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I'm new to the topic guys, but as there are literally too many encryption methods out there, too that I could even come up with many ideas of them, how to we actually test/calculate "how secure" an encryption algorithm is?

Do we a standard or a formula that we can use to test security level of encryption algorithm?

And how strong would a monoalphabetic cipher would be?

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    $\begingroup$ Hello and welcome. You're new to cryptography, so you're lucky to be up for a nice ride! I would recommend reading introductory books on the subject. Do start there and don't give up; if you have more precise questions come back here. As for your question, no, we don't have "a formula". What we do is try to provide a mathematical proof that goes as follows: if you break my cryptosystem, then you are capable of solving a super-hard (public) problem that nobody (publicly) knows the solution for. Or, if you break my cryptosystem, then you also know how to break that other cryptosystem as well. $\endgroup$
    – zugzwang
    Oct 24 at 11:38

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There's no single formula to quantify the security of an encryption algorithm. However, we do estimate a measure, the "security level", for various cryptographic functions. Security level is measured in "bits", where $n$-bit security means that an attacker would have to perform $2^n$ operations to break the system in question. Sometimes we'll further quantify different sorts of operations, or how much memory is needed. At least about $2^{112}$ bits of security is commonly considered the minimum for any system to be "secure" against practical attackers.

"Security" is a rather broad concept. There are several different notions of security. For encryption, we use the IND- definitions, which define what capabilities an attacker has. We usually require the strongest of those definitions, IND-CCA3 (AKA AE-security) to be met for a system to be considered secure, though individual components of that system may only meet lesser security definitions.

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