The unsolved brutal murder of 30-year-old dalit law student, which had shocked the conscience of the state, was a "challenge" to the police force, said Behara, who replaced T P Senkumar.
"The case is a challenge to Kerala police," he told reporters soon after taking charge.
First priority is to detect the accused and make a prosecutable case.
"I will put my best foot forward," he said and expressed confidence that within two days, some new facts may come out in the case.
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The DGP said he was confident that his officers, given proper direction and ideas, will bring out good results.
Hinting that he was keen to conduct "CBI model" investigations, Behara said though the state lacked infrastructure, there was no legal bar on using scientific facilities elsewhere which "will do wonders".
"There was need to improve investigation, which has taken a back seat. There were lots of cases lying undetected, including rape cases. There is need to have better infrastructure in police," he said.
Women's security was among his priorities, he said.
In 2009, he joined the National Investigation Agency (NIA) and headed the Terror Financing and Fake Currency specialized cell of the NIA and was also part of the team that travelled to the US to question David Coleman Headley in 2010.
Prior to being appointed as the DGP of Kerala, he served as Director, Kerala Fire & Rescue Services.