Prepare an ice-water bath. In a medium saucepan, blanch mint leaves in boiling water for 30 seconds, then place immediately in an ice-water bath. Squeeze out all excess liquid from mint, and set aside. Bring sugar and 1 cup water to a boil in a medium saucepan and cook until sugar is completely dissolved, about 1 minute. Remove from heat, stir in lime zest and mint, and let sit at room temperature for 30 minutes to infuse the syrup. Puree in a blender until fine bits remain. Strain to remove the mint and zest, then stir in lime juice and white rum. Refrigerate syrup, covered, until cold. For each mojito, pour 2 tablespoons syrup over 1/2 cup crushed ice.