How is the stream cipher key shared on GSM?

Question

I read that phones encrypt communication (GSM as implemented in 2G,3G..) - particularly voice as SMS are unencrypted - using a stream cipher.

Symmetric Stream ciphers use the flip-flop machinery to start (a true random generator imho), and then they follow some algorithm to change message bitwise ( and can be broken with simple linear algebra if enough x and y are intercepted. )

But there is no clear explanation (in the Christopher Paar course at Youtube, a neat course) as to how the phones agree on this key.

Any pointers?

Answer 1

Symmetric Stream ciphers use the flip-flop machinery to start (a true random generator imho)

Not sure what you mean by "flip-flop machinery", but a stream cipher is not a true random number generator, it is a pseudorandom number generator. The initial key selection may be done by a true random number generator, but can also be done based on a password or through a key agreement protocol.

and can be broken with simple linear algebra if enough x and y are intercepted.

If you are using a cryptographically secure stream cipher, and are not using it improperly (no key-nonce pair reuse), then it cannot be broken with simple linear algebra. However, the ciphers used by GSM are not cryptographically secure, hence why they can be broken.

But there is no clear explanation (in the Christopher Paar course at Youtube, a neat course) as to how the phones agree on this key

From https://www.tutorialspoint.com/gsm/gsm_security.htm:

A 128-bit Random Number (RAND) is sent to the MS (phone)

...

The SIM contains the ciphering key generating algorithm (A8) that is used to produce the 64-bit ciphering key (Kc). This key is computed by applying the same random number (RAND) used in the authentication process to ciphering key generating algorithm (A8) with the individual subscriber authentication key (Ki).