If you are carrying tomato paste in your carry-on bag, it is subject to the 3-1-1 liquids rule. Even though it is thick, the TSA classifies pastes, gels, and creams as "liquids." This means your tomato paste must be in a container of 3.4 ounces (100ml) or less, and it must fit inside your single quart-sized clear plastic bag. Most standard cans or tubes of tomato paste found in grocery stores are 6 ounces or larger, which means they will be confiscated at the security checkpoint if they are in your carry-on. However, there are no such restrictions for checked luggage. You can pack as much tomato paste as you want in your checked bags, provided you pack it securely to prevent it from bursting due to pressure changes. If you are traveling internationally, you should also check the customs regulations of your destination country; while processed, shelf-stable items like canned tomato paste are usually allowed, some countries have strict "bio-security" laws against bringing in any vegetable-based products. To be safe, if the tube is larger than a travel-sized toothpaste, just put it in your suitcase that goes under the plane.