6, 86, 82], [18, 91, 126, 115], [26, 11, 30, 35], [88, 78, 76, 74], [51, 75, 76, 15], [60, 24, 72, 27], [91, 72, 44, 104], [84, 113, 39, 116], [41, 83, 91, 74], [84, 17, 94, 119], [46, 95, 85, 5], [109, 58, 71, 42], [126, 29, 114, 73], [27, 70, 7, 125], [121, 66, 97, 111], [8, 21, 10, 57], [15, 62, 65, 8], [101, 79, 32, 74], [69, 42, 38, 58], [65, 81, 72, 16], [20, 81, 1, 126], [91, 111, 69, 33], [56, 84, 65, 66], [47, 78, 43, 100], [43, 90, 80, 25], [46, 55, 10, 60], [116, 110, 49, 116], [72, 115, 38, 104], [79, 43, 74, 106], [86, 113, 84, 76], [102, 2, 119, 3], [126, 25, 83, 44], [37, 83, 46, 40], [13, 75, 101, 101], [76, 93, 3, 63], [69, 9, 84, 37], [103, 47, 106, 80], [72, 104, 85, 19], [124, 118, 34, 81], [57, 25, 52, 119], [44, 56, 63, 90], [123, 46, 124, 31], [19, 116, 23, 77], [126, 78, 37, 93], [34, 95, 43, 98], [37, 90, 32, 97], [106, 8, 80, 8], [90, 5, 113, 68], [99, 40, 39, 18], [90, 37, 48, 45], [56, 13, 76, 6], [68, 33, 52, 102], [62, 45, 29, 123], [100, 21, 73, 92], [92, 18, 118, 23], [84, 86, 42, 83], [107, 8, 71, 52], [114, 106, 78, 85], [10, 120, 115, 119], [27, 49, 124, 16], [65, 40, 48, 37], [69, 42, 8, 29], [35, 39, 55, 102], [58, 19, 41, 75], [17, 2, 113, 12], [8, 34, 72, 75], [91, 32, 19, 52], [62, 50, 109, 78], [9, 115, 35, 50], [42, 83, 78, 41], [34, 94, 97, 58], [56, 73, 25, 115], [55, 12, 16, 86], [97, 95, 30, 92], [47, 105, 70, 68], [50, 18, 51, 23], [46, 57, 80, 29], [4, 66, 123, 24], [55, 53, 26, 36], [71, 59, 104, 91], [94, 3, 1, 34], [57, 8, 85, 102], [89, 73, 115, 25], [13, 38, 81, 76], [104, 30, 81, 104], [55, 101, 95, 101], [69, 65, 5, 11], [123, 105, 84, 125], [38, 110, 4, 28], [112, 115, 92, 71], [90, 120, 112, 39], [50, 18, 107, 71], [95, 63, 118, 93], [93, 111, 59, 55], [17, 15, 2, 88], [78, 126, 37, 12], [56, 112, 53, 12], [65, 34, 82, 100], [9, 94, 72, 99], [78, 76, 43, 91], [7, 88, 107, 31], [43, 91, 97, 4], [113, 112, 36, 15], [8, 97, 23, 84], [65, 92, 31, 63], [54, 38, 119, 103], [89, 50, 57, 50], [61, 37, 87, 0], [21, 35, 44, 22], [20, 32, 95, 116], [10, 94, 103, 84], [59, 29, 7, 50], [98, 33, 87, 33], [7, 96, 36, 67], [85, 10, 35, 98], [65, 49, 19, 62], [56, 67, 14, 91], [30, 49, 111, 77], [121, 49, 108, 119], [89, 67, 115, 69], [65, 8, 0, 82], [117, 57, 117, 23], [23, 38, 2, 98], [60, 28, 94, 93], [23, 65, 8, 114], [121, 105, 122, 40], [120, 12, 21, 112], [55, 51, 2, 77], [48, 41, 113, 62], [66, 82, 117, 119], [4, 15, 5, 21], [41, 14, 12, 80], [23, 61, 106, 16], [23, 53, 122, 68], [6, 54, 5, 101], [69, 49, 7, 79], [17, 70, 64, 88], [103, 30, 76, 31], [108, 82, 90, 109], [55, 56, 113, 37], [93, 99, 126, 44], [1, 46, 105, 124], [55, 54, 35, 115], [0, 89, 53, 97], [67, 111, 107, 80], [92, 122, 40, 64], [75, 2, 126, 118], [90, 84, 43, 74], [101, 69, 60, 17], [104, 10, 4, 122], [94, 4, 115, 91], [15, 11, 111, 105], [9, 7, 32, 101], [77, 18, 55, 56], [66, 7, 117, 108], [116, 121, 33, 66], [32, 41, 83, 125], [60, 52, 70, 58], [125, 54, 93, 15], [70, 19, 10, 58], [83, 94, 61, 126], [95, 85, 80, 44], [25, 89, 117, 74], [12, 17, 63, 87], [118, 80, 96, 26], [6, 97, 79, 38], [97, 3, 107, 95], [7, 82, 106, 92], [83, 100, 119, 95], [81, 26, 99, 56], [25, 60, 51, 122], [56, 18, 22, 84], [9, 72, 107, 114], [80, 97, 92, 52], [108, 47, 58, 46], [9, 47, 7, 47], [115, 68, 91, 7], [14, 120, 87, 122], [97, 15, 40, 79], [5, 92, 85, 93], [4, 97, 73, 63], [25, 22, 92, 108], [88, 4, 34, 86], [0, 43, 21, 57], [67, 90, 36, 50], [15, 126, 37, 12], [92, 73, 96, 71], [76, 107, 27, 115], [79, 8, 68, 55], [38, 12, 120, 126], [54, 46, 7, 69], [72, 114, 93, 60], [59, 98, 27, 102], [50, 76, 87, 19], [77, 107, 29, 40], [36, 73, 