Don’t Trust GPT — Off Topic and Wrong!

Can You Trust GPT — When It’s Off-Topic and Wrong?

I will be demo’ing some AI and Cybersecurity over the next few weeks. So, let’s see if GPT actually has superficial knowledge or not. Let’s ask a fairly trivial question of:

The answer looks to be well written — although rather lacking any type of style. It is bland and just looks like a standard Stack Overflow answer. But, while it seems authoritative, it is poorly described:

In ECC, the public key is a point on an elliptic curve, and the private key is a random number. To encrypt a message, the sender computes a point on the elliptic curve using the receiver’s public key and then uses this point to derive a shared secret key. The sender then uses this shared secret key to encrypt the message, which can only be decrypted by the receiver, who knows the corresponding private key.

For a simple answer, it is acceptable but misses a good deal — as the short answers it gives tend to generalise things. And when it comes to why the security is better, it can only say that the keys are smaller — and which goes off-topic :

And then:

Again, it goes off-topic, and goes into the type of answer you get in Stack Overflow for answers that are not quite right:

I won’t go into detail, but again the symmetric key part of this never appears, and there are too many k values used. In a real life system the sender generates a random value, and the result is not k². If you probe for a little more detail, I will prompt itself to give more detail. Again, looks like it’s straight out the textbooks:

But let’s get it to do some computation:

And the answer is:

This is completely wrong! 14 times 14 is 196. If we take 196 (mod 97) we get 2, but 2³ + 7 (mod 97) is 15. The other points are wrong too!

The correct answers are [here]:

y^2 = x^3 + 7 (mod 97)

[(1, 28), (1, 69), (5, 61), (5, 36), (12, 38), (12, 59), (13, 78), 
(13, 19), (14, 61), (14, 36), (17, 19), (17, 78), (20, 21), 
(20, 76), (21, 76), (21, 21), (23, 90), (23, 7), (27, 75), 
(27, 22), (29, 7), (29, 90), (32, 59), (32, 38), (33, 32), 
(33, 65), (35, 69), (35, 28), (36, 54), (36, 43), (44, 5), 
(44, 92), (45, 7), (45, 90), (52, 81), (52, 16), (53, 59), 
(53, 38), (55, 30), (55, 67), (56, 76), (56, 21), (57, 67), 
(57, 30), (60, 45), (60, 52), (61, 69), (61, 28), (62, 43), 
(62, 54), (63, 45), (63, 52), (65, 92), (65, 5), (67, 78), (67, 19), 
(68, 16), (68, 81), (71, 45), (71, 52), (72, 22), (72, 75), (73, 65), 
(73, 32), (74, 81), (74, 16), (78, 61), (78, 36), (82, 30), (82, 67), 
(85, 92), (85, 5), (88, 65), (88, 32), (95, 75), (95, 22), (96, 54), 
(96, 43)]

For example for (1,28), we get 28² (mod 97) and which is 8, and where 1³+7 is also 8.

So, can it show that it was wrong:

And, so (2,14) is wrong, as GPT has shown.

Conclusions

For the teaching professional, we must all be worried about the power of GPT. Not because of its technical abilities, but in the ability to short-circuit the education process. If you are in Edinburgh on 2 March 2023, why not pop along to: