Advanced Data Encryption in Excel: Implementing RSA Algorithm and Digital Signatures

Hi, Excel enthusiasts! Today I want to share with you a super cool advanced application of Excel—data encryption.

That’s right, today we are going to implement the RSA encryption algorithm and digital signatures in Excel! Sounds impressive, right? Don’t worry, I will explain each step in an easy-to-understand way.

Through this article, you will learn how to protect sensitive data in Excel, verify the authenticity of data, and even show off your geek skills. Are you ready? Let’s embark on this exciting journey of Excel encryption together!

What is the RSA Encryption Algorithm?

Before we dive deeper, let me first explain what the RSA encryption algorithm is. RSA is an asymmetric encryption algorithm that uses a pair of keys: a public key and a private key. The public key can be shared with anyone to encrypt data; while the private key must be kept secret to decrypt the data.

Imagine if you had a special safe where anyone can put things in (using the public key to encrypt), but only you can open it (using the private key to decrypt). This is the basic principle of the RSA algorithm!

Basics: Generating Large Prime Numbers

The security of the RSA algorithm is based on the difficulty of factoring large prime numbers. So, we first need a function to generate large prime numbers. Here we use a simple method to generate primes:

Function IsPrime(n As Long) As Boolean
    If n <= 1 Then
        IsPrime = False
        Exit Function
    End If
    
    Dim i As Long
    For i = 2 To Sqr(n)
        If n Mod i = 0 Then
            IsPrime = False
            Exit Function
        End If
    Next i
    
    IsPrime = True
End Function

Function GeneratePrime(min As Long, max As Long) As Long
    Dim n As Long
    Do
        n = Int((max - min + 1) * Rnd + min)
        If IsPrime(n) Then
            GeneratePrime = n
            Exit Function
        End If
    Loop
End Function

What does this function do? The IsPrime function checks whether a number is prime, while the GeneratePrime function randomly generates a prime number within a given range.

Tip: In actual RSA implementations, we need to use larger primes (usually hundreds of bits long) and more complex prime generation algorithms to ensure security. But for our demonstration, this simple method is sufficient.

Advanced: Implementing RSA Key Generation

Now that we have a method to generate primes, let’s implement the RSA key generation process:

Function GCD(a As Long, b As Long) As Long
    If b = 0 Then
        GCD = a
    Else
        GCD = GCD(b, a Mod b)
    End If
End Function

Function ModInverse(a As Long, m As Long) As Long
    Dim m0 As Long, y As Long, x As Long
    
    If m = 1 Then
        ModInverse = 0
        Exit Function
    End If
    
    m0 = m
    y = 0
    x = 1
    
    While a > 1
        Dim q As Long, t As Long
        q = a \ m
        t = m
        
        m = a Mod m
        a = t
        t = y
        
        y = x - q * y
        x = t
    Wend
    
    If x < 0 Then
        x = x + m0
    End If
    
    ModInverse = x
End Function

Sub GenerateRSAKeys()
    Dim p As Long, q As Long, n As Long, phi As Long, e As Long, d As Long
    
    ' Generate two distinct primes
    p = GeneratePrime(100, 1000)
    Do
        q = GeneratePrime(100, 1000)
    Loop While q = p
    
    n = p * q
    phi = (p - 1) * (q - 1)
    
    ' Choose public key exponent e
    Do
        e = Int((phi - 2) * Rnd + 2)
    Loop While GCD(e, phi) <> 1
    
    ' Calculate private key exponent d
    d = ModInverse(e, phi)
    
    ' Output results
    Cells(1, 1).Value = "Public Key (e, n)"
    Cells(1, 2).Value = e
    Cells(1, 3).Value = n
    Cells(2, 1).Value = "Private Key (d, n)"
    Cells(2, 2).Value = d
    Cells(2, 3).Value = n
End Sub

This code implements the RSA key generation process. It first generates two distinct primes p and q, then computes n = p * q and φ(n) = (p-1) * (q-1). Next, it selects a number e that is coprime to φ(n) as the public key exponent, and finally calculates the private key exponent d.

Note: In actual applications, we need to use larger numbers to ensure security. The small numbers used here are only for demonstration purposes.

Advanced: RSA Encryption and Decryption

With the keys, we can implement RSA encryption and decryption:

Function ModPow(base As Long, exponent As Long, modulus As Long) As Long
    Dim result As Long
    result = 1
    base = base Mod modulus
    
    While exponent > 0
        If exponent Mod 2 = 1 Then
            result = (result * base) Mod modulus
        End If
        exponent = exponent \ 2
        base = (base * base) Mod modulus
    Wend
    
    ModPow = result
End Function

Function RSAEncrypt(message As Long, e As Long, n As Long) As Long
    RSAEncrypt = ModPow(message, e, n)
End Function

Function RSADecrypt(ciphertext As Long, d As Long, n As Long) As Long
    RSADecrypt = ModPow(ciphertext, d, n)
End Function

Here, the ModPow function implements modular exponentiation, which is the core operation of the RSA algorithm. The RSAEncrypt and RSADecrypt functions implement encryption and decryption, respectively.