21, 123], [36, 89, 82, 74], [24, 73, 118, 86], [58, 89, 115, 106], [12, 27, 33, 72], [28, 94, 21, 26], [0, 79, 48, 110], [72, 62, 82, 57], [65, 84, 114, 97], [80, 68, 52, 52], [119, 35, 103, 101], [10, 67, 68, 69], [101, 17, 54, 40], [98, 46, 21, 42], [30, 39, 56, 118], [27, 33, 77, 114], [66, 74, 61, 63], [23, 13, 14, 47], [88, 30, 122, 119], [15, 58, 55, 52], [56, 27, 47, 45], [119, 95, 59, 14], [84, 69, 5, 83], [21, 35, 39, 36], [10, 92, 68, 17], [79, 67, 111, 38], [36, 1, 4, 117], [117, 30, 5, 7], [112, 15, 115, 123], [54, 47, 18, 93], [102, 111, 3, 68], [91, 91, 5, 44], [123, 118, 57, 32], [12, 121, 31, 103], [114, 52, 105, 12], [100, 28, 117, 102], [51, 42, 12, 124], [47, 1, 42, 47], [28, 3, 22, 100], [103, 105, 119, 24], [101, 59, 13, 78], [79, 36, 61, 54], [11, 46, 75, 116], [31, 73, 118, 0], [92, 32, 0, 124], [77, 85, 25, 90], [29, 21, 74, 7], [3, 66, 11, 8], [112, 91, 50, 53], [45, 113, 99, 123], [35, 65, 85, 22], [108, 99, 42, 1], [103, 113, 116, 72], [125, 74, 112, 24], [75, 79, 80, 12], [83, 44, 94, 86], [64, 20, 0, 8], [104, 126, 31, 120], [85, 75, 61, 74], [36, 93, 36, 102], [70, 54, 101, 83], [90, 46, 109, 83], [112, 126, 114, 23], [16, 123, 97, 62], [118, 86, 108, 53], [99, 18, 2, 18], [103, 3, 38, 8], [99, 49, 123, 81], [37, 75, 89, 53], [34, 77, 27, 122], [29, 8, 40, 66], [119, 13, 64, 83], [4, 108, 116, 121], [49, 87, 1, 92], [15, 63, 80, 62], [27, 81, 100, 83], [7, 90, 16, 0], [13, 50, 61, 65], [51, 64, 76, 5], [55, 100, 106, 66], [52, 102, 105, 2], [49, 34, 89, 116], [24, 55, 11, 27], [91, 48, 73, 38], [27, 5, 1, 126], [66, 55, 80, 19], [52, 118, 104, 43], [36, 1, 111, 60], [65, 4, 34, 17], [54, 22, 0, 39], [52, 30, 64, 62], [26, 40, 32, 86], [93, 71, 41, 47], [77, 23, 15, 9], [11, 20, 51, 31], [64, 50, 37, 50], [17, 49, 80, 37], [119, 115, 115, 50], [20, 86, 27, 5], [101, 65, 17, 78], [56, 25, 125, 56], [16, 118, 2, 96], [114, 108, 69, 121], [14, 37, 76, 101], [113, 124, 121, 82], [43, 120, 35, 94], [82, 67, 23, 43], [9, 79, 47, 122], [39, 28, 110, 31], [35, 48, 27, 16], [72, 8, 115, 66], [54, 46, 122, 19], [77, 77, 30, 74], [58, 63, 81, 96], [6, 122, 75, 63], [115, 31, 119, 110], [82, 86, 89, 1], [79, 100, 6, 110], [117, 67, 15, 13], [4, 15, 63, 0], [106, 108, 122, 107], [34, 72, 0, 114], [20, 0, 32, 56], [121, 104, 66, 3], [86, 28, 76, 84], [85, 9, 60, 45], [95, 80, 78, 65], [39, 85, 50, 49], [42, 103, 36, 90], [70, 99, 116, 117], [34, 15, 40, 52], [24, 49, 19, 31], [98, 90, 95, 89], [63, 45, 40, 77], [114, 14, 30, 106], [10, 35, 116, 9], [103, 111, 112, 16], [71, 112, 71, 32], [77, 31, 105, 64], [84, 87, 24, 67], [1, 27, 123, 57], [104, 29, 87, 123], [110, 39, 67, 7], [28, 70, 108, 113], [96, 9, 101, 36], [13, 28, 6, 13], [69, 81, 89, 26], [79, 113, 77, 91], [112, 62, 104, 117], [109, 95, 55, 83], [78, 68, 98, 14], [73, 79, 96, 12], [108, 39, 97, 49], [27, 111, 106, 100], [82, 70, 9, 36], [48, 31, 90, 70], [99, 92, 45, 35], [55, 100, 31, 37], [75, 17, 69, 35], [12, 38, 119, 112], [103, 34, 63, 76], [26, 19, 91, 111], [74, 122, 12, 78], [64, 117, 16, 60], [2, 97, 122, 106], [62, 79, 56, 30], [71, 47, 13, 22], [38, 78, 116, 16], [87, 28, 94, 76], [77, 126, 94, 116], [83, 46, 104, 90], [5, 95, 13, 26], [47, 10, 46, 115], [82, 19, 91, 70], [111, 72, 49, 65], [18, 103, 59, 72], [17, 37, 56, 24], [19, 120, 24, 64], [28, 40, 11, 20], [18, 19, 80, 62], [37, 11, 74, 14], [109, 97, 75, 72], [116, 65, 52, 121], [95, 63, 82, 122], [88, 93, 54, 93], [77, 30, 65, 121], [99, 121, 42, 87], [62, 52, 44, 6], [79, 60, 55, 4], [96, 64, 6, 20], [94, 114, 90, 8], [123, 98, 29, 27], [116, 84, 31, 80], [9, 77, 45, 45], [120, 33, 63, 15], [51, 