After watching 'How to Break Cryptography' and 'This Video was Not Encrypted with RSA' my curiosity motivated me to demystify RSA cryptography. Inspired by Neal Koblitz's article 'Cryptography As a Teaching Tool' this module was programmed following his 'Kid-RSA' example.

The beauty of this demonstration is the simplicity of arithmetic operations to encrypt and decrypt with minimal computational steps.

This demonstration (just as the article's example) explains the following two procedures:

• How to convert plain text message into simple-substitution cipher that gets encrypted by the sender and then decrypted by the recipient. The recipient then runs, the now decrypted cipher, thru an inverse simple-substitution algorithm to retrieve the plain text message.

• How a digital signature is created and sent.

This is a demonstration, not suitable for production. The longer the message to encrypt, the more likely this demonstration will fail.

To install, run the following command in PowerShell.

$ Install-Module KidRSA

Copy-and-paste the first six lines of code into PowerShell after installing this module. Shift + Enter to paste multiple lines of code such as below. Use the Up Arrow to repeat previous command followed by an Enter and see that the generated RSA keys are different than previously. With a new generated set of (asymmetric) keys will have a different encrypted value but the ConvertTo-PlainText (simple-substitution cipher) function will output the same plain text value.

Interestingly this function will fail to retrieve the plain text value at times (roughly 1 out 15). Since Get-RSAKey function generate keys with numbers less than 1000, it limits the plain text message to be a length no greater than 5 or 4 at times. Read more on this limitation here.

$AlicesKeys = Get-RSAKey -Verbose
$PlainText = "HELLO"
$CipherText = ConvertTo-CipherText $PlainText -Verbose
$EncryptedCipherText = ConvertTo-PublicEncryptionValue -CipherText $CipherText -PublicKey $AlicesKeys.e -N $AlicesKeys.n -Verbose
$CipherText = ConvertTo-PrivateDecryptionValue -EncryptedCipherText $EncryptedCipherText -PrivateKey $AlicesKeys.d -N $AlicesKeys.n -Verbose
ConvertTo-PlainText $CipherText -Verbose
VERBOSE: The value for 'a' is: 672
VERBOSE: The value for 'b' is: 263
VERBOSE: The value for 'a_' is: 342
VERBOSE: The value for 'b_' is: 543
VERBOSE: The value of Private key 'e' (encrypt) is: 60444042
VERBOSE: The value of Public key 'd' (decrypt) is: 95967368
VERBOSE: The value of 'n' is: 32821204753
VERBOSE: Ciphertext value is : 32768720
VERBOSE: Encrypted cipher value is : 12644736949
VERBOSE: Decrypted cipher value is : 32768720
VERBOSE: PlainText value is : HELLO
HELLO
E:\>