Student Security Act of 2017 This bill amends the Higher Education Act of 1965 to require the Department of Education and the Social Security Administration to jointly carry out a student loan forgiveness program that will forgive Federal Direct loans in exchange for delayed eligibility for old-age insurance benefits under the Social Security Act. In addition, the bill authorizes the transfer of amounts from the Federal Old-Age and Survivors Insurance Trust Fund into the Federal Disability Insurance Trust Fund if borrowing is necessary to pay full benefit payments from the Federal Disability Insurance Trust Fund. The bill amends the Internal Revenue Code to expand the exclusion from gross income of income attributable to the discharge of student loan indebtedness to include indebtedness discharged under the program.