44, 66, 25], [2, 46, 72, 94], [107, 113, 50, 46], [115, 64, 126, 85], [64, 10, 28, 78], [84, 112, 64, 103], [59, 114, 15, 82], [65, 122, 104, 89], [113, 122, 21, 11], [69, 106, 19, 78], [42, 93, 125, 0], [7, 123, 82, 70], [103, 114, 62, 92], [15, 30, 78, 114], [4, 78, 111, 60], [40, 80, 34, 55], [3, 87, 120, 27], [122, 64, 3, 122], [24, 49, 31, 81], [26, 43, 100, 19], [52, 78, 2, 97], [116, 45, 15, 33], [21, 119, 92, 86], [28, 118, 71, 24], [106, 15, 0, 79], [36, 4, 52, 73], [22, 43, 8, 60], [96, 22, 9, 100], [19, 64, 26, 96], [97, 61, 22, 39], [6, 112, 76, 38], [58, 6, 97, 94], [103, 87, 87, 101], [17, 49, 80, 37], [117, 33, 26, 8], [59, 108, 78, 91], [113, 28, 30, 44], [119, 78, 72, 20], [49, 101, 77, 2], [26, 18, 35, 7], [34, 38, 99, 37], [45, 52, 90, 27], [108, 31, 118, 67], [3, 37, 29, 88], [111, 96, 12, 111], [91, 111, 106, 100], [52, 78, 117, 80], [14, 51, 87, 0], [1, 52, 116, 1], [117, 2, 33, 48], [57, 0, 48, 34], [59, 14, 84, 63], [82, 83, 8, 82], [58, 100, 32, 33], [75, 29, 112, 103], [0, 49, 45, 54], [94, 9, 51, 110], [54, 61, 27, 47], [88, 89, 23, 37], [73, 43, 0, 32], [123, 6, 35, 78], [73, 72, 119, 64], [81, 46, 11, 102], [42, 124, 47, 8], [50, 66, 3, 40], [116, 7, 51, 20], [47, 112, 99, 7], [42, 37, 86, 89], [18, 74, 78, 101], [57, 85, 75, 7], [26, 90, 35, 10], [72, 126, 10, 77], [55, 12, 5, 78], [37, 87, 85, 96], [91, 9, 114, 68], [79, 76, 44, 20], [84, 52, 63, 56], [95, 9, 22, 117], [96, 38, 50, 67], [43, 114, 45, 56], [94, 21, 74, 107], [92, 82, 81, 71], [40, 10, 10, 90], [20, 18, 15, 56], [72, 2, 30, 22], [50, 31, 123, 20], [85, 40, 115, 115], [93, 1, 48, 47], [111, 118, 45, 34], [9, 122, 37, 121], [60, 27, 77, 41], [122, 38, 22, 39], [115, 66, 74, 126], [77, 67, 90, 78], [96, 3, 53, 52], [5, 26, 120, 101], [45, 100, 72, 6], [106, 56, 87, 77], [52, 68, 102, 95], [1, 13, 36, 33], [58, 27, 35, 8], [52, 5, 38, 35], [102, 82, 63, 47], [24, 71, 119, 43], [11, 36, 90, 13], [11, 93, 27, 23], [4, 107, 26, 125], [85, 9, 5, 13], [116, 25, 55, 119], [73, 82, 73, 2], [40, 123, 77, 41], [10, 98, 51, 111], [23, 79, 120, 54], [56, 18, 22, 84], [61, 115, 51, 109], [33, 5, 12, 121], [8, 81, 35, 70], [22, 39, 103, 2], [38, 74, 66, 126], [83, 20, 117, 85], [8, 32, 91, 98], [37, 31, 94, 119], [7, 30, 45, 43], [68, 16, 124, 97], [86, 124, 37, 21], [29, 101, 15, 30], [27, 31, 52, 45], [47, 37, 102, 3], [117, 49, 54, 89], [48, 94, 126, 66], [42, 115, 63, 104], [14, 74, 6, 112], [68, 125, 4, 5], [66, 3, 78, 52], [108, 33, 6, 77], [77, 99, 16, 52], [61, 78, 73, 70], [108, 106, 124, 0], [23, 35, 119, 118], [125, 124, 37, 65], [69, 30, 61, 110], [77, 10, 120, 118], [53, 121, 24, 30], [87, 32, 29, 63], [54, 64, 1, 3], [16, 59, 104, 25], [30, 6, 59, 102], [43, 120, 35, 94], [89, 13, 69, 39], [87, 78, 100, 14], [83, 17, 14, 4], [24, 49, 31, 81], [73, 32, 72, 10], [0, 22, 61, 54], [81, 42, 70, 13], [108, 56, 52, 2], [25, 99, 116, 72], [66, 23, 18, 102], [121, 115, 47, 12], [96, 37, 123, 48], [64, 69, 4, 39], [78, 38, 124, 31], [27, 69, 10, 70], [5, 29, 2, 85], [30, 45, 56, 7], [31, 25, 120, 61], [36, 89, 89, 118], [98, 63, 18, 21], [121, 83, 36, 57], [60, 5, 86, 17], [121, 55, 117, 58], [12, 96, 4, 27], [119, 63, 124, 37], [96, 27, 45, 91], [42, 119, 8, 103], [104, 42, 68, 37], [104, 55, 41, 38], [120, 3, 50, 87], [120, 121, 20, 67], [58, 123, 50, 28], [103, 62, 58, 20], [97, 27, 89, 102], [7, 51, 56, 108], [73, 60, 10, 77], [56, 72, 103, 69], [101, 89, 18, 66], [115, 35, 80, 36], [98, 103, 39, 63], [29, 126, 67, 76], [27, 97, 15, 79], [36, 6, 17, 90], [126, 54, 101, 42], [115, 66, 74, 126], [78, 80, 62, 83], [60, 11, 31, 88], [16, 73, 108, 13]]

