Universal Composability: 
The IITM Model and iUC Framework

Flexible Universal Composability Made Simple

The IITM Model for Universal Composability

The IITM model, developed by our institute and originally published at [CSFW06] with a full and revised version published in [JournalOfCryptology2020], is a general model for universal composability. Universal composability is a central tool for taming the complexity of protocols in formal security analyses: It allows protocol designers to modularize their security proofs by first analyzing small parts of a protocol in isolation. A so-called composition theorem provided by the underlying model then directly implies security of the combined protocol without requiring further proofs.

Main Features of the IITM Model

The IITM model offers a highly general composition theorem that enables modular analyses for a very wide range of protocols and composition types unified within a single model, including all of the following:

  • All types of protocols considered in the universal composability literature, such as real, ideal, hybrid, joint-state, and global state protocols
  • Many interesting protocol features such as:
    • flexible protocol structures that allow for connecting individual protocol components in arbitrary ways
    • protocols with and without disjoint sessions
    • state that can be shared arbitrarily, even across sessions
    • locally chosen and/or globally managed session identifiers
    • protocols with and without runtime exhaustion
    • arbitrary combinations of all of the above
  • All composition types from the universal composability literature, including composition of protocols with/without disjoint sessions, composition with joint-state, composition with global state
  • Composition types that have not typically been considered in the literature so far, such as a joint-state compositions for multiple different protocols (instead of joint state for multiple sessions of the same protocol) as well as combinations of the above composition types.

Both the IITM model and its instantiation the iUC framework (see next) have already been used successfully to model and analyze a wide range of protocols in a modular way (see literature).

In [EuroCrypt2022] we further formally showed that the IITM model is strictly more expressive than Canetti's UC model for universal composability: The IITM model not just covers all protocols, security results, and composition types that can be obtained in Canetti's UC model as special cases. It further also supports natural protocols from practice that cannot faithfully be expressed as well as security results that cannot be proven in Canetti's UC model.

The iUC Framework:
A Simple and Flexible Instantiation of the IITM Model

While the IITM model is very expressive, it, however, does not come with any modeling tools out of the box. To further support protocol designers and simplify the process of modeling protocols, these tools and modeling conventions are added on top of the IITM model by the iUC framework, published at [AsiaCrypt2019].

The iUC framework provides the so far best combination of expressiveness and ease of use in a universal composability model: it offers modeling conventions, including a template for specifying arbitrary protocols, and comes with a clear and simple syntax as well as sensible default values for many optional parts. At the same time, the iUC framework is highly customizable and includes only very minimal technical requirements, which allows for capturing a wide range of protocols and settings in natural and intuitive ways.

The iUC framework retains the generality of the underlying IITM model, including support of for all of the aforementioned protocol and composition types, while combining all of these features in just a single protocol template and a single main composition theorem. This is is in contrast to many other universal composability models and is an important property that makes iUC more user friendly.

Literature and Publications

  1. 2026

    1. Paul Gerhart, Daniel Rausch, and Dominique Schröder, “Universally Composable Adaptor Signatures,” in ACM Conference on Computer and Communications Security (CCS 2026), ACM, 2026. To appear.
  2. 2025

