She wrote in her blog that the administration is taking action following a rise in the doxxing of judges, legislators and lawyers last year after police officers had first been targeted.
A temporary injunction is already in place to ban people from doxxing judges and judicial officers, she noted, and anyone who breaches it risks imprisonment.
Doxxing activities violate Hongkongers' privacy rights and must be stopped, Cheng said.
"It falls upon each of us to join hands and condemn these actions so that the law and order that has been restored after the passing of the national security law is maintained so that people are free to exercise their rights while respecting those of others," Cheng added.
"All of us should jointly bear the responsibility to respect, promote and further the rule of law as a fundamental basis of our society."
Cheng said police officers and their families had been targeted and seen their personal information leaked since the second half of 2019 along with legislators, judges and lawyers.
Many people online have "weaponized" personal data against those who have opposite political views, she declared.
"The [high court] expressed [that] the persons who commit such crimes are simply and properly described as 'criminals.' Criminal activity does not cease to be criminal activity simply because the actor believes himself or herself to be acting for a particular, perhaps higher, cause."
Although the court has issued injunctions to prevent doxxing activities, Cheng said some people still "blatantly violated these orders.
"As a result, the Department of Justice has lodged committal applications for contempt of court. Contemnors, who admitted liability for contempt of court, were sentenced, with some receiving immediate imprisonment.
Contempt of court is a serious matter and fundamental to the rule of law that court orders are made to be obeyed, she added.
"Thus, the starting penalty for both civil and criminal contempt of court in breaching an injunction order is imprisonment," she said, adding the sentence should be a deterrent to the public.
Cheng warned too that rights and freedoms "do not exist in a vacuum" and come with responsibilities.
"Any person exercising their own rights and freedom must simultaneously have respect for the rights and freedom of others. Freedom of speech certainly does not embrace any right to harass or intimidate, threaten or menace."
And proper channels exist to express "one's views legitimately and properly irrespective of a person's political stance."
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