# 从P中提取A和b
A = np.array([[-row[1], -row[2], -row[3]] for row in P], dtype=np.int32)
b = np.array([row[0] for row in P], dtype=np.int32)

# 穷举t的所有可能组合
found = False
for t in product(range(64), repeat=3):
    t_vector = np.array(t, dtype=np.int32)
    # 计算A*t mod q
    A_t = np.dot(A, t_vector) % q
    # 计算差异并调整到[-63, 63]
    diff = (A_t - b) % q
    diff = np.where(diff > q//2, diff - q, diff)
    # 检查所有差异是否较小（假设误差<=2）
    if np.all(np.abs(diff) <= 2):
        print("找到正确的t:", t)
        found = True
        break

if not found:
    print("未找到正确的t，可能需要扩大搜索范围或调整误差阈值。")
    exit()

s = [1, 26, 24, 54]
q = 127
P=[[87, -27, -52, -29], [57, -41, -24, -60], [76, -17, -55, -37], [75, -46, -33, -21], [121, -55, -33, -34], [47, -4, -34, -45], [112, -33, -44, -16], [74, -44, -5, -25], [20, -21, -16, -49], [89, -21, -54, -24], [18, -23, -53, -1], [35, -40, -4, -29], [105, -54, -2, -8], [44, -24, -43, -36], [111, -15, -15, -54]]

for row in P:
    product = sum(s_i * p_i for s_i, p_i in zip(s, row)) % q
    if product > 10 and product < q-10:  # 检查是否为小误差
        print("s 可能不正确")
        break
else:
    print("s 验证通过")


