This came in the form of a stack of Agatha Christie novels lapped up by his mother. The young Miller had never touched them until one night when the 1945 film adaptation of Christie's 1939 novel And Then There Were None was broadcast on television. Christie's pot-boiler drew inspiration from a British nursery rhyme and charted how 10 people are lured to an island by persons unknown, whereupon they are picked off one by one in a manner already set down by the rhyme.
Miller was smitten and, with his mother's approval, turned his attention to the mini Agatha Christie library he already had access to. While this may go some way to explaining some of his directorial choices over the years - from a compendium of true-life Glasgow murder stories, Blood On The Thistle, to a version of 10 Rillington Place, which dissected the crimes of serial killer John Christie, and a production of Dial M For Murder - it has also led to Miller directing a new production of Agatha Christie's own stage adaptation of her novel with Dundee Rep's ensemble company.
"I have wanted to do it for years," Miller says, as he outlines his own motivation for doing a play that continues to captivate audiences despite its seemingly old-fashioned execution. "My mother was obsessed with Agatha Christie. Hers were the only books in the house, and I think she loved the nostalgia and the innocence of them. There is no blood and gore in them, so they were something she could use to get her kids used to reading. I remember sitting there and watching the film for the first time and being really shocked, then thinking afterwards, 'Well, what were the clues?'"
It is a question that readers and audiences have been asking themselves ever since Christie opted to adapt And Then There Were None for the stage in 1943, when the author was advised by producers to graft on a feel-good ending to appease what was perceived to be a sensitive audience.
"It was the first stage adaptation of her own work that Christie had done," Miller says. "There had already been a lot of them done by other people, but Christie was never happy with them. This one is a lot more psychological than the book. The audience have to use their brains to find out who did it. It can be a bit creaky and a bit clunky, and because there is no blood and guts it can look quite sanitised at first, but that also makes it quite creepy, especially the way no-one ever responds to any of the deaths."
With this in mind, and with the permission of the Agatha Christie estate, Miller has reinstated the book's original ending, as well as making a few minor tweaks to the script to make things even more dramatic. "If we are going to do an Agatha Christie, I want to do it as a homage," Miller says, "both to my mother, and to Christie."
And Then There Were None has been played all over the world, with its original literary source remaining one of the best-selling books ever and inspiring an entire industry of murder mystery weekends.
It has not, however, remained immune to parody. The 1976 film Murder By Death is the most notable example of this, with a more recent episode of adult cartoon series Family Guy joining in the fun with an episode titled And Then There Were Fewer. Miller's version, on the other hand, will be playing it straight.
"I have no interest in doing a Carry On version," he says. "I don't see any point in doing that. To me these people in the play are real, and have to be played as such. Some people might think it quite a retro thing to do an Agatha Christie in that way, but I quite like that."
Miller's production of And Then There Were None is an all-too-rare sighting of a stage production of Christie's work that is not a commercial touring venture by the much-loved Agatha Christie Theatre Company, which was set up in 2005 solely to produce the mistress of crime's stage works. Indeed, The Agatha Christie Company itself will be arriving in Edinburgh in a couple of weeks with their production of Christie's Hercule Poirot thriller, Black Coffee, with Robert Powell as the inscrutable detective.
In 2005, a new version of And Then There Were None by Kevin Elyot starred Tara Fitzgerald on the West End and Broadway. Steven Pimlott's production also looked to the story's dark side. "It was fun," says Miller, "but it was very Grand Guignol. Very heightened."
Apart from its style, the technicalities of putting And Then There Were None on stage are enough to try any director's patience.
"Following all these glasses and drinks being passed round is quite a choreographic feat," says Miller, "especially when you have 10 people on the stage, and you are trying to put these very real red herrings in there to throw the audience off the scent. It was the same when I did Dial M For Murder at the Citz. That was a nightmare."
Miller's take on And Then There Were none coincides with last week's announcement of a new deal between the BBC and the Christie estate to present new versions of some of the author's major works on television. This will include a three-part adaptation of And then There Were None by Sarah Phelps.
With Miller just appointed an associate director at Perth Theatre for a year as it becomes a mobile operation during the building's renovation, it is unlikely Christie's dramas will become a regular feature of Miller's work. "The only other one I would want to do is Sparkling Cyanide," he says, "and not for a few years yet."
With Christie's original novel And Then There Were None having shifted more than 100 million copies since it was first published, it is the book's spirit Miller is intent on capturing.
"The biggest thing for the journey the characters go on is revisiting the novel," he says. "It stops things being creaky and elevates it to something a bit more surreal. And that makes far more sense to me."
And Then There Were None is at Dundee Rep, March 5-29