Unfortunately, there is no "secure" method. Access at the field level is not something you can limit.
That said, you can create alternative forms and simply show / hide links from these forms using audience targeting.
Next, you want to configure manual links using Webparts components whose audience targeting is set to the respective users / groups with access to each form.
Link 1, target users a, b, c, points to NewForm1.aspx
Link 2, targeting users of e, g, points to NewForm2.aspx
To add these links, use the content editor webparts or the script editor webparts. In the Webpart, simply add an anchor tag like this.
Form 1. Give it a style if you are familiar.
Newform1.aspx can be added by opening the site / list in SharePoint Designer. Or you could probably use the view of Windows Explorer in IE to copy-paste a newform.aspx into the Forms folder of the list. I recommend however SPD.
Finish the change
Another secure option would be to code a solution hosted by a provider that uses high authorization and restrict publishing access to the list through the provider-hosted application only.
I hope this helps you!