I Can E(M,K) = C Replace Ek(M) = C in Cryptography Notation?

AI Thread Summary
The discussion centers on the notation used in cryptography, specifically whether E(M,K) = C can replace Ek(M) = C, given that E depends on K. Participants agree that the choice of notation is largely a matter of style rather than a strict rule. The original poster seeks clarification on this notation and its implications. The conversation highlights the flexibility in representing encryption functions while maintaining clarity. Ultimately, the consensus is that both notations can be valid depending on context and preference.
Teachme
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I was just reading a cryptography book and have a question about something the author states I highlighed the statement in yellow and included a pictures.
So I was wondering if the function could be written as E(M,K) = C instead of Ek(M)=C since the fact that E is dependent on K. If not why couldn't you write it as this?

Thanks
 

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Sorry thanks,
here is fixed pic
 

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It is more a matter of style than anything else.
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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