C=[[24, 75, 81, 85], [24, 14, 85, 102], [115, 1, 5, 21], [58, 118, 104, 77], [65, 42, 101, 103], [33, 38, 50, 67], [7, 81, 38, 58], [117, 101, 54, 11], [44, 29, 81, 8], [59, 114, 70, 121], [62, 13, 9, 105], [11, 43, 97, 23], [39, 82, 75, 97], [122, 113, 14, 30], [70, 102, 116, 5], [58, 44, 61, 20], [73, 119, 59, 28], [119, 68, 57, 122], [61, 91, 83, 44], [103, 29, 1, 73], [47, 60, 120, 125], [17, 126, 14, 21], [104, 8, 78, 123], [72, 121, 54, 74], [48, 104, 49, 66], [72, 56, 27, 69], [34, 110, 41, 54], [33, 54, 74, 44], [70, 65, 11, 113], [122, 3, 69, 35], [58, 7, 39, 64], [59, 106, 49, 66], [77, 92, 87, 92], [95, 21, 96, 83], [67, 55, 30, 73], [99, 54, 18, 90], [101, 102, 126, 107], [81, 46, 104, 83], [38, 24, 94, 60], [114, 105, 76, 97], [22, 115, 20, 67], [40, 72, 110, 65], [111, 92, 106, 117], [5, 123, 21, 96], [41, 14, 23, 114], [113, 75, 43, 65], [56, 3, 61, 48], [40, 101, 16, 114], [42, 84, 95, 13], [36, 110, 91, 107], [4, 13, 60, 74], [24, 80, 125, 76], [123, 26, 27, 119], [31, 87, 6, 123], [61, 106, 73, 120], [66, 10, 36, 65], [91, 38, 46, 9], [121, 20, 106, 48], [123, 21, 78, 27], [22, 74, 55, 110], [47, 49, 118, 76], [30, 10, 16, 118], [43, 19, 52, 61], [100, 9, 37, 35], [20, 102, 111, 94], [116, 63, 55, 43], [13, 110, 42, 14], [46, 65, 71, 28], [82, 5, 76, 74], [86, 34, 117, 84], [28, 44, 82, 50], [76, 79, 77, 11], [68, 39, 51, 89], [83, 93, 95, 2], [54, 108, 101, 82], [99, 90, 122, 37], [16, 92, 79, 12], [67, 86, 24, 36], [80, 94, 106, 59], [50, 56, 95, 98], [33, 68, 89, 40], [74, 124, 14, 82], [88, 93, 54, 93], [51, 17, 124, 31], [17, 17, 45, 35], [113, 71, 76, 44], [48, 6, 120, 4], [36, 91, 108, 11], [2, 41, 58, 72], [42, 59, 51, 81], [73, 22, 79, 27], [85, 35, 29, 98], [76, 76, 37, 22], [82, 29, 42, 27], [75, 114, 37, 106], [40, 69, 53, 73], [39, 44, 33, 121], [94, 85, 92, 54], [91, 77, 124, 46], [108, 31, 101, 84], [35, 33, 97, 45], [99, 32, 17, 14], [1, 66, 11, 35], [78, 100, 95, 81], [73, 49, 14, 37], [70, 9, 107, 2], [84, 98, 92, 62], [123, 87, 87, 110], [3, 81, 111, 28], [20, 2, 91, 37], [93, 101, 77, 93], [27, 16, 31, 105], [95, 81, 87, 17], [10, 103, 21, 102], [81, 57, 118, 82], [15, 92, 60, 71], [16, 84, 126, 49], [35, 26, 2, 120], [70, 86, 45, 9], [29, 8, 40, 66], [99, 77, 14, 9], [12, 70, 50, 52], [21, 21, 85, 54], [91, 94, 100, 85], [9, 42, 47, 14], [117, 55, 17, 99], [53, 45, 4, 72], [49, 10, 27, 121], [108, 61, 73, 42], [121, 42, 41, 71], [49, 63, 50, 117], [5, 78, 24, 101], [0, 117, 21, 46], [90, 43, 47, 32], [74, 85, 118, 84], [13, 73, 18, 66], [95, 24, 120, 18], [94, 21, 111, 34], [66, 68, 80, 21], [102, 49, 57, 55], [25, 85, 107, 98], [8, 18, 88, 12], [18, 6, 86, 82], [18, 91, 126, 115], [26, 11, 30, 35], [88, 78, 76, 74], [51, 75, 76, 15], [60, 24, 72, 27], [91, 72, 44, 104], [84, 113, 39, 116], [41, 83, 91, 74], [84, 17, 94, 119], [46, 95, 85, 5], [109, 58, 71, 42], [126, 29, 114, 73], [27, 70, 7, 125], [121, 66, 97, 111], [8, 21, 10, 57], [15, 62, 65, 8], [101, 79, 32, 74], [69, 42, 38, 58], [65, 81, 72, 16], [20, 81, 1, 126], [91, 111, 69, 33], [56, 84, 65, 66], [47, 78, 43, 100], [43, 90, 80, 25], [46, 55, 10, 60], [116, 110, 49, 116], [72, 115, 38, 104], [79, 43, 74, 106], [86, 113, 84, 76], [102, 2, 119, 3], [126, 25, 83, 44], [37, 83, 46, 40], [13, 75, 101, 101], [76, 93, 3, 63], [69, 9, 84, 37], [103, 47, 106, 80], [72, 104, 85, 19], [124, 118, 34, 81], [57, 25, 52, 119], [44, 56, 63, 90], [123, 46, 124, 31], [19, 116, 23, 77], [126, 78, 37, 93], [34, 95, 43, 98], [37, 90, 32, 97], [106, 8, 80, 8], [90, 5, 113, 68], [99, 