THE NEW FORMAL METHOD CALCULUS FOR CRYPTOGRAPHIC PROTOCOLS Hasan M. Al-Refai halrefai@philadelphia.edu.jo Hasan_alrefai@yahoo.com Mobile Phone #: 00962-777357755 Abstract The history of the application of formal methods to cryptographic protocols analysis spans over twenty years. Recently has been showing signs of new maturity and consolidation. This paper will introduce a new variant of the spi-calculus which introduced by M.Abadi and A.Gordan. By using this revised spi-calculus, which called spi-H-calculus, we will illustrate and prove that our calculi is decidable for main security properties: Authenticity and Secrecy than M.Abadi and A.Gordan . Keywords: Cryptographic protocols, testing equivalence, Bisimulation , authenticity and secrecy