Section 34A. Whoever knowingly and willfully furnishes a false name, Social Security number, date of birth, home address, mailing address or phone number, or other information as may be requested for the purposes of establishing the person's identity, to a law enforcement officer or law enforcement official following an arrest shall be punished by a fine of not more than $1,000 or by imprisonment in a house of correction for not more than 1 year or by both such fine and imprisonment. Such sentence shall run from and after any sentence imposed as a result of the underlying offense. The court may order that restitution be paid to persons whose identity has been assumed and who have suffered monetary losses as a result of a violation of this section.