40, 39, 18], [90, 37, 48, 45], [56, 13, 76, 6], [68, 33, 52, 102], [62, 45, 29, 123], [100, 21, 73, 92], [92, 18, 118, 23], [84, 86, 42, 83], [107, 8, 71, 52], [114, 106, 78, 85], [10, 120, 115, 119], [27, 49, 124, 16], [65, 40, 48, 37], [69, 42, 8, 29], [35, 39, 55, 102], [58, 19, 41, 75], [17, 2, 113, 12], [8, 34, 72, 75], [91, 32, 19, 52], [62, 50, 109, 78], [9, 115, 35, 50], [42, 83, 78, 41], [34, 94, 97, 58], [56, 73, 25, 115], [55, 12, 16, 86], [97, 95, 30, 92], [47, 105, 70, 68], [50, 18, 51, 23], [46, 57, 80, 29], [4, 66, 123, 24], [55, 53, 26, 36], [71, 59, 104, 91], [94, 3, 1, 34], [57, 8, 85, 102], [89, 73, 115, 25], [13, 38, 81, 76], [104, 30, 81, 104], [55, 101, 95, 101], [69, 65, 5, 11], [123, 105, 84, 125], [38, 110, 4, 28], [112, 115, 92, 71], [90, 120, 112, 39], [50, 18, 107, 71], [95, 63, 118, 93], [93, 111, 59, 55], [17, 15, 2, 88], [78, 126, 37, 12], [56, 112, 53, 12], [65, 34, 82, 100], [9, 94, 72, 99], [78, 76, 43, 91], [7, 88, 107, 31], [43, 91, 97, 4], [113, 112, 36, 15], [8, 97, 23, 84], [65, 92, 31, 63], [54, 38, 119, 103], [89, 50, 57, 50], [61, 37, 87, 0], [21, 35, 44, 22], [20, 32, 95, 116], [10, 94, 103, 84], [59, 29, 7, 50], [98, 33, 87, 33], [7, 96, 36, 67], [85, 10, 35, 98], [65, 49, 19, 62], [56, 67, 14, 91], [30, 49, 111, 77], [121, 49, 108, 119], [89, 67, 115, 69], [65, 8, 0, 82], [117, 57, 117, 23], [23, 38, 2, 98], [60, 28, 94, 93], [23, 65, 8, 114], [121, 105, 122, 40], [120, 12, 21, 112], [55, 51, 2, 77], [48, 41, 113, 62], [66, 82, 117, 119], [4, 15, 5, 21], [41, 14, 12, 80], [23, 61, 106, 16], [23, 53, 122, 68], [6, 54, 5, 101], [69, 49, 7, 79], [17, 70, 64, 88], [103, 30, 76, 31], [108, 82, 90, 109], [55, 56, 113, 37], [93, 99, 126, 44], [1, 46, 105, 124], [55, 54, 35, 115], [0, 89, 53, 97], [67, 111, 107, 80], [92, 122, 40, 64], [75, 2, 126, 118], [90, 84, 43, 74], [101, 69, 60, 17], [104, 10, 4, 122], [94, 4, 115, 91], [15, 11, 111, 105], [9, 7, 32, 101], [77, 18, 55, 56], [66, 7, 117, 108], [116, 121, 33, 66], [32, 41, 83, 125], [60, 52, 70, 58], [125, 54, 93, 15], [70, 19, 10, 58], [83, 94, 61, 126], [95, 85, 80, 44], [25, 89, 117, 74], [12, 17, 63, 87], [118, 80, 96, 26], [6, 97, 79, 38], [97, 3, 107, 95], [7, 82, 106, 92], [83, 100, 119, 95], [81, 26, 99, 56], [25, 60, 51, 122], [56, 18, 22, 84], [9, 72, 107, 114], [80, 97, 92, 52], [108, 47, 58, 46], [9, 47, 7, 47], [115, 68, 91, 7], [14, 120, 87, 122], [97, 15, 40, 79], [5, 92, 85, 93], [4, 97, 73, 63], [25, 22, 92, 108], [88, 4, 34, 86], [0, 43, 21, 57], [67, 90, 36, 50], [15, 126, 37, 12], [92, 73, 96, 71], [76, 107, 27, 115], [79, 8, 68, 55], [38, 12, 120, 126], [54, 46, 7, 69], [72, 114, 93, 60], [59, 98, 27, 102], [50, 76, 87, 19], [77, 107, 29, 40], [36, 73, 21, 123], [36, 89, 82, 74], [24, 73, 118, 86], [58, 89, 115, 106], [12, 27, 33, 72], [28, 94, 21, 26], [0, 79, 48, 110], [72, 62, 82, 57], [65, 84, 114, 97], [80, 68, 52, 52], [119, 35, 103, 101], [10, 67, 68, 69], [101, 17, 54, 40], [98, 46, 21, 42], [30, 39, 56, 118], [27, 33, 77, 114], [66, 74, 61, 63], [23, 13, 14, 47], [88, 30, 122, 119], [15, 58, 55, 52], [56, 27, 47, 45], [119, 95, 59, 14], [84, 69, 5, 83], [21, 35, 39, 36], [10, 92, 68, 17], [79, 67, 111, 38], [36, 1, 4, 117], [117, 30, 5, 7], [112, 15, 115, 123], [54, 47, 18, 93], [102, 111, 3, 68], [91, 91, 5, 44], [123, 118, 57, 32], [12, 121, 31, 103], [114, 52, 105, 12], [100, 28, 117, 102], [51, 42, 12, 124], [47, 1, 42, 47], [28, 3, 22, 100], [103, 105, 119, 24], [101, 59, 13, 78], [79, 36, 61, 54], [11, 46, 75, 116], [31, 73, 118, 