暴力破解字典中固定长度密码的位置计算方法及示例

Got it, let's break down exactly how to find where your password sits in that 8-character dictionary starting from 00000000. First, we need to lock down a few key details that make this calculation work.

Key Prerequisite: Character Set Order #

The order of characters in your dictionary is make-or-break here—different orderings will give totally different positions. For this example, we'll use the standard alphanumeric order used in most brute-force dictionaries:

• Digits first: 0 → index 0, 1 → index 1, ..., 9 → index 9
• Lowercase letters next: a → index 10, b → index 11, ..., z → index 35

If your dictionary uses a different order (like letters first), just adjust the character-to-index mapping— the formula structure stays identical.

Core Formula #

This problem is exactly like converting a base-36 number to a decimal number, with a small tweak if you want 1-based instead of 0-based positioning.

Let your 8-character password be [c1, c2, c3, c4, c5, c6, c7, c8] (where c1 is the leftmost character, c8 is the rightmost):

1. Map each character ci to its index value vi using the mapping above
2. Calculate the 0-based position (where 00000000 is position 0):

   position_0 = v1*(36^7) + v2*(36^6) + v3*(36^5) + v4*(36^4) + v5*(36^3) + v6*(36^2) + v7*(36^1) + v8*(36^0)
   

3. If you want the 1-based position (where 00000000 is the 1st entry), just add 1:

   position_1 = position_0 + 1
   

Example Calculation for cocoso12 #

Let's walk through the example step by step:

Step 1: Map each character to its index #

Step 2: Calculate each term #

Compute each part of the formula:

• v1*36^7 = 12 * 78364164096 = 940369969152
• v2*36^6 =24 * 2176782336 = 52242776064
• v3*36^5=12 * 60466176 = 725594112
• v4*36^4=24 * 1679616 = 40310784
• v5*36^3=28 * 46656 = 1306368
• v6*36^2=24 * 1296 = 31104
• v7*36^1=1 *36=36
• v8*36^0=2*1=2

Step3: Sum all terms for position_0 #

Adding these up gives:
940369969152 + 52242776064 + 725594112 + 40310784 + 1306368 + 31104 +36 +2 = 993379987622

So:

• 0-based position of cocoso12: 993379987622
• 1-based position (if you count 00000000 as the first entry): 993379987623

Quick Notes #

• If your dictionary uses a different character order (e.g., letters before digits), update the index mapping accordingly. For example, if a=0, z=25, 0=26, then c would be index 2 instead of 12, which would change the final position.
• The exponent values make sense because each leftmost character represents a larger block of passwords: the first character has 36^7 possible combinations for the remaining 7 positions, hence multiplying by 36^7.

内容的提问来源于stack exchange，提问作者Robert