> You won't be able to ride the Tube in London or Subway in NYC with a card that does not support it, for example.
Those systems all perform online auths at the gate, they don’t rely on offline transactions at all.
Asymmetric encryption is used to prove the identity of the card itself, I.e. prove it’s a real card owned by a real issuer. But it’s not used to sign the transaction itself.
Transaction cryptograms, the cryptographic blob that’s built using data like transaction amounts, method of customer authentication etc only use symmetric encryption. The produced cryptogram itself is then also signed using an asymmetric key, but the asymmetric and symmetric blobs are distinct entities and processes separately by the card network.
Now this is the really important, and completely non-obvious part. Only the symmetrically encrypted transaction cryptogram is sent over the card network to the issuer. All of the asymmetric parts are only used locally by the terminal for validation, then thrown away. So the data produced by the card that is actually stored and eventually sent to the issuer can’t be used for cryptographic non-repudiation, because there’s no mechanism for the merchant to prove using only the transaction cryptogram, and public keys, that a specific transaction was signed by a specific card issued by a specific issuer.
This may seem very strange from a technical perspective, but only because people think that the technical elements of card networks is what prevents fraud. In reality fraud, at least between network participants, is entirely prevented using legal contracts, escrow accounts, and the simple fact that the benefit of abusing the technical measures to commit fraud is simply not worth the consequences. Being a network participant requires you to put millions of dollars in escrow, and be a large enough company that you can realistically move millions of dollars in transactions everyday. Fraud between companies at that level is solved using very expensive lawyers, the technical measures only need to provide enough evidence of tampering to stand up in a court of law, where everyone is under oath, and at risk of personal repercussions for perjury. There is no need for them to be completely fool proof, it’s much easier to just depose the engineers who were ordered to circumvent the technical controls, under threat of prison time, than it is to get every network participant to adopt some complex cryptographic non-repudiation scheme to protect against scenarios that don’t actually occur in reality.