ECC key decompression in X-CUBE-CRYPTOLIB

[ncat1]

I am using the X-CUBE-CRYPTOLIB (V4.2.0) in a project for STM32F207.

I am successfully able to generate ECC key pair using cmox_ecdsa_keyGen() and generate ECDSA signature using cmox_ecdsa_sign() but I am now needing to generate a shared secret using cmox_ecdh() function. 

The problem I have is that the cmox_ecdh() function expects the public key in raw data format (64 bytes) but I only have the public key available in compressed format (33 bytes) where 32 bytes is the x component and the other byte indicates if the y component is odd or even. The y component can be derived from this information but I could not find a function within the  X-CUBE-CRYPTOLIB that does this which means I am unable to generate the shared secret.

Is there a way of achieving this with the  X-CUBE-CRYPTOLIB?

[STea]

Hello @ncat1 ,

This compressed format is not supported for the NIST curves. so, you will need to decompress the key manually to make it suitable for use by cmox_ecdh() function.
see example in en.STM32CubeExpansion_Crypto\STM32CubeExpansion_Crypto_V4.1.0\Projects\NUCLEO-L552ZE-Q\Applications\ECC\ECDH_SharedSecretGeneration available in the Xcube_cryprolib as a reference.

the decompression can be done following this formula :

To decompress a point, we can calculate its two possible y coordinates by the formula

y1 = mod_sqrt(x3 + ax + b, p)

y2 = p - mod_sqrt(x3 + ax + b, p)

then using the odd even bit we can choose the correct one. this can be done using a python script python (see this link)
Regards