重合因子计算器

Tool Introduction

The Index of Coincidence Calculator is a professional online tool designed to help users calculate the Index of Coincidence (IC index) for a given text. The Index of Coincidence is an important statistical measure in cryptography and linguistics, often used to evaluate text randomness, identify text language, or assist in breaking polyalphabetic ciphers. This tool specifically supports frequency analysis of English letters (A-Z) in text to derive an accurate IC index.

What is the Index of Coincidence (IC Index)?

The Index of Coincidence (IC index) is a statistical measure used to quantify the probability that two randomly chosen characters in a given text are identical. In cryptography, the IC index is a key tool for frequency analysis, especially when analyzing polyalphabetic substitution ciphers (such as the Vigenère cipher), where it can help determine the key length. Different languages have their unique average IC index values (e.g., English is approximately 0.067, random text is approximately 0.0385). By calculating the IC index of the text to be analyzed, one can infer its linguistic characteristics or determine if an encryption pattern exists.

How to Use

1. Enter Text Content: Paste or type the text you wish to analyze into the “Text Content” area. This input box supports a large amount of text and is required.
2. Select Analysis Scope: In “Options”, select “Letters A-Z Only”. This will ensure the tool only performs statistical analysis on English letters (case-insensitive) in the text, ignoring numbers, symbols, spaces, and other language characters.
3. Execute Calculation: Click the “Calculate” button (if present) on the tool page to start processing.
4. View Results: The calculation result will be displayed in the “IC Index” column, which is a floating-point number representing the text's Index of Coincidence.

Frequently Asked Questions

• Q: What input formats are supported?
• A: The tool supports any text format as input, but the IC index calculation will be performed according to your selected “Options”, such as English letters (A-Z) only.
• Q: What is the format of the output result?
• A: The output result is a floating-point number representing the calculated Index of Coincidence (IC index), displayed in a list format.
• Q: What is the significance of a high or low Index of Coincidence?
• A: A higher IC index (closer to the IC value of a natural language, such as 0.067 for English) usually indicates that the text has statistical regularity and may be a natural language; a lower IC index (closer to 0.0385 for random text) may indicate that the text is random or has been effectively encrypted.

Notes

• Input Data Format: In the “Text Content” input box, you can freely type or paste any text. If “Letters A-Z Only” is selected, the tool will automatically ignore numbers, symbols, spaces, and other non-English letter characters in the text, and it will be case-insensitive for English letters.
• Result Interpretation: The Index of Coincidence is a statistical indicator, and its accuracy and representativeness are closely related to the length of the input text. Generally, the longer the input text, the more stable and meaningful the calculated IC index.
• Performance Considerations: For extremely long texts (e.g., millions of characters), although the tool will attempt to process them, the calculation time may increase accordingly. It is recommended to appropriately segment very long texts before analysis.