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Does anybody know if the concepts behind elliptic curve cryptography be applied to analog data?

by noworriesnate 5y ago

marcan_42 5y ago
Cryptography only works with digital data. That's quite fundamental to how it works, as far as I know.
- kadoban 5y ago
  That's mostly but not strictly true, possibly depending on your definition. One example of analog encryption would be there was a system around WWII times where noise from a phonograph was added to a call to avoid evesdropping, and then on the receiving end it was subtracted out using a specially synchronized phonograph. Another that I'm not sure on exactly, but back when TV was analog, there were some channels designed not to be watchable without paying. Not sure how those worked, it may technically qualify.
  - marcan_42 5y ago
    You're thinking of SIGSALY. Not only was it not analog, it was the first digital system to use PCM for audio. https://en.m.wikipedia.org/wiki/SIGSALY https://en.m.wikipedia.org/wiki/SIGSALY The analog TV stuff isn't encryption, it's scrambling. Those systems used proper digital crypto to generate the keystream, then scrambled video lines using a digital line buffer. They aren't secure (you can decode the picture by correlating lines without having the key) and they still rely on digital bits to do the processing, even if the image itself is transmitted as analog. So no, analog crypto doesn't exist, though you can certainly obfuscate analog signals in various ways. For crypto to be analog the actual cryptography would have to be performed in the analog domain. To my knowledge, that doesn't exist and can't exist.
    - kadoban 5y ago
      Thanks, I did not know that was digital.
SAI_Peregrinus 5y ago
Not really, assuming you mean "continuous" by "analog". ECC relies on the existence of an elliptic curve group to be reversible. Groups are inherently discrete structures, I'm not aware of any continuous structures with similarly useful properties.
- joppy 5y ago
  Groups are not inherently discrete - there are many continuous groups (called Lie groups) such as the circle, group of rotations in 3D, etc etc. You can also see this turn up in Fourier theory: the discrete Fourier transform has an underlying discrete group, Fourier series for a periodic function are really using the circle group underneath, and the Fourier transform on the real line is using the continuous group of the real line, with addition as the group operation. Elliptic curves are nice because they are algebraic groups, so by plugging in complex or real numbers you get a continuous group, and by plugging in finite fields you get a discrete group.
BearsAreCool 5y ago
While elliptic curves may sound like they're related to analog data (sinusoidal curves etc), they're actually used in an incredibly discrete way. You have discrete points on an elliptic curves modulo a prime and use them in elliptic curve algebra by multiplying them by integer values, which correspond to drawing lines between different curve points.

Does anybody know if the concepts behind elliptic curve cryptography be applied to analog data?

marcan_42 5y ago

Cryptography only works with digital data. That's quite fundamental to how it works, as far as I know.

kadoban 5y ago
That's mostly but not strictly true, possibly depending on your definition. One example of analog encryption would be there was a system around WWII times where noise from a phonograph was added to a call to avoid evesdropping, and then on the receiving end it was subtracted out using a specially synchronized phonograph. Another that I'm not sure on exactly, but back when TV was analog, there were some channels designed not to be watchable without paying. Not sure how those worked, it may technically qualify.
- marcan_42 5y ago
  You're thinking of SIGSALY. Not only was it not analog, it was the first digital system to use PCM for audio. https://en.m.wikipedia.org/wiki/SIGSALY https://en.m.wikipedia.org/wiki/SIGSALY The analog TV stuff isn't encryption, it's scrambling. Those systems used proper digital crypto to generate the keystream, then scrambled video lines using a digital line buffer. They aren't secure (you can decode the picture by correlating lines without having the key) and they still rely on digital bits to do the processing, even if the image itself is transmitted as analog. So no, analog crypto doesn't exist, though you can certainly obfuscate analog signals in various ways. For crypto to be analog the actual cryptography would have to be performed in the analog domain. To my knowledge, that doesn't exist and can't exist.
  - kadoban 5y ago
    Thanks, I did not know that was digital.

SAI_Peregrinus 5y ago

Not really, assuming you mean "continuous" by "analog". ECC relies on the existence of an elliptic curve group to be reversible. Groups are inherently discrete structures, I'm not aware of any continuous structures with similarly useful properties.

joppy 5y ago
Groups are not inherently discrete - there are many continuous groups (called Lie groups) such as the circle, group of rotations in 3D, etc etc. You can also see this turn up in Fourier theory: the discrete Fourier transform has an underlying discrete group, Fourier series for a periodic function are really using the circle group underneath, and the Fourier transform on the real line is using the continuous group of the real line, with addition as the group operation. Elliptic curves are nice because they are algebraic groups, so by plugging in complex or real numbers you get a continuous group, and by plugging in finite fields you get a discrete group.

BearsAreCool 5y ago

While elliptic curves may sound like they're related to analog data (sinusoidal curves etc), they're actually used in an incredibly discrete way. You have discrete points on an elliptic curves modulo a prime and use them in elliptic curve algebra by multiplying them by integer values, which correspond to drawing lines between different curve points.