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Kent and R. Atkinson, “Security Architecture for the Internet Protocol,” RFC 2401, Nov. 1998. [2] D. Harkins and D. Carrel, “The Internet Key Exchange (IKE),” RFC 2409, Nov 1998. [3] C. Xenakis, E. Gazis and L. Merakos, “Secure VPN Deployment in GPRS Mobile Networks”, 2002. [4] C. Perkins, “IP Encapsulation within IP” RFC 2003, Mayo 1996 [5] Phifer, L., "IP Security and NAT: Oil and Water?" ISP-Planet, Junio 15, 2000 Disponible desde http://www.isp-planet.com/technology/nat_ipsec.html [6] Bernard Adoba, “IPSec-NAT, Compatibility Requirements” Internet Draft (work in progress) draft-ietf-ipsec-nat-reqts-00.txt, Junio 2001. [7] Nicolas Gabriel, “VPN and Firewall Traversal”, Nov. 2000. [8] Phifer, L., "Realm-Specific IP for VPNs and Beyond" ISP-Planet, June 23, 2000 available from http://www.isp-planet.com/technology/rsip.html [9] Borella M., Grabelsky D., Lo J., Taniguchi K., Realm-Specific IP:Protocol Specification“ Internet Draft (work in progress) draft-ietf-nat-rsipprotocol-07.txt, Julio 2000. [10] GSM 03.60, GPRS, Service Description, 1998. [11] L. Phifer, “The Trouble with NAT”, Cisco publications, The Internet Protocol Journal, Vol. 4, Dec. 2000. '( )* + , ' B9 [12] C. Xenakis and L. Merakos, “DYNAMIC NETWORK-BASED SECURE VPN DEPLOYMENT IN GPRS”, 2002. [13] R. Kopeikin and S. Sommars,” Wireless GPRS Access to Virtual Private Networks For Carriers and ESPs”, 2000 [14] S. Aust, D. Proetel, A. Könsgen, C. Pampu and C. Görg, “Design Issues of Mobile IP Handoffs between General Packet Radio Service (GPRS) Networks and Wireless LAN (WLAN) Systems” , 2002. [15] Dung Chang, “Security Along the Path Through GPRS Towards 3G Mobile Telephone Network Data Services”, Enero 2002. [16] Georgios Karagiannis, “QoS in GPRS”, Diciembre 2000. [17] NetScreen Technologies Inc, “GPRS Security Threats and Solutions”, Marzo 2002. [18] C. Bettstetter, H. Vögel, and J. Eberspächer, Technische Universität München. GSM Phase 2+ General Packet Radio Service GPRS: Architecture, Protocols, and Air Interface. 1999 [19] Peter Schefczik. Performance Simulation for the General Packet Radio Service, GPRS. Lucent Technologies/Global Wireless Systems Research. Germany [20] Iñigo Sedano . Tutorial de GPRS. Junio 203 [21] John Scourias. University of Waterloo. Overview of GSM: the Global System for Mobile Communications. Marzo 1996 [22] N. Ferguson and B. Schneier. A cryptographic evaluation of IPsec. Enero 2000. Disponible en: http://www.counterpane.com/ipsec.html BA '( )* + , '