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The most famous proposed COVID-19 application is DP3T. In this app a user constantly broadcasts EphIDs generated from a secret key as follows:

$$EphID 1 || ... || EphID n = PRG( PRF(SK_t , “broadcast key”) )$$

where PRF is a pseudo-random function (e.g., HMAC-SHA256), “broadcast key” is a fixed and public string, and PRG is a stream cipher (e.g. AES in counter mode) producing $16 \cdot n$ bytes, which we split into 16-byte chunks to obtain the $n$ ephemeral Bluetooth identifiers EphID of the day.

The secret key is composed of 32 random generated bytes, and changes everyday in following manner: $ SK_t = H( SK_t-_1 ) $

As I understand, $PRF(SK_t , “broadcast key”)$ is used as keystream to AES in counter mode. But what is the purpose of this? Why isn't the secret key $SK_t$ used as keystream?

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  • $\begingroup$ That is simple right? To arrive at different keys for different broadcastkey? $\endgroup$ – kelalaka May 12 '20 at 18:20
  • $\begingroup$ @kelalaka I do not understand what you mean. The string "broadcastkey" is the same for every user and is not changed, it further has no purpose I think. If you use the secret key, SK_t, or you use a hmac/hash of that SK_t, what is the difference? $\endgroup$ – Ruben_G May 12 '20 at 18:42
  • $\begingroup$ It might be the same today, but it might be different in the future, See Multiple AES Key Derivation from a master key. They may ask, hey, tomorrow we will change the broadcaster? $\endgroup$ – kelalaka May 12 '20 at 18:44
  • $\begingroup$ $SK_t$ is probably also used elsewhere? It is good cryptographic practice to derive a distinct key for each use-case to avoid unexpected interactions. $\endgroup$ – SEJPM♦ May 13 '20 at 10:26
  • $\begingroup$ @SEJPM I understand what you mean. Thx for that explanation. But no, $SK_t$ is not used anywhere else. $\endgroup$ – Ruben_G May 13 '20 at 11:34

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