About prime numbers, cryptography and brain damage
It's Friday, right?
Recently I read a fairly well-known book called The Man Who Took His Wife for a Hat. The book is really worth being read, but this is not about me now.
In one of the plots, the author is a practicing physician who works with people with varying degrees of brain damage and encounters autistic twins playing a game with each other. At first, one of them calls a six-digit number, after some time the other is clearly pleased with this chila, as if he had seen something in it, and in turn, calls another six-digit number. The process is repeated many times.
The author quietly comes up and writes the numbers called to himself in a notebook, and then at his leisure he discovers that all the numbers mentioned are simple! Then he takes, finds the table of the largest known then prime numbers (the middle of the last century!), Writes out some eight-digit ones, goes to the twins, and calls them one of them. A pause on their part lasts significantly longer, but then there is a flash of joy, and they continue to play, this time with 8-digit numbers, then move to 9 and 10-digit ones. After a couple of hours, they were already playing their game with twenty-digit numbers! As the author notes, at that time there was no way to test twenty-digit numbers for simplicity.
')
Another episode about these same twins - a box of matches falls off and crumbles from the table, and they both exclaim "one hundred and eleven", adding "thirty-seven". I think it is not necessary to say that when the author counted the matches - they turned out to be 111 = 37 * 3.
The twenty-digit number is a number on the order of 70 bits. The product of two such numbers is 140 bits. In modern cryptography, this is still a fairly complex computational problem.
At the same time, there is repeated evidence that there are people, most often with some kind of damage to the brain, who in some incomprehensible way can directly "see" simple numbers, and, possibly, also see the multipliers of numbers. The author of the above book refers to other similar examples.
What if the ability of these people works for numbers of the magnitude of modern cryptokey? Will this not be the very expected crisis of modern asymmetric cryptography?
Recently I read a fairly well-known book called The Man Who Took His Wife for a Hat. The book is really worth being read, but this is not about me now.
In one of the plots, the author is a practicing physician who works with people with varying degrees of brain damage and encounters autistic twins playing a game with each other. At first, one of them calls a six-digit number, after some time the other is clearly pleased with this chila, as if he had seen something in it, and in turn, calls another six-digit number. The process is repeated many times.
The author quietly comes up and writes the numbers called to himself in a notebook, and then at his leisure he discovers that all the numbers mentioned are simple! Then he takes, finds the table of the largest known then prime numbers (the middle of the last century!), Writes out some eight-digit ones, goes to the twins, and calls them one of them. A pause on their part lasts significantly longer, but then there is a flash of joy, and they continue to play, this time with 8-digit numbers, then move to 9 and 10-digit ones. After a couple of hours, they were already playing their game with twenty-digit numbers! As the author notes, at that time there was no way to test twenty-digit numbers for simplicity.
')
Another episode about these same twins - a box of matches falls off and crumbles from the table, and they both exclaim "one hundred and eleven", adding "thirty-seven". I think it is not necessary to say that when the author counted the matches - they turned out to be 111 = 37 * 3.
The twenty-digit number is a number on the order of 70 bits. The product of two such numbers is 140 bits. In modern cryptography, this is still a fairly complex computational problem.
At the same time, there is repeated evidence that there are people, most often with some kind of damage to the brain, who in some incomprehensible way can directly "see" simple numbers, and, possibly, also see the multipliers of numbers. The author of the above book refers to other similar examples.
What if the ability of these people works for numbers of the magnitude of modern cryptokey? Will this not be the very expected crisis of modern asymmetric cryptography?
Source: https://habr.com/ru/post/192038/
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