Strengthening Children's Safety Act of 2017 (Sec. 2) This bill amends the federal criminal code to add violent state crimes to the list of violent offenses that trigger an additional five-year consecutive mandatory minimum prison term for a defendant who fails to comply with sex offender registration requirements and commits such offense. (Sec. 3) Additionally, it expands the prior military sex offense convictions that trigger an enhanced mandatory minimum prison term for a defendant who subsequently commits aggravated child sex abuse or certain child pornography offenses.