The paper introduces a general framework for describing and analyzing the security of cryptographic protocols, focusing on the concept of universal composition. This framework allows for specifying security requirements in a unified and systematic way and ensures that protocols remain secure even when composed with other protocols in complex and unpredictable environments. The key contributions include: 1. **Universal Composition**: A general operation that preserves the security of protocols when they are composed together, even in the presence of an unbounded number of concurrent sessions run adversarially. 2. **Modular Design**: The framework enables modular design and analysis of complex cryptographic protocols from simpler building blocks. 3. **Expressiveness**: The framework is expressive enough to capture a wide range of cryptographic tasks and real-life protocols. 4. **Simplicity**: The framework is designed to be simple and intuitive, making it easier to understand and use. The paper also discusses the challenges in formulating security definitions for cryptographic protocols, such as capturing the threats from the execution environment and ensuring security under concurrent composition. It highlights the limitations of previous approaches and explains how the proposed framework addresses these issues. The framework is based on a model of computation involving interactive Turing machines (ITMs) and introduces concepts like protocol execution, emulation, and ideal functionalities. The universal composition theorem guarantees that secure protocols remain secure when composed, even in complex and adversarially controlled environments.The paper introduces a general framework for describing and analyzing the security of cryptographic protocols, focusing on the concept of universal composition. This framework allows for specifying security requirements in a unified and systematic way and ensures that protocols remain secure even when composed with other protocols in complex and unpredictable environments. The key contributions include: 1. **Universal Composition**: A general operation that preserves the security of protocols when they are composed together, even in the presence of an unbounded number of concurrent sessions run adversarially. 2. **Modular Design**: The framework enables modular design and analysis of complex cryptographic protocols from simpler building blocks. 3. **Expressiveness**: The framework is expressive enough to capture a wide range of cryptographic tasks and real-life protocols. 4. **Simplicity**: The framework is designed to be simple and intuitive, making it easier to understand and use. The paper also discusses the challenges in formulating security definitions for cryptographic protocols, such as capturing the threats from the execution environment and ensuring security under concurrent composition. It highlights the limitations of previous approaches and explains how the proposed framework addresses these issues. The framework is based on a model of computation involving interactive Turing machines (ITMs) and introduces concepts like protocol execution, emulation, and ideal functionalities. The universal composition theorem guarantees that secure protocols remain secure when composed, even in complex and adversarially controlled environments.