A small aircraft instructor pilot with a student reported they taxied through a Security Identification Display Area at OGD due to insufficient ramp and taxiway markings and a confusing depiction of the area on the airport diagram.

Narrative

My student and I were on the ground; leaving the ramp in Ogden; Utah. We were cleared via Ogden ground to taxi to runway 35 via A; B. From the ramp to A; there are numerous options. As we were making our way to A; it wasn't clear that we were approaching a SIDA (Security Identification Display Area) area. I noticed the area boundaries and had us turn just as two ramp agents motioned for us to turn away. We continued via taxiway A; then B. Before our planned departure; Ground Control gave me a number to report to however; I opted to taxi back and resolve the situation in person. They approved and I spoke to the personnel instead of talking to ground once I shut down. The personnel were concerned about our intentions. I assured them that confusion arose from position of the SIDA. We are not locals and weren't sure which path to take to get to taxiway A at the time. At the time we saw the SIDA boundary; we turned as they started to motion us to turn away. After shutting down; the personnel wanted photos of us; photos of our driver's licenses; and a photo of my pilot certificate. I allowed them to take photos. They told me they were going to report it to the airport manager. While we did not see the red SIDA boundary; there are some considerations to discuss from the vantage point of a pilot who is not local here. The SIDA markings weren't obvious until we were near them. Possible recommendation of repainting them. There are three routes from where I could get to taxiway A while parked. This is not clearly labeled on the airport diagram. My student and I took the one in front of us but it was expected for us to make an immediate left turn to intercept A. Again; per the airport diagram; this is not obvious; especially for transient pilots. There were no other aircraft taxiing nearby at the time of this occurrence. It was just me and my student at the time.