You can use these functions like this:

Sub TestRSA()
    Dim message As Long, encrypted As Long, decrypted As Long
    Dim e As Long, d As Long, n As Long
    
    ' Assume we have already generated the keys
    e = Cells(1, 2).Value
    n = Cells(1, 3).Value
    d = Cells(2, 2).Value
    
    ' Encrypt and decrypt a message
    message = 42  ' Assume we want to encrypt the number 42
    encrypted = RSAEncrypt(message, e, n)
    decrypted = RSADecrypt(encrypted, d, n)
    
    ' Output results
    Cells(4, 1).Value = "Original Message"
    Cells(4, 2).Value = message
    Cells(5, 1).Value = "Encrypted Message"
    Cells(5, 2).Value = encrypted
    Cells(6, 1).Value = "Decrypted Message"
    Cells(6, 2).Value = decrypted
End Sub

Tip: In actual applications, we typically do not encrypt the message itself directly, but encrypt a randomly generated symmetric key and then use this symmetric key to encrypt the actual message. This method is called a hybrid encryption system.

Super Advanced: Implementing Digital Signatures

Digital signatures are another important application of the RSA algorithm. They can be used to verify the integrity of messages and the identity of the sender. Let’s implement a simple digital signature system:

Function Hash(message As String) As Long
    Dim i As Integer, hash As Long
    For i = 1 To Len(message)
        hash = (hash * 31 + Asc(Mid(message, i, 1))) Mod 1000000007
    Next i
    Hash = hash
End Function

Function Sign(message As String, d As Long, n As Long) As Long
    Dim hash As Long
    hash = Hash(message)
    Sign = ModPow(hash, d, n)
End Function

Function Verify(message As String, signature As Long, e As Long, n As Long) As Boolean
    Dim hash As Long, decrypted_hash As Long
    hash = Hash(message)
    decrypted_hash = ModPow(signature, e, n)
    Verify = (hash = decrypted_hash)
End Function

Here, the Hash function implements a simple hash algorithm. The Sign function uses the private key to sign the hash of the message, while the Verify function uses the public key to verify the signature.

You can use these functions like this:

Sub TestSignature()
    Dim message As String, signature As Long
    Dim e As Long, d As Long, n As Long
    
    ' Assume we have already generated the keys
    e = Cells(1, 2).Value
    n = Cells(1, 3).Value
    d = Cells(2, 2).Value
    
    ' Sign and verify a message
    message = "Hello, RSA!"
    signature = Sign(message, d, n)
    
    ' Output results
    Cells(8, 1).Value = "Message"
    Cells(8, 2).Value = message
    Cells(9, 1).Value = "Signature"
    Cells(9, 2).Value = signature
    Cells(10, 1).Value = "Verification Result"
    Cells(10, 2).Value = Verify(message, signature, e, n)
End Sub

Note: The hash function used here is very simple and not suitable for actual applications. In real scenarios, we should use standard cryptographic hash functions like SHA-256.

Real-World Applications

RSA encryption and digital signatures in Excel have many practical applications, such as:

Protecting sensitive data: When sharing Excel files, important data can be encrypted.
Verifying data integrity: Using digital signatures to ensure data has not been tampered with.
Implementing secure communication: Secure data exchange between different Excel files or users.
Educational purposes: Demonstrating and teaching basic cryptographic concepts.

Conclusion

Today, we learned how to implement the RSA encryption algorithm and digital signatures in Excel. We started with basic prime generation, then implemented RSA key generation, encryption, decryption, and finally covered the creation and verification of digital signatures.

Although these implementations are relatively simple and mainly for educational purposes, they demonstrate the core principles of the RSA algorithm. Remember, in actual applications, we need to use larger numbers, more complex algorithms, and standard cryptographic libraries to ensure security.

Exercise: Try to create a simple encrypted communication system using what you learned today. First, generate a pair of RSA keys, then encrypt a message with the public key and decrypt it with the private key. Finally, attempt to sign and verify the message.

Alright, that’s it for today’s lesson. If you have any questions, feel free to let me know. Remember, cryptography is a very deep field, and today we only scratched the surface. If you’re interested, you can continue to dive deeper into more cryptography knowledge. Enjoy your Excel encryption journey, and see you next time!