Ron Was Wrong, Whit Was Right

While I try to read the latest research papers in my field, I also try and read some of the classic ones. One of these classic papers is [1]:

The title itself is a classic one and references two of the giants of cybersecurity: Ron Rivest and Whitfield Diffie. With the paper, Lenstra and others sampled encryption keys and found that although the value of the encryption exponent (e) was typically 65,537, there were some keys which used strange values of 3, 5, 7 17 and 35:

The e value is fundamental for security as a low value can cause a serious weakness in the encryption. Normally, in RSA, we select two prime numbers of equal length (p and q), and then multiply these to give a modulus:

We then compute the cipher as:

But, if M^e≤N, we get:

Then the message can be determined from [2]:

If the value of M^e that is less than N, it becomes easy to crack (with just one line of Python) to crack the RSA cipher: