# Maximum secret key length from a time series shared signal

Alice and Bob share a common time series signal.

1. What can be the largest possible secret key?

2. Will the entropy and secrecy of system depends on this length?

Ideally if after passing though analog to digital converter(ADC) number of bits a signal gives depends on $N_S$ sampling rate. Suppose I had s 1 second window of signal. Through ADC I got $N_S$ samples. I apply threshold on these samples and generate keys. Maximum length hence is $N_S$ bits of secret keys.

Is this the best key? I mean is there any relation between entropy/secrecy of the key vs length I choose from $N_S$?

1. What can be the largest possible secret key?

Any size. You can use the entropy as input for a DRBG (deterministic random bit generator) or KDF (key derivation function) and generate as many bits you want out of that.

1. Will the entropy and secrecy of system depends on this length?

No.

Assumption: Maximum length hence is $N_S$ bits of secret keys

No, it isn't. That's just the input data that contains a certain amount of entropy - or at least that's what we'll assume for the sake of argument.

1. Is this the best key?

No $N_S$ (or any specific part of $N_S$) is not the best key. You want to explicitly extract the randomness from your data. $N_S$ may be biased.