I need to encode a small message (12bytes) into less than 32 bytes
(ideally) or to produce signatures with a similar size.

RSA or other integer factorization based algorithms are not good
because they need big key size (at least 1024bits) for security
reasons:
cipher size with RSA 1024 is 128 bytes at least and same for
signature.

ECC based algorithms are better because a 160 bits key size is
equivalent to RSA1024.
For signature, I get 42 bytes.
Encoding a 12 bytes message, I get 73 bytes. If I use point
compression and Jeffery's trick to remove the 'TAG' in the encrypted
message, I manage to get 37 bytes.

Anyone has better suggestion?


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