I read a book once about radio contact with an alien civilization. They sent a questionnaire to be filled by all humans. Based on the answers, they chose a person to raise an alien kid on Earth, created from DNA information they sent. What was its title and author?
This is Rollback by Robert Sawyer. The story is set in 2048; Don and Sarah Halifax are celebrating their sixtieth anniversary when a reply arrives from Sigma Draconis.
As Don stood, looking at Sarah, the moment came back to him, and he shook his head in amazement. It had been front-page news, back when there were front pages, all over the world. On March first, 2009, a radio message had been received from a planet orbiting the star Sigma Draconis.
The world had puzzled over the message for months, trying to make sense of what the aliens had said. And then, finally, Sarah Halifax herself had figured out what they were getting at, and it was she who had led the team composing the official reply that had been sent on the one-year anniversary of the receipt of the original signal.
The public had initially been hungry for more news, but Sigma Draconis was 18.8 light-years from Earth, meaning the reply wouldn’t reach there until 2028, and any response the Dracons might make couldn’t have gotten here until October 2047 at the earliest.
The reply starts arriving that day, but it's encrypted. The Dracons send the algorithm, but not the key.
This second message from the aliens also had two parts. But in this case, the beginning was the explanation of how to decrypt the rest, assuming the right decryption key could be provided, and the rest, well, that was anybody’s guess.
Because it was encrypted, not even a single symbol that had been established in the original message was visible in the second part of this one.
It's Sarah that figures out the key is the answers that were sent in response to the questionnaire in the previous message, but just one specific set of answers; hers. And the reason that nobody else has been able to crack it, even having tried all the answers, is that she changed one of her answers between the time that the message was saved for posterity and the time it was sent. So the message is encoded just to her.
"The decryption key was my set of answers," she said.
"But I thought you’d tried that."
She told him about the last-minute change she'd made in Arecibo. While she did so, Gunter knelt next to her, and began scrolling rapidly through pages on the screen.
"Ah," Don said. "But wait — wait! If it's your answers that unlocked it, that means the message is for you personally."
A SETI-supporting billionaire, Cody McGavin, sponsors the "rollback" (rejuvenation) process for her and Don so that she can send a reply and be alive for the next response from the Dracons.
"Rejuvenation; a rollback. We'll make you young again. Surely you've heard about the process."
Unfortunately the rollback only works on Don, so before she dies she gives Don the same questionnaire and when his answers are close enough to hers, she gives him the key and the authority over the project.
(Don having rolled back successfully causes problems between them, and Don ends up having an affair with Lenore, a grad student in the Astronomy department. Don only ends it when he realizes how much pain he's causing Sarah.)
The message decodes to the description for a complete set of alien DNA an a mechanism to create an embryo and bear it, as well as a set of differences to create a second embryo.
"Actually, Sarah," said Gunter, standing back up now, "I've been reading further into the document. It's true that they only sent one master genome, but they've appended a tiny subset of modifications that can be substituted into the master sequence to make a second individual.
After Sarah dies, Don negotiates with Cody to continue the project, and after a standard mourning period travels to New Zealand to ask Lenore to marry him.
Two aliens are born and are raised by Don and Lenore along with their children.