Fix a few typos

high-assurance-zk/lpzk/README.md

@@ -8,11 +8,11 @@ In this work, we develop an end-to-end machine-checked implementation of LPZK, t
 * Optimization based on the execution model: where we explore the usage of parallelism to speed up the computation
 * Optimization based on memory management: where we replace and augment the data structures used to store input and randomness values in order to reduce access overhead
 
-Our development was derived from a machine-checked security proof of LPZK that was developed in EasyCrypt, an interactive proof-assistant tailored for cryptographic proofs. All the afore mentioned optimization have also been formalized in EasyCrypt, before code was generated from the proof.
+Our development was derived from a machine-checked security proof of LPZK that was developed in EasyCrypt, an interactive proof-assistant tailored for cryptographic proofs. All the aforementioned optimization have also been formalized in EasyCrypt, before the code was generated from the proof.
 
 ## Disclaimer
 
-The reviewer may notice that some modifications to the folder were done January 23, therefore after then January 19 submission deadline. These modifications were done **ONLY** at the implementation level, not at the proof level. Concretely, the implementation version submitted January 19 was the test version, that **did not** use correlated randomness and, therefore, produced incorrect results. This version is faster to just benchmark the performance of the implementation without considering it's correctness. 
+The reviewer may notice that some modifications to the folder were done January 23, therefore, after the January 19 submission deadline. These modifications were done **ONLY** at the implementation level, not at the proof level. Concretely, the implementation version submitted January 19 was the test version, that **did not** use correlated randomness and, therefore, produced incorrect results. This version is faster to just benchmark the performance of the implementation without considering it's correctness.
 
 We have resubmitted the correct version, that creates correlated version before executing the protocol, thus producing the correct result.
 
@@ -45,4 +45,4 @@ The `Makefile` at the top level directory makes available the following targets:
 - `test-list <prime=P> <size=N> <cores=K>` - runs list-based LPZK implementation matrix multiplication of size N, over field P and using K cores;
 - `test-array <prime=P> <size=N> <cores=K>` - runs array-based LPZK implementation matrix multiplication of size N, over field P and using K cores;
 
-Notice that running these targets depends on the availability of the required dependencies. Typing just `make` shows a brief help with information on some additional targets. In addition, each component has specific `Makefile`s that may give access to some additional targets.
+Notice that running these targets depends on the availability of the required dependencies. Typing just `make` shows a brief help with information on some additional targets. In addition, each component has specific `Makefile`s that may give access to some additional targets.