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Strong secrecy is a term used in formal proof-based cryptography for making propositions about the security of cryptographic protocols. It is a stronger notion of security than syntactic (or weak) secrecy. Strong secrecy is related with the concept of semantic security or indistinguishability used in the computational proof-based approach. Bruno Blanchet provides the following definition for strong secrecy:
For example, if a process encrypts a message m an attacker can differentiate between different messages, since their ciphertexts will be different. Thus m is not a strong secret. If however, probabilistic encryption were used, m would be a strong secret. The randomness incorporated into the encryption algorithm will yield different ciphertexts for the same value of m.
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