The sexual abuse of children has left "scars" on victims and society, the chair of an inquiry into historical abuse in England and Wales has said.
Justice Lowell Goddard was speaking as she opened the independent inquiry, which she said could last until 2020.
It will examine how public bodies handled their duty of care to protect children from abuse.
Justice Goddard said there were suggestions that one child out of every 20 in the UK had been sexually abused.
She said many who are sexually abused as a child do not tell adults - and that if they do "their reports may go unheeded".
There may also have been systematic under-recording and mis-recording of child sex abuse by the police and other agencies, she added, meaning that "the true picture may be even worse than the current figures indicate".
Speaking about the scale of the problem, she said: "The need for accurate recording is one of the issues that the inquiry will have to confront."
The inquiry was first announced by Home Secretary Theresa May in July 2014.
It followed claims of a high-level cover-up of historical child sex abuse involving public figures, including politicians.
The New Zealand High Court judge, who led an inquiry into police handling of child abuse cases in her own country, was the third person named to chair the inquiry - her two predecessors resigned over concerns about their links with the establishment.
In her opening remarks, she said the task ahead was daunting, but that it could expose past failures of institutions to defend children.
Justice Goddard said the sexual abuse of children "has left permanent scars not only on successive generations, has left permanent scars not only on victims themselves, but on society as a whole".
But she added: "This inquiry provides a unique opportunity to expose past failures of institutions to protect children, to confront those responsible, to uncover systemic failures... and to make recommendations that will help prevent the sexual abuse and exploitation of children in the future."
Justice Goddard also said it was important to emphasise that this was the largest and most ambitious public inquiry ever established in England and Wales.
Despite the size of the investigation, she was "determined to ensure that it does not become bogged down in the delays that have bedevilled some other public inquiries in this jurisdiction".
What are the allegations?
In July last year, Labour MP Simon Danczuk called on Leon Brittan to say what he knew about paedophile allegations passed to him when he was home secretary in the 1980s.
The files were given to Lord Brittan, who died in January, by the late Conservative MP Geoffrey Dickens, a long-standing campaigner against child abuse.
Mr Dickens's son has said the files - now missing - contained "explosive" paedophile allegations about powerful and famous figures, including politicians.
Since Mr Danczuk's comments brought the so-called "Dickens dossier" to the fore, the focus has moved to the wider issue of how historical child sex abuse allegations were dealt with by public bodies and other institutions across the country.
Previously there had been calls for an overarching investigation into historical abuse claims in the wake of revelations that TV entertainer Jimmy Savile abused hundreds of victims at hospitals, children's homes and schools.
The inquiry, which was given statutory powers and a new panel in February, will investigate whether "public bodies and other non-state institutions have taken seriously their duty of care to protect children from sexual abuse in England and Wales".
Justice Goddard has decided abuse victims will not sit on her advisory panel, but there will be a separate Victims and Survivors Consultative Panel.
The advisory panel comprises Prof Alexis Jay of Strathclyde University, Drusilla Sharpling of the police inspectorate, Prof Malcolm Evans of Bristol University, and child protection barrister Ivor Frank.
Justice Goddard said she was determined to put as much information into the public domain as she could, as soon as possible. She also referred to annual reports being published, the first of which would be next year.
As she was giving her statement, the office of Attorney General Jeremy Wright QC confirmed that immunity from prosecution under the Official Secrets Act will be offered to current or former public servants prepared to testify about allegations of child sex abuse.
It will not protect anyone who admits taking part in child sexual abuse.
Justice Goddard ended her statement by issuing a call for anyone with information about sexual abuse cases to come forward.
And she urged institutions responsible for caring for children, which may come under scrutiny, to take a "proactive stance towards the inquiry".
The NSPCC said a team of trained counsellors would operate a free dedicated helpline to offer support on its behalf.
Peter Wanless, the charity's chief executive, said many victims had "harrowing stories to tell", adding that the charity wanted to make "what could be a tortuous journey as easy as possible".
The chairman of the Commons home affairs committee, Keith Vaz, said the inquiry, which he described as a "once in a lifetime opportunity", could last a decade.
"And of course we wish [Justice Goddard] luck in the very difficult job that she's got, which could take up to ten years. I mean, this is going to be a very long inquiry."
In February, it was announced Justice Goddard had been chosen to lead the inquiry because she was "as removed as possible from the organisations and institutions that might become the focus of the inquiry", Mrs May said.
Baroness Butler-Sloss, the first inquiry chairwoman, resigned a week after it was set up.
This followed calls for her to quit because her late brother, Sir Michael Havers, had been attorney general in the 1980s.
Her replacement, the then Lord Mayor of London Fiona Woolf, stood down on 31 October amid concerns over her links to former Home Secretary Lord Brittan.