A court in Milan is considering charges of corruption against Eni and Shell in a controversial oil deal that led to Nigeria losing an estimated $6bn.
The campaign group Global Witness has calculated the OPL 245 deal in 2011 deprived Nigeria of double its annual education and healthcare budget.
Eni and Shell are accused of knowing the money they paid to Nigeria would be used for bribes.
The Italian and Anglo-Dutch energy giants deny any wrongdoing.
This unfolding scandal, which is being played out in an Italian court, has involved former MI6 officers, the FBI, a former President of Nigeria, as well as current and former senior executives at the two oil companies.
The former Nigerian oil minister, Dan Etete, was found guilty by a court in France of money laundering and it emerged he used illicit funds to buy a speed boat and a chateau. It is also claimed he had so much cash in $100 bills that it weighed five tonnes.
Global Witness has spent years investigating the deal which gave Shell and Eni the rights to explore OPL 245, an offshore oil field in the Niger Delta.
It has commissioned new analysis of the way the contract was altered in favour of the energy companies and concluded Nigeria's losses over the lifetime of the project would amount to $5.86bn, compared to terms in place before 2011.
The analysis was carried out by Resources for Development Consulting on behalf of Global Witness, as well as the NGOs HEDA, RE:Common and The Corner. The estimated losses were calculated using an oil price of $70 a barrel as a basis.
Eni has criticised the way it was calculated because it ignores the possibility that Nigeria had the right to revise the deal to claim a 50% share of the production revenues.
Deal or no deal
Campaigners say the deal should be cancelled.
"We discovered that Shell had constructed a deal that cut Nigeria out of their share of profit oil from the block," Ava Lee, a campaigner at Global Witness told the BBC's World Business Report.
"This amount of money would be enough to educate six million teachers in Nigeria. It really can't be underestimated just how big a deal this could be for a country that right now has the highest rates of extreme poverty in the world."
Nigeria is the richest economy in Africa, but despite having large resources of oil and gas millions of people are poor.
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