    1. Paul Gerhart, Daniel Rausch, and Dominique Schröder, “Universally Composable Adaptor Signatures,” Cryptology ePrint Archive, Technical Report 2025/1363, 2025.
    2. Behzad Abdolmaleki, Ruben Baecker, Paul Gerhart, Mike Graf, Mojtaba Khalili, Daniel Rausch, and Dominique Schröder, “Universally Composable Password-Hardened Encryption,” in Advances in Cryptology - ASIACRYPT 2025, Springer, 2025, pp. 235–267.
    3. Behzad Abdolmaleki, Ruben Baecker, Paul Gerhart, Mike Graf, Mojtaba Khalili, Daniel Rausch, and Dominique Schröder, “Universally Composable Password-Hardened Encryption,” Cryptology ePrint Archive, Technical Report 2025/1647, 2025.
    4. Daniel Rausch, Nicolas Huber, and Ralf Küsters, “Verifiable E-Voting with a Trustless Bulletin Board,” in 38th IEEE Computer Security Foundations Symposium (CSF 2025), IEEE, 2025, pp. 506–521.
    5. Daniel Rausch, Nicolas Huber, and Ralf Küsters, “Verifiable E-Voting with a Trustless Bulletin Board,” Cryptology ePrint Archive, Technical Report 2025/841, 2025.
    6. Ruben Baecker, Paul Gerhart, Daniel Rausch, and Dominique Schröder, “A Fully-Adaptive Threshold Partially-Oblivious PRF,” in Advances in Cryptology - CRYPTO 2025, Y. T. Kalai and S. F. Kamara (Eds.), Springer, 2025, pp. 569–597.
    7. Ruben Baecker, Paul Gerhart, Daniel Rausch, and Dominique Schröder, “A Fully-Adaptive Threshold Partially-Oblivious PRF,” Cryptology ePrint Archive, Technical Report 2025/1433, 2025.
  3. 2023

    1. Mike Graf, Ralf Küsters, and Daniel Rausch, “AUC: Accountable Universal Composability,” in IEEE Symposium on Security and Privacy (S&P 2023), IEEE, 2023, pp. 1148–1167.
  4. 2022

    1. Mike Graf, Ralf Küsters, and Daniel Rausch, “AUC: Accountable Universal Composability,” Cryptology ePrint Archive, Technical Report 2022/1606, 2022.
    2. Daniel Rausch, Ralf Küsters, and Céline Chevalier, “Embedding the UC Model into the IITM Model,” in Advances in Cryptology - EUROCRYPT 2022, O. Dunkelman and S. Dziembowski (Eds.), Springer, 2022, pp. 242–272.
    3. Daniel Rausch, Ralf Küsters, and Céline Chevalier, “Embedding the UC Model into the IITM Model,” Cryptology ePrint Archive, Technical Report 2022/224, 2022.
  5. 2021

    1. Mike Graf, Daniel Rausch, Viktoria Ronge, Christoph Egger, Ralf Küsters, and Dominique Schröder, “A Security Framework for Distributed Ledgers,” in ACM Conference on Computer and Communications Security (CCS 2021), ACM, 2021, pp. 1043–1064.
    2. Mike Graf, Daniel Rausch, Viktoria Ronge, Christoph Egger, Ralf Küsters, and Dominique Schröder, “A Security Framework for Distributed Ledgers,” Cryptology ePrint Archive, Technical Report 2021/145, 2021.
  6. 2020

    1. Daniel Rausch, “Simple and flexible universal composability: definition of a framework and applications,” PhD thesis. University of Stuttgart, Germany, 2020.
    2. Ralf Küsters, Max Tuengerthal, and Daniel Rausch, “Joint State Theorems for Public-Key Encryption and Digital Signature Functionalities with Local Computation,” Journal of Cryptology, vol. 33, pp. 1585–1658, 2020.
    3. Ralf Küsters, Max Tuengerthal, and Daniel Rausch, “The IITM Model: a Simple and Expressive Model for Universal Composability,” Journal of Cryptology, vol. 33, pp. 1461–1584, 2020.
  7. 2019

    1. Jan Camenisch, Stephan Krenn, Ralf Küsters, and Daniel Rausch, “iUC: Flexible Universal Composability Made Simple,” in Advances in Cryptology - ASIACRYPT 2019, S. D. Galbraith and S. Moriai (Eds.), Springer, 2019, pp. 191–221.
    2. Jan Camenisch, Stephan Krenn, Ralf Küsters, and Daniel Rausch, “iUC: Flexible Universal Composability Made Simple,” Cryptology ePrint Archive, Technical Report 2019/1073, 2019.
  8. 2018

    1. Ralf Küsters, Max Tuengerthal, and Daniel Rausch, “The IITM Model: a Simple and Expressive Model for Universal Composability,” Cryptology ePrint Archive, Technical Report 2013/025, 2018.
  9. 2017

