Logical Analysis and Verification of Cryptographic Protocols - Loria
Logical Analysis and Verification of Cryptographic Protocols - Loria
Logical Analysis and Verification of Cryptographic Protocols - Loria
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
6 CHAPTER 1. INTRODUCTION<br />
“G”. The key generation algorithm takes as input an agent name A <strong>and</strong> a r<strong>and</strong>om<br />
generated number <strong>and</strong> returns a pair <strong>of</strong> public <strong>and</strong> secret keys, respectively<br />
denoted by P k(A) <strong>and</strong> Sk(A), corresponding to that agent. This r<strong>and</strong>om<br />
number allows any agent to have a different pair <strong>of</strong> keys for each session while<br />
using the same key generation algorithm. The encryption algorithm takes as input<br />
a clear message, called plaintext, <strong>and</strong> an agent’s public key, <strong>and</strong> outputs the<br />
encryption <strong>of</strong> that plaintext, called ciphertext, with respect to the given public<br />
key. The decryption algorithm takes an input a ciphertext <strong>and</strong> an agent’s private<br />
key, <strong>and</strong> outputs the decryption <strong>of</strong> that ciphertext with respect to the given<br />
private key provided that the ciphertext has been obtained using the public key<br />
correspondant to the given private key.<br />
Example 3 One <strong>of</strong> the most common public encryption schemes is the encryption<br />
scheme due to R. Rivest, A. Shamir <strong>and</strong> L. Adleman [174] <strong>and</strong> denoted by “RSA public<br />
encryption scheme”.<br />
A perfect public encryption scheme is represented by the following equation:<br />
Symmetric encryption schemes<br />
dec p (enc p (x, P k(y)), Sk(y)) = x<br />
A symmetric encryption scheme is similar to the asymmetric encryption scheme with<br />
the condition that the same key is used to encrypt <strong>and</strong> decrypt messages. This<br />
means that in these schemes, the key generation algorithm outputs one key instead<br />
<strong>of</strong> a pair <strong>of</strong> keys. Furthermore, in these schemes, the encryption algorithm<br />
is denoted by enc s , <strong>and</strong> the decryption algorithm by dec s .<br />
A perfect symmetric encryption scheme is represented by the following equation:<br />
dec s (enc s (x, y), y) = x<br />
Algebraic properties<br />
An (asymmetric or symmetric) encryption scheme may use some operators<br />
such as the concatenation “·”, or XOR “⊕”, or multiplication “∗”, or pairing<br />
“〈−, −〉”. Such schemes may have some <strong>of</strong> the following algebraic properties:<br />
Commuting. The commuting property is represented by the following equation<br />
enc(enc(x, y), z) = enc(enc(x, z), y). One <strong>of</strong> the most important commuting<br />
encryption schemes is RSA public encryption scheme with common modulus<br />
[69].<br />
Homomorphism. The homomorphism property is represented by the following<br />
equation enc(x, y) ∗ enc(z, y) = enc(x ∗ z, y), <strong>and</strong> it means that one can get