Logical Analysis and Verification of Cryptographic Protocols - Loria

2.1. PRELIMINARIES 39
form. If there is no ambiguity on the intruder deduction system I we write Ē
instead of ĒI .
Example 7 (The Dolev-Yao deduction system with implicit destructors) We present
here the Dolev-Yao deduction system with implicit destructors.
Let < −, − > (concatenation), enc s (symmetric encryption), enc p (public encryption)
and −1 (the inverse key) be the cryptographic primitives. The rules L are
defined as follows:
The rules Lencs are defined as follows:
The rules Lencp are defined as follows:
x, y →< x, y > (2.1)
< x, y >→ x (2.2)
< x, y >→ y (2.3)
x, y → enc s (x, y) (2.4)
enc s (x, y), y → x (2.5)
x, y → enc p (x, y) (2.6)
enc p (x, y), y −1 → x (2.7)
enc p (x, y −1 ), y → x (2.8)
The Dolev-Yao deduction system with implicit destructors is given by
where
• FDY = {< −, − >, enc s , enc p , −1 },
• LDY = L ∪ Lencs ∪ Lencp. I i DY = 〈FDY , LDY , ∅〉
Example 8 (The Dolev-Yao deduction system with explicit destructors) We present
here the Dolev-Yao deduction system with explicit destructors.
Let < −, − > (concatenation), enc s (symmetric encryption), dec s (symmetric decryption),
enc p (public encryption), dec p (public decryption), and −1 (the inverse key)
be cryptographic primitives. The rules L are defined as follows:
x, y →< x, y > (2.9)
x → π1(x) (2.10)
x → π2(x) (2.11)