In seven prior attempts across 66 years, no New Zealander has scored a test century at the ground. Stephen Fleming came closest in 2004 with 97 and Brun Smith made 96 in 1949.
The Yorkshire venue was the site of the country's first away test win against England in 1983. John Wright anchored the first innings with 93, but New Zealand have regularly struggled there with the bat.
A century would build a platform towards helping the team achieve one of their tour goals - play with enough credibility to boost the chances of returning to three-test series.
"We've got to earn the right to that," captain Brendon McCullum said. "For so long we've sat in the doldrums and our performances didn't warrant teams playing us in three-test series. We need to get back to a level of respect where teams want to do that. The first test at Lord's was a full house every day, hopefully we keep doing that."
A New Zealand victory in the second test against England, which starts tonight, would also add to a reign of six undefeated test series.
McCullum said they would not relinquish their intention to attack.
"Playing this style gives us our greatest opportunity to win the test and the series. We went down [at Lord's] but played some pretty good cricket throughout. It was a credit to England being good enough to run us down. The more we do that, the more we become comfortable with that, although at times we will be beaten.
"When you lose a test, people's thoughts head in a different direction. The first thing they attack is the way we played our cricket, but I make no apologies."
During the 2013 tour, Kane Williamson said the swinging Duke ball compounded the difficulty of scoring at the ground.
"If you have limited experience with it, it's concerning how late it moves. [Because of that] the decisions you make need to be later. If you play the first line [out of the hand] you start nicking half volleys, whereas at home you'd smash those straight or through the covers. You eventually adjust but it takes some working out."
Williamson's experience in English conditions could come to the fore, as they did at Lord's when he reached the honours board with 132, his 10th test century.
He has featured in four English first-class seasons -- two each with Gloucestershire and Yorkshire. He's signed for a fifth, again with Yorkshire, who he helped to last year's county championship.
Headingley has become his home away from home. During 2013 and 2014, he made 1032 runs at 54.32.
- By Andrew Alderson of the Herald on Sunday at Headingley