    1. Ralf Küsters and Daniel Rausch, “A Framework for Universally Composable Diffie-Hellman Key Exchange,” in 38th IEEE Symposium on Security and Privacy (S&P 2017), IEEE, 2017, pp. 881–900.
    2. Ralf Küsters and Daniel Rausch, “A Framework for Universally Composable Diffie-Hellman Key Exchange,” Cryptology ePrint Archive, Technical Report 2017/256, 2017.
  10. 2016

    1. Jan Camenisch, Robert R. Enderlein, Stephan Krenn, Ralf Küsters, and Daniel Rausch, “Universal Composition with Responsive Environments,” in Advances in Cryptology - ASIACRYPT 2016, J. H. Cheon and T. Takagi (Eds.), Springer, 2016, pp. 807–840.
    2. Jan Camenisch, Robert R. Enderlein, Stephan Krenn, Ralf Küsters, and Daniel Rausch, “Universal Composition with Responsive Environments,” Cryptology ePrint Archive, Technical Report 2016/034, 2016.
  11. 2013

    1. Max Tuengerthal, “Analysis of real-world security protocols in a universal composability framework,” University of Trier, 2013.
    2. Ralf Küsters and Max Tuengerthal, “The IITM Model: a Simple and Expressive Model for Universal Composability,” Cryptology ePrint Archive, 2013/025, 2013. http://eprint.iacr.org/2013/025/.
  12. 2011

    1. Ralf Küsters and Max Tuengerthal, “Composition Theorems Without Pre-Established Session Identifiers,” in Proceedings of the 18th ACM Conference on Computer and Communications Security (CCS 2011), Y. Chen, G. Danezis, and V. Shmatikov (Eds.), ACM Press, 2011, pp. 41–50.
    2. Ralf Küsters and Max Tuengerthal, “Composition Theorems Without Pre-Established Session Identifiers,” Cryptology ePrint Archive, 2011/406, 2011. http://eprint.iacr.org/2011/406/.
    3. Ralf Küsters and Max Tuengerthal, “Ideal Key Derivation and Encryption in Simulation-Based Security,” in Topics in Cryptology - CT-RSA 2011, The Cryptographers’ Track at the RSA Conference 2011, Proceedings, A. Kiayias (Ed.), Springer, 2011, pp. 161–179.
  13. 2010

    1. Ralf Küsters and Max Tuengerthal, “Ideal Key Derivation and Encryption in Simulation-based Security,” Cryptology ePrint Archive, 2010/295, 2010. http://eprint.iacr.org/2010/295/.
  14. 2009

    1. Ralf Küsters and Max Tuengerthal, “Universally Composable Symmetric Encryption,” in Proceedings of the 22nd IEEE Computer Security Foundations Symposium (CSF 2009), IEEE Computer Society, 2009, pp. 293–307.
    2. Ralf Küsters and Max Tuengerthal, “Universally Composable Symmetric Encryption,” Cryptology ePrint Archive, 2009/055, 2009. http://eprint.iacr.org/2009/055/.
  15. 2008

    1. Ralf Küsters and Max Tuengerthal, “Joint State Theorems for Public-Key Encryption and Digital Signature Functionalities with Local Computation,” in Proceedings of the 21st IEEE Computer Security Foundations Symposium (CSF 2008), IEEE Computer Society, 2008, pp. 270–284.
    2. Ralf Küsters and Max Tuengerthal, “Joint State Theorems for Public-Key Encryption and Digital Signature Functionalities with Local Computation,” Cryptology ePrint Archive, 2008/006, 2008. http://eprint.iacr.org/2008/006/.
  16. 2006

    1. Ralf Küsters, “Simulation-Based Security with Inexhaustible Interactive Turing Machines,” in Proceedings of the 19th IEEE Computer Security Foundations Workshop (CSFW-19 2006), IEEE Computer Society, 2006, pp. 309–320.
    2. Ralf Küsters, “Simulation-Based Security with Inexhaustible Interactive Turing Machines,” Cryptology ePrint Archive, 2006/151, 2006. http://eprint.iacr.org/2006/151/.

Acknowledgements

This work has been supported by Deutsche Forschungsgemeinschaft (DFG).

This image showsRalf Küsters

Ralf Küsters

Prof. Dr.

Head of Institute

To the top of the page