The best analogy of a trapdoor function I've come across is a padlock and key. Alice sends Bob an unlocked padlock but keeps the key. Bob puts his message in a box and locks it with the Alice's padlock. He send it back to Alice and she opens it with her key.
The traditional CIA solution is Eve sleeps with Bob or Alice! There are no commutative trapdoor functions (Bouncing Theorem for multifunctions) - there is an invertible function composed out of bounces. Polynomial wheels invert!
There is a story of someone who collected a large number of RSA keys actually in use, and pairwise calculated hcfs. Because some of the p and q were not random, several were found by the hcf calculation. Hope it was an academic study rather than the start of a malicious fraud.
Let me see if I understood the blockchain part correctly: Let h be the hash function and B(n) be the n'th block. Then the relation is B(n) = h(B(n+1)) and not the other way around. So given B(2) we can easily find B(1) by applying h, but we cannot easily find B(3).
Yesterday i commented for lecture over mathematical cryptography , and today it appears. Professor it is my humble request make a long series of video for mathematical cryptography, it will be a big help for me.
@@richarde.borcherds7998 My guess would be the automatically generated captions; there's the ability to view a transcript, and so a bot can trivially search through that. (Specifically, the word does appear in the entry for 9:23)
Very ironic for this type of content to be taken over by bots targeting the most naive people. Anyhow, interesting as always. Thank you professor.
The best analogy of a trapdoor function I've come across is a padlock and key. Alice sends Bob an unlocked padlock but keeps the key. Bob puts his message in a box and locks it with the Alice's padlock. He send it back to Alice and she opens it with her key.
The traditional CIA solution is Eve sleeps with Bob or Alice!
There are no commutative trapdoor functions (Bouncing Theorem for multifunctions) - there is an invertible function composed out of bounces.
Polynomial wheels invert!
Great stuff. Within the current internet security setup how many different "pq" combinations in use? How are the factors p and q kept secret?
There is a story of someone who collected a large number of RSA keys actually in use, and pairwise calculated hcfs. Because some of the p and q were not random, several were found by the hcf calculation. Hope it was an academic study rather than the start of a malicious fraud.
Let me see if I understood the blockchain part correctly: Let h be the hash function and B(n) be the n'th block. Then the relation is
B(n) = h(B(n+1))
and not the other way around. So given B(2) we can easily find B(1) by applying h, but we cannot easily find B(3).
Did you ubderstand it?
Yesterday i commented for lecture over mathematical cryptography , and today it appears. Professor it is my humble request make a long series of video for mathematical cryptography, it will be a big help for me.
What's wrong with the comment section?
The professor mentioned bitcoin, and obviously there are bitcoin bots that scour the internet looking for any video that mentions bitcoin.
@@annaclarafenyo8185 Oh, that makes sense. Thank you!
This seems odd as the video description says nothing about b**c***. Are bots now good enough to listen to videos and pick out words they mention?
@@richarde.borcherds7998 My guess would be the automatically generated captions; there's the ability to view a transcript, and so a bot can trivially search through that. (Specifically, the word does appear in the entry for 9:23)
That seems to explain it. I guess I will have to be a little more careful about what I say in lectures.
There is something wrong with the sound.
Idk, I think it's fine.
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