This paper presents general definitions of security for multiparty cryptographic protocols, focusing on secure function evaluation. It shows that security is preserved under natural composition operations. The definitions follow a general paradigm but include modifications and simplifications. The composition operation is formalized by Micali and Rogaway. The paper considers various settings, including eavesdropping, Byzantine, nonadaptive, and adaptive adversaries, as well as information-theoretic and computational models. In the computational model, the paper provides the first definition of protocol security that is preserved under composition. The paper discusses secure function evaluation, where parties evaluate a probabilistic function of their inputs. It also considers other tasks and defines a general approach for capturing their security requirements. The paper introduces a definitional approach that formalizes the "ideal process" for secure multiparty function evaluation. This process involves a trusted party evaluating the function and returning results to the parties. The paper defines secure protocols as those that emulate this ideal process. The paper also discusses modular composition, where secure protocols can be combined to evaluate more complex functions. The paper shows that its definition of security preserves security under composition in several standard settings. The paper also discusses other related work and provides a detailed analysis of secure function evaluation, including the challenges of active adversaries and probabilistic functions. The paper concludes with a discussion of the broader implications of its findings for the design and analysis of secure cryptographic protocols.This paper presents general definitions of security for multiparty cryptographic protocols, focusing on secure function evaluation. It shows that security is preserved under natural composition operations. The definitions follow a general paradigm but include modifications and simplifications. The composition operation is formalized by Micali and Rogaway. The paper considers various settings, including eavesdropping, Byzantine, nonadaptive, and adaptive adversaries, as well as information-theoretic and computational models. In the computational model, the paper provides the first definition of protocol security that is preserved under composition. The paper discusses secure function evaluation, where parties evaluate a probabilistic function of their inputs. It also considers other tasks and defines a general approach for capturing their security requirements. The paper introduces a definitional approach that formalizes the "ideal process" for secure multiparty function evaluation. This process involves a trusted party evaluating the function and returning results to the parties. The paper defines secure protocols as those that emulate this ideal process. The paper also discusses modular composition, where secure protocols can be combined to evaluate more complex functions. The paper shows that its definition of security preserves security under composition in several standard settings. The paper also discusses other related work and provides a detailed analysis of secure function evaluation, including the challenges of active adversaries and probabilistic functions. The paper concludes with a discussion of the broader implications of its findings for the design and analysis of secure cryptographic protocols.