Statistics, Cybersecurity [Year 2024 - 25]

Topics on Statistics with intensive computer applications

$ \int_0^t d S_u = \int_0^t \mu(S_u, u) du + \int_0^t\sigma(S_u, u) dW_u $

Supporto al corso e alla didattica telematica, by T. Gastaldi   #Sapienzanonsiferma  #Sapienzadoesnotstop

(Instructor: tommaso.gastaldi@gmail.com,
https://www.datatime.eu/public/cybersecurity/)

Whatsapp group for the students of this course
Invitation to join the Whatsapp group for this course: https://chat.whatsapp.com/Kk3wRGmmxWH9RNUo01zFdX

(When first joining, send a message with your name and id ("matricola"))

    Function CaesarShift(input As String, shift As Integer) As String
        Dim result As New System.Text.StringBuilder()

        For Each ch As Char In input
            If Char.IsUpper(ch) Then
                ' Handle uppercase letters
                Dim offset As Integer = Asc("A")
                Dim shiftedChar As Char = Chr((Asc(ch) - offset + shift) Mod 26 + offset)
                result.Append(shiftedChar)
            ElseIf Char.IsLower(ch) Then
                ' Handle lowercase letters
                Dim offset As Integer = Asc("a")
                Dim shiftedChar As Char = Chr((Asc(ch) - offset + shift) Mod 26 + offset)
                result.Append(shiftedChar)
            ElseIf Char.IsDigit(ch) Then
                ' Handle digits (0-9)
                Dim offset As Integer = Asc("0")
                Dim shiftedChar As Char = Chr((Asc(ch) - offset + shift) Mod 10 + offset)
                result.Append(shiftedChar)
            Else
                ' Non-letter characters are not shifted
                result.Append(ch)
            End If
        Next

        Return result.ToString()
    End Function
	
	//-----------------------
	
	function caesarShift(input, shift) {
    let result = '';

    for (let ch of input) {
        if (ch >= 'A' && ch <= 'Z') {
            // Handle uppercase letters
            let offset = 'A'.charCodeAt(0);
            let shiftedChar = String.fromCharCode(((ch.charCodeAt(0) - offset + shift) % 26 + offset));
            result += shiftedChar;
        } else if (ch >= 'a' && ch <= 'z') {
            // Handle lowercase letters
            let offset = 'a'.charCodeAt(0);
            let shiftedChar = String.fromCharCode(((ch.charCodeAt(0) - offset + shift) % 26 + offset));
            result += shiftedChar;
        } else if (ch >= '0' && ch <= '9') {
            // Handle digits (0-9)
            let offset = '0'.charCodeAt(0);
            let shiftedChar = String.fromCharCode(((ch.charCodeAt(0) - offset + shift) % 10 + offset));
            result += shiftedChar;
        } else {
            // Non-letter characters are not shifted
            result += ch;
        }
    }

    return result;
}

// Example usage
console.log(caesarShift("Hello, World! 123", 3)); // Output: "Khoor, Zruog! 456"


### English (EN) Letter Frequency Distribution
1. **K. M. O’Hara's Studies**: This study provides a comprehensive analysis of letter frequencies in English text. Here's a rough frequency distribution based on various sources:

    - E: 12.70%
    - T: 9.06%
    - A: 8.17%
    - O: 7.51%
    - I: 7.00%
    - N: 6.75%
    - S: 6.33%
    - H: 6.09%
    - R: 5.99%
    - D: 4.25%
    - L: 4.03%
    - C: 2.78%
    - U: 2.76%
    - M: 2.41%
    - W: 2.36%
    - F: 2.23%
    - Y: 1.97%
    - P: 1.93%
    - B: 1.49%
    - V: 0.98%
    - K: 0.77%
    - J: 0.15%
    - X: 0.15%
    - Q: 0.10%
    - Z: 0.07%
   
2. **Wikipedia**: The page on [Letter Frequencies](https://en.wikipedia.org/wiki/Letter_frequency) provides a good overview and includes references to original studies.
   
3. **Cryptography and Information Security**: There are many cryptography textbooks that discuss letter frequency, including authors like Bruce Schneier and William Stallings.

### Italian (ITA) Letter Frequency Distribution 
1. **Italian Language Studies**: Here’s a common frequency distribution for the Italian language:

    - E: 11.79%
    - A: 10.49%
    - I: 9.96%
    - O: 8.76%
    - T: 6.87%
    - N: 6.73%
    - R: 6.52%
    - S: 5.38%
    - L: 5.26%
    - U: 3.33%
    - D: 3.41%
    - C: 3.29%
    - M: 2.51%
    - P: 2.49%
    - H: 0.77%
    - B: 0.81%
    - F: 0.84%
    - X: 0.10%
    - J: 0.12%
    - K: 0.03%
    - Q: 0.52%
    - Z: 0.39%
    - W: 0.00%