Logical Analysis and Verification of Cryptographic Protocols - Loria

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6 CHAPTER 1. INTRODUCTION “G”. The key generation algorithm takes as input an agent name A and a random generated number and returns a pair of public and secret keys, respectively denoted by P k(A) and Sk(A), corresponding to that agent. This random number allows any agent to have a different pair of keys for each session while using the same key generation algorithm. The encryption algorithm takes as input a clear message, called plaintext, and an agent’s public key, and outputs the encryption of that plaintext, called ciphertext, with respect to the given public key. The decryption algorithm takes an input a ciphertext and an agent’s private key, and outputs the decryption of that ciphertext with respect to the given private key provided that the ciphertext has been obtained using the public key correspondant to the given private key. Example 3 One of the most common public encryption schemes is the encryption scheme due to R. Rivest, A. Shamir and L. Adleman [174] and denoted by “RSA public encryption scheme”. A perfect public encryption scheme is represented by the following equation: Symmetric encryption schemes dec p (enc p (x, P k(y)), Sk(y)) = x A symmetric encryption scheme is similar to the asymmetric encryption scheme with the condition that the same key is used to encrypt and decrypt messages. This means that in these schemes, the key generation algorithm outputs one key instead of a pair of keys. Furthermore, in these schemes, the encryption algorithm is denoted by enc s , and the decryption algorithm by dec s . A perfect symmetric encryption scheme is represented by the following equation: dec s (enc s (x, y), y) = x Algebraic properties An (asymmetric or symmetric) encryption scheme may use some operators such as the concatenation “·”, or XOR “⊕”, or multiplication “∗”, or pairing “〈−, −〉”. Such schemes may have some of the following algebraic properties: Commuting. The commuting property is represented by the following equation enc(enc(x, y), z) = enc(enc(x, z), y). One of the most important commuting encryption schemes is RSA public encryption scheme with common modulus [69]. Homomorphism. The homomorphism property is represented by the following equation enc(x, y) ∗ enc(z, y) = enc(x ∗ z, y), and it means that one can get
1.2. CRYPTOGRAPHIC PRIMITIVES 7 from the encryption of the messages m1 and m2 the encryption of the new message m1 ∗ m2 without knowing the encryption key. The RSA public encryption scheme possesses this property [112]. Prefix property. The prefix property means that one can get from an encrypted message the encryption of any of its prefixes, and it is formally represented as follows: from a message enc(< x, y >, z) one can get the message enc(x, z). 1.2.5 Signature Digital signature schemes first appeared in W. Diffie and M.E. Hellman’s seminal paper [101]. Their most important goal is to demonstrate the authenticity of a digital message or document: a valid digital signature gives a recipient reason to believe that the message was created by a known sender, and that it was not altered in transit. Such schemes are described by three algorithms: the signature generation “sig”, the verification “ver”, and the key generation “G” algorithms. The key generation algorithm takes as input an agent name A and a random generated number and returns a pair of public and secret keys, respectively denoted by P k(A) and Sk(A), corresponding to that agent. This random number allows any agent to have a different pair of keys for each session, and that using the same key generation functions. The signature generation algorithm inputs a message and an agent’s private key, and outputs the signature of the given agent for the given message. There are two types of verification algorithms: • The verification algorithm of the first type takes as input a message, a signature, and an agent public key, and outputs “succeeds” if the given signature corresponds to the signature done by the given agent for the given message. • A verification algorithm of the second type takes as input a signature and an agent’s public key, recovers the message that has been signed from the signature and returns it provided that the given signature is done by the given agent. When the verification algorithm is of the first type, we call the signature scheme “a signature scheme with appendix” and when the verification algorithm is of the second type, we call the signature scheme “a signature scheme with message recovery”. A perfect signature scheme with appendix is represented by the following equation ver(x, sig(x, Sk(y)), P k(y)) = 1
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112 CHAPTER 5. SATURATED DEDUCTION
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178 CHAPTER 7. VOTER VERIFIABILITY
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202 BIBLIOGRAPHY [12] M. Abadi and
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204 BIBLIOGRAPHY [36] M. Bellare, A
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206 BIBLIOGRAPHY [60] U. Hustadt Ch
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208 BIBLIOGRAPHY [83] H. Comon-Lund
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210 BIBLIOGRAPHY [108] B. Donovan,
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212 BIBLIOGRAPHY [132] T. Kohno, A.
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214 BIBLIOGRAPHY [160] J. C. Mitche
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216 BIBLIOGRAPHY [187] H. Seidl and
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Logical Analysis and Verification of Cryptographic Protocols - Loria

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