Chidamabaram said the "government is completely deaf" to any reasoning against linking Aadhaar to everything under the sun speaking at IIT-Bombay's annual Mood Indigo festival.
However Mr Murthy argued that "Like any other modern country, there is a need to establish individual identities in the form of a driving licence, at the same time ensuring that there is no violation of privacy with such an identification."
The matter of linking Aadhaar number to bank accounts, mobile SIMs, and other government-backed services is currently being considered by a 5-member Constitution bench in the Supreme Court which is hearing the bunch of petitions protesting the mandatory linking over privacy concerns.
Chidambaram argued that using Aadhaar for every transaction has "serious consequences" that will turn the country into an "Orwellian state", compromising the ideals of a liberal democracy and an open society.
"If a young man and a young woman want to have a private holiday, they may not be married, what's wrong with that? If a young man wants to buy condoms, why should he disclose his Aadhaar or identity?" the former finance minister quipped.
"Why should the state, that is the government, know what medicines I buy, what cinemas I visit, what hotels I stay in, who are my friends?" he asked further.
"If I am in the government, I should resist the temptation to know about all these activities which individual citizens do," he said.
He further said right now, all the Aadhaar linking is being done not voluntarily by the people but as a tool to "conform" because of the barrage of SMSes and mails. "The question is: there are many agencies which say, 'give me your Aadhaar. And even crematorium is asking for Aadhaar today!," Chidambaram said, clarifying that he doesn't oppose Aadhaar as a means to establish identities and help extend government subsidies.
When pointed out about the potential misuse of the individual data while availing of services by the chair of the panel, Murthy said we should not "trash" Aadhaar and took jibes at Parliamentarians for not coming out with a privacy law that can help protect an individual's data.
In the wake of criticism of hiding wrongful transactions against those opposing Aadhaar, Chidambaram made it clear that there is nothing to hide and any investigative agencies can access details if needed.
"...that record should not be accessed by a hacker or a big brother in the government using my Aadhaar. That's my objection," he said.
The former two-time finance minister in the Manmohan Singh government that brought in the Aadhaar pointed out that the original idea of Aadhaar was to help transfer government benefits and subsidies and plug the leaks.
"Where there are no government subsidies or benefit being transferred, there is absolutely no reason to link to Aadhaar. There are serious consequences of doing that. But this government seems to be completely deaf to any reasoning against linking Aadhaar to everything under the sun." Picking up quickly on it, Murthy shot back saying "that responsibility is of Parliament...to ensure that the executive does not do it. You have all the powers."