Cryptocurrency do not compulsorily require blockchain.. What is important is the consensus algorithm and how nodes come to a consensus.. But most of them use blockchain because of blockchain's features. There are technologies like IOTA and many more advanced technology that can be used for cryptocurrency but they are not as popular as blockchain. Look up to "Bitcoin White Paper" to know why is has become so popular and why it is mostly used. And after that go through IOTA White Paper so you can understand how to can implement cryptocurrency without blockchain..