Timeline for Extending Vigenère method using arbitrary function
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 30, 2020 at 22:26 | comment | added | Joe Silverman | Sounds reasonable, although since $p$ is your secret key, it would need to be quite large. And probably you'd want to take the part of the base 26 expansion starting after the decimal point, i.e., the expansion of the $\sqrt{p}-\lfloor\sqrt p\rfloor$. | |
| Jul 30, 2020 at 21:29 | comment | added | somenxavier | OK. I have an educated guess: if $f$ is eventually non-periodic, then cipher is not vulnerable to Kasiski's method or frequency analysis. Eg. decimal expansion of $\sqrt{p}$ with base 26 where $p$ is prime. | |
| Jul 30, 2020 at 10:30 | comment | added | Joe Silverman | I don't know a reference, but isn't it obvious that it's a one-time pad? If you replace $\mathbb Z/26\mathbb Z$ with $\mathbb Z/2\mathbb Z$, then you get exactly the usual one-time pad where each bit of the message is XOR'd with the corresponding bit of the random list of bits. As for the concrete example that $f$ is an unknown quadratic polynomial, that's a great question, but comes back down to a Vigenere, since the sequence $\{f(i)\bmod26:i\ge1\}$ is eventually periodic. It's an example of a dynamical system over $\mathbb Z/26\mathbb Z$. So some version of Kasiski should work. | |
| Jul 30, 2020 at 9:28 | comment | added | somenxavier | For being concrete, what about quadratic function: $f(x) = ax^2 + bx + c$ | |
| Jul 30, 2020 at 9:27 | comment | added | somenxavier | Can you give me some references about that "The net effect is that we're using a one-time pad, so that's secure"? | |
| Jul 29, 2020 at 18:53 | history | answered | Joe Silverman | CC BY-SA 4.0 |