0], [92, 32, 0, 124], [77, 85, 25, 90], [29, 21, 74, 7], [3, 66, 11, 8], [112, 91, 50, 53], [45, 113, 99, 123], [35, 65, 85, 22], [108, 99, 42, 1], [103, 113, 116, 72], [125, 74, 112, 24], [75, 79, 80, 12], [83, 44, 94, 86], [64, 20, 0, 8], [104, 126, 31, 120], [85, 75, 61, 74], [36, 93, 36, 102], [70, 54, 101, 83], [90, 46, 109, 83], [112, 126, 114, 23], [16, 123, 97, 62], [118, 86, 108, 53], [99, 18, 2, 18], [103, 3, 38, 8], [99, 49, 123, 81], [37, 75, 89, 53], [34, 77, 27, 122], [29, 8, 40, 66], [119, 13, 64, 83], [4, 108, 116, 121], [49, 87, 1, 92], [15, 63, 80, 62], [27, 81, 100, 83], [7, 90, 16, 0], [13, 50, 61, 65], [51, 64, 76, 5], [55, 100, 106, 66], [52, 102, 105, 2], [49, 34, 89, 116], [24, 55, 11, 27], [91, 48, 73, 38], [27, 5, 1, 126], [66, 55, 80, 19], [52, 118, 104, 43], [36, 1, 111, 60], [65, 4, 34, 17], [54, 22, 0, 39], [52, 30, 64, 62], [26, 40, 32, 86], [93, 71, 41, 47], [77, 23, 15, 9], [11, 20, 51, 31], [64, 50, 37, 50], [17, 49, 80, 37], [119, 115, 115, 50], [20, 86, 27, 5], [101, 65, 17, 78], [56, 25, 125, 56], [16, 118, 2, 96], [114, 108, 69, 121], [14, 37, 76, 101], [113, 124, 121, 82], [43, 120, 35, 94], [82, 67, 23, 43], [9, 79, 47, 122], [39, 28, 110, 31], [35, 48, 27, 16], [72, 8, 115, 66], [54, 46, 122, 19], [77, 77, 30, 74], [58, 63, 81, 96], [6, 122, 75, 63], [115, 31, 119, 110], [82, 86, 89, 1], [79, 100, 6, 110], [117, 67, 15, 13], [4, 15, 63, 0], [106, 108, 122, 107], [34, 72, 0, 114], [20, 0, 32, 56], [121, 104, 66, 3], [86, 28, 76, 84], [85, 9, 60, 45], [95, 80, 78, 65], [39, 85, 50, 49], [42, 103, 36, 90], [70, 99, 116, 117], [34, 15, 40, 52], [24, 49, 19, 31], [98, 90, 95, 89], [63, 45, 40, 77], [114, 14, 30, 106], [10, 35, 116, 9], [103, 111, 112, 16], [71, 112, 71, 32], [77, 31, 105, 64], [84, 87, 24, 67], [1, 27, 123, 57], [104, 29, 87, 123], [110, 39, 67, 7], [28, 70, 108, 113], [96, 9, 101, 36], [13, 28, 6, 13], [69, 81, 89, 26], [79, 113, 77, 91], [112, 62, 104, 117], [109, 95, 55, 83], [78, 68, 98, 14], [73, 79, 96, 12], [108, 39, 97, 49], [27, 111, 106, 100], [82, 70, 9, 36], [48, 31, 90, 70], [99, 92, 45, 35], [55, 100, 31, 37], [75, 17, 69, 35], [12, 38, 119, 112], [103, 34, 63, 76], [26, 19, 91, 111], [74, 122, 12, 78], [64, 117, 16, 60], [2, 97, 122, 106], [62, 79, 56, 30], [71, 47, 13, 22], [38, 78, 116, 16], [87, 28, 94, 76], [77, 126, 94, 116], [83, 46, 104, 90], [5, 95, 13, 26], [47, 10, 46, 115], [82, 19, 91, 70], [111, 72, 49, 65], [18, 103, 59, 72], [17, 37, 56, 24], [19, 120, 24, 64], [28, 40, 11, 20], [18, 19, 80, 62], [37, 11, 74, 14], [109, 97, 75, 72], [116, 65, 52, 121], [95, 63, 82, 122], [88, 93, 54, 93], [77, 30, 65, 121], [99, 121, 42, 87], [62, 52, 44, 6], [79, 60, 55, 4], [96, 64, 6, 20], [94, 114, 90, 8], [123, 98, 29, 27], [116, 84, 31, 80], [9, 77, 45, 45], [120, 33, 63, 15], [51, 44, 66, 25], [2, 46, 72, 94], [107, 113, 50, 46], [115, 64, 126, 85], [64, 10, 28, 78], [84, 112, 64, 103], [59, 114, 15, 82], [65, 122, 104, 89], [113, 122, 21, 11], [69, 106, 19, 78], [42, 93, 125, 0], [7, 123, 82, 70], [103, 114, 62, 92], [15, 30, 78, 114], [4, 78, 111, 60], [40, 80, 34, 55], [3, 87, 120, 27], [122, 64, 3, 122], [24, 49, 31, 81], [26, 43, 100, 19], [52, 78, 2, 97], [116, 45, 15, 33], [21, 119, 92, 86], [28, 118, 71, 24], [106, 15, 0, 79], [36, 4, 52, 73], [22, 43, 8, 60], [96, 22, 9, 100], [19, 64, 26, 96], [97, 61, 22, 39], [6, 112, 76, 38], [58, 6, 97, 94], [103, 87, 87, 101], [17, 49, 80, 37], [117, 33, 26, 8], [59, 108, 78, 91], [113, 28, 30, 44], [119, 78, 72, 20], [49, 101, 77, 2], [26, 