About prime numbers, cryptography and brain damage
Today is Friday, right?
I recently read a rather well-known book, “The Man Who Took His Wife for a Hat”. The book is really worth being read, but I'm not talking about that right now.
In one of the stories, the author, a practicing doctor who works with people with varying degrees of brain damage, encounters autistic twins playing a game with each other. First, one of them calls a six-digit number, after some time the other clearly rejoices at this chill, as if having discerned something in him, and, in turn, calls another six-digit number. The process is repeated many times.
The author quietly approaches and writes the called numbers to himself in a notebook, and then, in his spare time, discovers that all of the named numbers are simple! Then he takes it, finds a table of the largest known prime numbers then (the middle of the last century!), Writes out several eight-digit ones, goes to the twins, and calls them one of them. The pause on their part lasts significantly longer, but then a flash of joy follows, and they continue the game, this time with 8-digit numbers, then switch 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 check twenty-digit numbers for simplicity.
Another episode about the same twins - a box of matches falls and scatters from the table, and they both exclaim “one hundred and eleven,” adding “thirty-seven.” I think it’s not worth saying that when the author counted the matches, they turned out to be 111 = 37 * 3. The
twenty-digit number is a number of the order of 70 bits. The product of two such numbers is 140 bits. In modern cryptography, this still presents a rather complicated computational task.
At the same time, there is repeated evidence that there are people, most often with one or another brain damage, who in some incomprehensible way can directly “see” prime numbers, and, possibly, also see multipliers of composite numbers. The author of the aforementioned book also refers to other similar examples.
What if the ability of these people works for numbers of the magnitude of modern crypto keys? Could this be the very long-awaited crisis of modern asymmetric cryptography?
I recently read a rather well-known book, “The Man Who Took His Wife for a Hat”. The book is really worth being read, but I'm not talking about that right now.
In one of the stories, the author, a practicing doctor who works with people with varying degrees of brain damage, encounters autistic twins playing a game with each other. First, one of them calls a six-digit number, after some time the other clearly rejoices at this chill, as if having discerned something in him, and, in turn, calls another six-digit number. The process is repeated many times.
The author quietly approaches and writes the called numbers to himself in a notebook, and then, in his spare time, discovers that all of the named numbers are simple! Then he takes it, finds a table of the largest known prime numbers then (the middle of the last century!), Writes out several eight-digit ones, goes to the twins, and calls them one of them. The pause on their part lasts significantly longer, but then a flash of joy follows, and they continue the game, this time with 8-digit numbers, then switch 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 check twenty-digit numbers for simplicity.
Another episode about the same twins - a box of matches falls and scatters from the table, and they both exclaim “one hundred and eleven,” adding “thirty-seven.” I think it’s not worth saying that when the author counted the matches, they turned out to be 111 = 37 * 3. The
twenty-digit number is a number of the order of 70 bits. The product of two such numbers is 140 bits. In modern cryptography, this still presents a rather complicated computational task.
At the same time, there is repeated evidence that there are people, most often with one or another brain damage, who in some incomprehensible way can directly “see” prime numbers, and, possibly, also see multipliers of composite numbers. The author of the aforementioned book also refers to other similar examples.
What if the ability of these people works for numbers of the magnitude of modern crypto keys? Could this be the very long-awaited crisis of modern asymmetric cryptography?