The BGPsec protocol, which is an extension of the border gateway protocol (BGP) for Internet routing known as BGPsec, uses digital signatures to guarantee the validity of routing information. However, the use of digital signatures in routing information on BGPsec causes a lack of memory in BGP routers, creating a gaping security hole in today's Internet. This problem hinders the practical realization and implementation of BGPsec. In this paper, we present APVAS (AS path validation based on aggregate signatures), a new protocol that reduces the memory consumption of routers running BGPsec when validating paths in routing information. APVAS relies on a novel aggregate signature scheme that compresses individually generated signatures into a single signature. Furthermore, we implement a prototype of APVAS on BIRD Internet Routing Daemon and demonstrate its efficiency on actual BGP connections. Our results show that the routing tables of the routers running BGPsec with APVAS have 20% lower memory consumption than those running the conventional BGPsec. We also confirm the effectiveness of APVAS in the real world by using 800,000 routes, which are equivalent to the full route information on a global scale.