2007-06-13 21:27:21 · 4 answers · asked by infinity to one 1 in Science & Mathematics ➔ Other - Science
Excellent question.
A trapdoor cipher is a cipher that derives its security from a certain mathematical problem that is easy to solve in one direction, but much harder to solve in the other direction.
For example, if I take two prime numbers and multiply them together, I get 552533. If you wanted to find which numbers I used, there is no shortcut. You have to keep trying numbers until you found one that was evenly divisible. Multiplying two prime numbers is easy. Factoring a number into its primes is hard. A computer could solve that problem fairly easily, yielding 673 and 821 as the factors.
But now I make my numbers much, much larger. Can you tell me what the factors of this number are?
4799608693649349724
8022562035315124551
4315565623354567610
4772083448800954212
3178405457892249140
1094839505330693667
6005397388171194334
3724209849821693189
6941513647344234345
4579104723637232151
7359878801603832145
3862625109851217287
7866467477138629770
2257957111772706038
1503807371817485779
9293344179995665372
19
(that's all one number)
Even the fastest computer in the world would take an incredibly long time (billions of years) to factor that, yet I was able to generate it in seconds by choosing two very large primes at random, then multiplying them together.
This makes factoring a good trapdoor function. There is a very famous cipher which makes use of this exact function. It's called "RSA". You can learn more about it here:
http://en.wikipedia.org/wiki/RSA
2007-06-13 21:39:37 · answer #1 · answered by lithiumdeuteride 7 · 1⤊ 0⤋
A cipher is encoded by technique of a mathematical function. A trapdoor cipher is a cipher that's ordinary to encode your archives yet very perplexing to decode. In cryptography that's many times performed by multiplying 2 very tremendous authentic numbers. that's ordinary to multiply the numbers, yet having executed so, that's amazingly not ordinary for everyone to aspect this kind of huge variety. The "trapdoor" is a the little bit of thoughts you want that could help you to decode the textual content . . . which should be ordinary once you've the right thoughts.
2016-11-23 20:05:30 · answer #2 · answered by deparvine 4 · 0⤊ 0⤋
a way to encode and decode cryptyc messages.
2007-06-13 21:41:50 · answer #3 · answered by sutil 3 · 0⤊ 0⤋
http://en.wikipedia.org/wiki/Trapdoor_function
2007-06-13 21:32:45 · answer #4 · answered by Matthew L 3 · 0⤊ 0⤋