add some cryptography stuff

computational-diffie-hellman.md

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+# Computational Diffie–Hellman
+
+- computational version of [[decisional-diffie-hellman|Decisional Diffie–Hellman]]
+- given a generator $`g`$ and uniformly selected $`\left(g^a, g^b\right)`$, compute $`g^{ab}`$

decisional-diffie-hellman.md

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+# Decisional Diffie–Hellman
+
+- decisional version of [[computational-diffie-hellman|Computational Diffie–Hellman]]
+- given a generator $`g`$ and uniformly selected $`\left(g^a, g^b\right)`$, discriminate $`g^{ab}`$ from a different group value $`c`$

ket.md

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+# Ket
+
+- $`\ket{u}`$ where $`u`$ is the _name_ of a _state_
+- [[push]] [[column-vector|Column Vector]]

np-complete.md

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+# NP Complete
+
+- a problem that all other [[np|NP]] problems can be reduced to
+- if you can solve the decision version in P-time, you can solve all decision problems in [[np|NP]] in P-time

np-hard.md

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+# NP Hard
+
+- may not necessarily be in [[np|NP]]
+- computational version of [[np-complete|NP Complete]]

np.md

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+# NP
+
+- class of languages whose membership proofs can be verified in polynomial time
+- the [[discrete-log|Discrete Log]] problem is an example of an NP problem
+  - from $`g^x`$ in a finite field it is hard to compute $`\log_g\left(g^x\right)`$, but easy to check $`g^x = g^y`$ to validate a knowledge proof of $`x`$

probabilistic-polynomial-time.md

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+# Probabilistic Polynomial Time
+
+- for a given problem, a PPT algorithm for the problem runs in P-time, with a high (likely non-one) probability of giving the correct answer
+  - takes randomness as an input
+  - impossible to guarantee the real solution without running the algorithm on all possible randomness (NP)