This question is a possible duplicate, but your question has the qualifier "if you are underpaid" to disclosing your current salary.
In general, your current salary has no bearing on the current role. Your current salary is typically used as a shortcut for HR to determine what to offer you while saving them money.
For the particular case that you are underpaid (actually applies in general):
- do not lie
- do not fluff, puff, inflate, etc...
- make clear your salary expectations and whether that is negotiable
You simply state something along the lines of "My current salary is not relevant to this discussion (and hold firm). I expect compensation commensurate with my experience and expected job responsibilities." If they push, just say since we are sharing personal details ask them what they are currently making, or ask what the budget is for the role (don't actually do this unless they just are not getting it). Watch as they deflect. That should be your clue as to their intention.
The key here is to research what salaries are commensurate for your level of experience and job title. This will give you the confidence to hold firm on your salary expectations and to make sure that your expectation is realistic with market conditions. This is especially true in the case you are underpaid.
Story time: I have been underpaid in the past, and it was uncomfortable holding my ground and refusing to answer the current salary question. Even the job application listed "current salary." I simply put "$0". Naturally, if they wanted to press the issue they could've said I lied on the application, but I made it clear that my current salary was not relevant--so I was not going to answer the question even on the application. Furthermore, HR even made statements "he must be underpaid, that's why he won't reveal his current salary." I simply let these statements roll off my back.
I do not care if they assume I am underpaid, overpaid, or not paid. As I said, holding the mindset that "current compensation is not relevant to this discussion" is critical. Also you have to be comfortable with the fact that you may lose job opportunities because of this. I was comfortable with that fact and things worked out in the end. The way I view it as, why should I be doing HR's job? Their job is to evaluate what compensation is fair for the services I will offer. It's not my job to give them a shortcut so they can shortchange me with the veneer of "well we gave him $x raise over his current salary so we did him a solid!" Yeah, no.
(As an aside, the other trick they will use is "what is your salary range" basically, do you think they will offer you the top of the range or the bottom?)