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There are two ways to achieve anonymity:
1) The first way is to ask your first name, last name, citizenship, address, passport number and other personal details. And then try to encrypt all this information using cryptography so that no one knows it.
2) The second way is just not to ask people for any personal information. Then there will be nothing to encrypt and no cryptography will be needed.
We have chosen the second way of ensuring anonymity, it seems to us that it is much more effective than the first one.
Almost all cryptocurrency and token choose 2nd way you mentioned and almost all of them only offer pseudonymity, so it's nothing special.
But what i specifically meant is cryptography used when you make a transaction which used to ensure only the owner with private key can spend the coin/token (for example Bitcoin uses ECDSA secp256k1 and Zcash uses zk-SNARKs)