Proofs in Cryptography Lecture 12 ROM Construction Example CPA secure RSA Encryption

In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that they know a value x, without conveying any information apart from the fact that they know the value x. The essence of zero-knowledge proofs is that it is trivial to prove that one possesses knowledge of certain information by simply revealing it; the challenge is to prove such possession without revealing the information itself or any additional information. If proving a statement requires that the prover possess some secret information, then the verifier will not be able to prove the statement to anyone else without possessing the secret information. The statement being proved must include the assertion that the prover has such knowledge, but not the knowledge itself. Otherwise, the statement would not be proved in zero-knowledge because it provides the verifier with additional information about the statement by the end of the protocol. A zero-knowledge proof of knowledge is a special case when the statement consists only of the fact that the prover possesses the secret information. Interactive zero-knowledge proofs require interaction between the individual (or computer system) proving their knowledge and the individual validating the proof. A protocol implementing zero-knowledge proofs of knowledge must necessarily require interactive input from the verifier. This interactive input is usually in the form of one or more challenges such that the responses from the prover will convince the verifier if and only if the statement is true, i.e., if the prover does possess the claimed knowledge. If this were not the case, the verifier could record the execution of the protocol and replay it to convince someone else that they possess the secret information. The new party's acceptance is either justified since the replayer does possess the information (which implies that the protocol leaked information, and thus, is not proved in zero-knowledge), or the acceptance is spurious, i.e., was accepted from someone who does not actually possess the information. Some forms of non-interactive zero-knowledge proofs exist, but the validity of the proof relies on computational assumptions (typically the assumptions of an ideal cryptographic hash function). Lecture 1 Encryption Schemes Lecture 2 Probabilistic and Game based Security Definitions Lecture 3 Reduction Proofs - What are they? Lecture 4 Reduction Proofs - How to do? Lecture 5 Pseudo Random Generators Lecture 6 Reduction Proof Example - PRG based Encryption Lecture 7 Reduction Proof Examples - PRF Family Lecture 8 PRG Output Expansion Lecture 9 Hybrid Proofs - Defining Hybrids Lecture 10 Hybrid Proof Example - PRG Output Expansion Lecture 11 Random Oracle Model ROM Lecture 12 ROM Construction Example - CPA secure RSA Lecture 13 ROM Proof Example - CPA secure RSA Lecture 14 ROM Construction Examples - RSA FDH Signatures Lecture 15 ROM Proof Examples - RSA FDH Signatures For more topics please check the link bellow: https://www.youtube.com/playlist?list=PLOBV8lhF_YPtE-P5D8mJZVqy3p4w2kWvp https://www.youtube.com/playlist?list=PLOBV8lhF_YPtujh1D7kzZw1Z2vve5huuZ