Caused by: com.mysql.jdbc.exceptions.jdbc4.MySQLNonTransientConnectionException: Client does not support authentication protocol requested by server; consider upgrading MySQL client
    at java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance0(Native Method)
    at java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance(Unknown Source)
    at java.base/jdk.internal.reflect.DelegatingConstructorAccessorImpl.newInstance(Unknown Source)
    at java.base/java.lang.reflect.Constructor.newInstance(Unknown Source)
    at com.mysql.jdbc.Util.handleNewInstance(Util.java:406)
    at com.mysql.jdbc.Util.getInstance(Util.java:381)
    at com.mysql.jdbc.SQLError.createSQLException(SQLError.java:984)
    at com.mysql.jdbc.SQLError.createSQLException(SQLError.java:956)
    at com.mysql.jdbc.MysqlIO.checkErrorPacket(MysqlIO.java:3558)
    at com.mysql.jdbc.MysqlIO.checkErrorPacket(MysqlIO.java:3490)
    at com.mysql.jdbc.MysqlIO.checkErrorPacket(MysqlIO.java:919)
    at com.mysql.jdbc.MysqlIO.secureAuth411(MysqlIO.java:3996)
    at com.mysql.jdbc.MysqlIO.doHandshake(MysqlIO.java:1284)
    at com.mysql.jdbc.ConnectionImpl.createNewIO(ConnectionImpl.java:2137)
    at com.mysql.jdbc.ConnectionImpl.<init>(ConnectionImpl.java:776)
    at com.mysql.jdbc.JDBC4Connection.<init>(JDBC4Connection.java:46)
    at java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance0(Native Method)
    at java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance(Unknown Source)
    at java.base/jdk.internal.reflect.DelegatingConstructorAccessorImpl.newInstance(Unknown Source)
    at java.base/java.lang.reflect.Constructor.newInstance(Unknown Source)
    at com.mysql.jdbc.Util.handleNewInstance(Util.java:406)
    at com.mysql.jdbc.ConnectionImpl.getInstance(ConnectionImpl.java:352)
    at com.mysql.jdbc.NonRegisteringDriver.connect(NonRegisteringDriver.java:284)
    at java.sql/java.sql.DriverManager.getConnection(Unknown Source)
    at java.sql/java.sql.DriverManager.getConnection(Unknown Source)
    at org.springframework.jdbc.datasource.DriverManagerDataSource.getConnectionFromDriverManager(DriverManagerDataSource.java:154)
    at org.springframework.jdbc.datasource.DriverManagerDataSource.getConnectionFromDriver(DriverManagerDataSource.java:145)
    at org.springframework.jdbc.datasource.AbstractDriverBasedDataSource.getConnectionFromDriver(AbstractDriverBasedDataSource.java:205)
    at org.springframework.jdbc.datasource.AbstractDriverBasedDataSource.getConnection(AbstractDriverBasedDataSource.java:169)
    at org.hibernate.engine.jdbc.connections.internal.DatasourceConnectionProviderImpl.getConnection(DatasourceConnectionProviderImpl.java:122)
    at org.hibernate.engine.jdbc.env.internal.JdbcEnvironmentInitiator$ConnectionProviderJdbcConnectionAccess.obtainConnection(JdbcEnvironmentInitiator.java:180)
    at org.hibernate.resource.transaction.backend.jdbc.internal.DdlTransactionIsolatorNonJtaImpl.getIsolatedConnection(DdlTransactionIsolatorNonJtaImpl.java:43)

Recibo este error incluso después de actualizar la contraseña de mysql. Leí en algunas publicaciones que mysql tiene un nuevo mecanismo de almacenamiento en caché y todos los clientes necesitan ejecutar lo siguiente, lo cual ya hice pero sigue siendo el mismo error:

 update user set authentication_string='test' where user='root';
 flush privileges