This paper presents a concrete security analysis of symmetric encryption schemes, focusing on the security of encryption under chosen-plaintext attacks. The authors introduce four different notions of security for symmetric encryption: real-or-random indistinguishability, left-or-right indistinguishability, find-then-guess security, and semantic security. They analyze the relationships between these notions, showing that some are stronger than others in terms of concrete security. The paper also provides tight bounds on the success probability of adversaries as a function of their resources for specific encryption schemes, including the popular CBC mode and XOR-based schemes. The authors show that the security of these schemes depends on the assumed security of the underlying pseudorandom function (PRF) or pseudorandom permutation (PRP) family. They demonstrate that stateful XOR schemes based on finite PRFs have the best security, as they are as good as one can hope to get. The paper also discusses the importance of concrete security in cryptography, emphasizing the need to consider the actual complexity of reductions between security notions rather than just polynomial-time equivalence. The authors conclude that concrete security is an important area of research in theoretical cryptography, providing a framework for analyzing the security of encryption schemes in a more precise and practical way.This paper presents a concrete security analysis of symmetric encryption schemes, focusing on the security of encryption under chosen-plaintext attacks. The authors introduce four different notions of security for symmetric encryption: real-or-random indistinguishability, left-or-right indistinguishability, find-then-guess security, and semantic security. They analyze the relationships between these notions, showing that some are stronger than others in terms of concrete security. The paper also provides tight bounds on the success probability of adversaries as a function of their resources for specific encryption schemes, including the popular CBC mode and XOR-based schemes. The authors show that the security of these schemes depends on the assumed security of the underlying pseudorandom function (PRF) or pseudorandom permutation (PRP) family. They demonstrate that stateful XOR schemes based on finite PRFs have the best security, as they are as good as one can hope to get. The paper also discusses the importance of concrete security in cryptography, emphasizing the need to consider the actual complexity of reductions between security notions rather than just polynomial-time equivalence. The authors conclude that concrete security is an important area of research in theoretical cryptography, providing a framework for analyzing the security of encryption schemes in a more precise and practical way.