The John Gosden-trained Cracksman got the better of Permian by a short head in Epsom's Derby Trial last month, but has not been seen in competitive action since.
Permian, meanwhile, has raised his game to win a Listed prize at Newmarket and the Dante Stakes at York and Johnston is quietly confident his charge can turn the tables on Cracksman in the world's most famous Flat race.
"Cracksman is our best guide. Obviously and quite understandably his connections are going to expect him to come on from that Epsom race," said the Middleham-based trainer.
"We pulled a bit of a fast one on him there. He was on the inside and Permian held him in for a few strides and got first run on him. Cracksman managed to get out, came after us and caught us by a nose.
"There's nothing in it. They would have expected Cracksman to improve on that and beat us further, but this is the same track and a different distance and I think we're the more assured of the pair to benefit from the step up in trip.
"I don't think there's any doubt in anybody's mind that Permian has come on considerably since that Epsom encounter and Cracksman is going to have to improve significantly to beat him this time."
Johnston is pleased with how Permian has bounced back from his Dante triumph less than a fortnight ago and is encouraged that jockey William Buick has chosen to ride him.
He told At The Races: "Everything is looking good. We've had a couple of days of quite heavy rain, we desperately needed that, and hopefully it's going to brighten up now and we'll have a good preparation for the last few days.
"He's owned by Sheikh Hamdan bin Mohammed, Sheikh Mohammed's son. We consider Sheikh Hamdan's horses to be subsidiary of the Godolphin team and William Buick is the retained jockey.
"In some ways, with them having four horses in the race, it's quite flattering that Permian is the choice of William Buick. To my mind, that makes him the number one.
"Franny (Norton) won the Dante on him, but William has won on the horse before and he has had a number of different jockeys."
Cracksman is one of five possible runners for Gosden, while Aidan O'Brien has seven contenders as he bids to win the premier Classic for a sixth time.
Johnston expects the versatile Permian to be unaffected by a potentially tactical affair.
"I can't question Aidan O'Brien's record in the Derby, it's absolutely fantastic," he said.
"He's dominated the race for years now and he has more runners this year than I've had in my career, so who am I to comment on how they've won the Derby?
"When they have these big teams, there tends to be a lot of talk about tactics. They've got horses that can go from anywhere in the field.
"But the important thing for us is we're going to go out there and do our own thing. We've got a very experienced horse and a very versatile horse.
"I would like to think William is not going to be influenced by what anyone else is doing."