18, 35, 7], [34, 38, 99, 37], [45, 52, 90, 27], [108, 31, 118, 67], [3, 37, 29, 88], [111, 96, 12, 111], [91, 111, 106, 100], [52, 78, 117, 80], [14, 51, 87, 0], [1, 52, 116, 1], [117, 2, 33, 48], [57, 0, 48, 34], [59, 14, 84, 63], [82, 83, 8, 82], [58, 100, 32, 33], [75, 29, 112, 103], [0, 49, 45, 54], [94, 9, 51, 110], [54, 61, 27, 47], [88, 89, 23, 37], [73, 43, 0, 32], [123, 6, 35, 78], [73, 72, 119, 64], [81, 46, 11, 102], [42, 124, 47, 8], [50, 66, 3, 40], [116, 7, 51, 20], [47, 112, 99, 7], [42, 37, 86, 89], [18, 74, 78, 101], [57, 85, 75, 7], [26, 90, 35, 10], [72, 126, 10, 77], [55, 12, 5, 78], [37, 87, 85, 96], [91, 9, 114, 68], [79, 76, 44, 20], [84, 52, 63, 56], [95, 9, 22, 117], [96, 38, 50, 67], [43, 114, 45, 56], [94, 21, 74, 107], [92, 82, 81, 71], [40, 10, 10, 90], [20, 18, 15, 56], [72, 2, 30, 22], [50, 31, 123, 20], [85, 40, 115, 115], [93, 1, 48, 47], [111, 118, 45, 34], [9, 122, 37, 121], [60, 27, 77, 41], [122, 38, 22, 39], [115, 66, 74, 126], [77, 67, 90, 78], [96, 3, 53, 52], [5, 26, 120, 101], [45, 100, 72, 6], [106, 56, 87, 77], [52, 68, 102, 95], [1, 13, 36, 33], [58, 27, 35, 8], [52, 5, 38, 35], [102, 82, 63, 47], [24, 71, 119, 43], [11, 36, 90, 13], [11, 93, 27, 23], [4, 107, 26, 125], [85, 9, 5, 13], [116, 25, 55, 119], [73, 82, 73, 2], [40, 123, 77, 41], [10, 98, 51, 111], [23, 79, 120, 54], [56, 18, 22, 84], [61, 115, 51, 109], [33, 5, 12, 121], [8, 81, 35, 70], [22, 39, 103, 2], [38, 74, 66, 126], [83, 20, 117, 85], [8, 32, 91, 98], [37, 31, 94, 119], [7, 30, 45, 43], [68, 16, 124, 97], [86, 124, 37, 21], [29, 101, 15, 30], [27, 31, 52, 45], [47, 37, 102, 3], [117, 49, 54, 89], [48, 94, 126, 66], [42, 115, 63, 104], [14, 74, 6, 112], [68, 125, 4, 5], [66, 3, 78, 52], [108, 33, 6, 77], [77, 99, 16, 52], [61, 78, 73, 70], [108, 106, 124, 0], [23, 35, 119, 118], [125, 124, 37, 65], [69, 30, 61, 110], [77, 10, 120, 118], [53, 121, 24, 30], [87, 32, 29, 63], [54, 64, 1, 3], [16, 59, 104, 25], [30, 6, 59, 102], [43, 120, 35, 94], [89, 13, 69, 39], [87, 78, 100, 14], [83, 17, 14, 4], [24, 49, 31, 81], [73, 32, 72, 10], [0, 22, 61, 54], [81, 42, 70, 13], [108, 56, 52, 2], [25, 99, 116, 72], [66, 23, 18, 102], [121, 115, 47, 12], [96, 37, 123, 48], [64, 69, 4, 39], [78, 38, 124, 31], [27, 69, 10, 70], [5, 29, 2, 85], [30, 45, 56, 7], [31, 25, 120, 61], [36, 89, 89, 118], [98, 63, 18, 21], [121, 83, 36, 57], [60, 5, 86, 17], [121, 55, 117, 58], [12, 96, 4, 27], [119, 63, 124, 37], [96, 27, 45, 91], [42, 119, 8, 103], [104, 42, 68, 37], [104, 55, 41, 38], [120, 3, 50, 87], [120, 121, 20, 67], [58, 123, 50, 28], [103, 62, 58, 20], [97, 27, 89, 102], [7, 51, 56, 108], [73, 60, 10, 77], [56, 72, 103, 69], [101, 89, 18, 66], [115, 35, 80, 36], [98, 103, 39, 63], [29, 126, 67, 76], [27, 97, 15, 79], [36, 6, 17, 90], [126, 54, 101, 42], [115, 66, 74, 126], [78, 80, 62, 83], [60, 11, 31, 88], [16, 73, 108, 13]]

bits = []
for c_row in C:
    c = c_row  # 例如 [24, 75, 81, 85]
    val = sum(s_i * c_i for s_i, c_i in zip(s, c)) % q
    # 判断逻辑：接近 63（q//2）则为 1，否则为 0
    if abs(val - 63) < 32:  # 阈值可根据误差调整
        bits.append(1)
    else:
        bits.append(0)

binary_str = ''.join(map(str, bits))
# 按 8 位分割
bytes_list = [int(binary_str[i:i+8], 2) for i in range(0, len(binary_str), 8)]
hint = bytes(bytes_list).decode('utf-8', errors='ignore')
print("Decrypted Hint:", hint)

但根据hint解iv，始终解不出来

$$sin(vi)+leak\cdot cos(vi)=0\\ tan(vi) = -leak$$

卡住的原因是不知道解出来的浮点数怎么转为标准iv的十六个字节

群里有师傅说可以非预期解aes，好像是直接爆破iv

happy

与2023 nkctf PsychoRandom相似

因式分解

等待官方wp复现