NISTIR 8214 Threshold Schemes for Cryptographic Primitives Challenges and Opportunities in Standardization and Validation of Threshold Cryptography Luís T. A. N. Brandão Nicky Mouha Apostol Vassilev This publication is available free of charge from: https://doi.org/10.6028/NIST.IR.8214 NISTIR 8214 Threshold Schemes for Cryptographic Primitives Challenges and Opportunities in Standardization and Validation of Threshold Cryptography Luís T. A. N. Brandão Nicky Mouha Apostol Vassilev Computer Security Division Information Technology Laboratory This publication is available free of charge from: https://doi.org/10.6028/NIST.IR.8214 March 2019 U.S. Department of Commerce Wilbur L. Ross, Jr., Secretary National Institute of Standards and Technology Walter G. Copan, NIST Director and Under Secretary of Commerce for Standards and TechnologyNational Institute of Standards and Technology Internal Report 8214 63 pages (March 2019) This publication is available free of charge from: https://doi.org/10.6028/NIST.IR.8214 Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by NIST, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. There may be references in this publication to other publications currently under development by NIST in accordance with its assigned statutory responsibilities. The information in this publication, including concepts and methodologies, may be used by federal agencies even before the completion of such companion publications. Thus, until each publication is completed, current requirements, guidelines, and procedures, where they exist, remain operative. For planning and transition purposes, federal agencies may wish to closely follow the development of these new publications by NIST. Organizations are encouraged to review all draft publications during public comment periods and provide feedback to NIST. Many NIST cybersecurity publications, other than the ones noted above, are available at https://csrc.nist.gov/publications. Comments on this publication may be submitted to: National Institute of Standards and Technology Attn: Computer Security Division, Information Technology Laboratory 100 Bureau Drive (Mail Stop 8930) Gaithersburg, MD 20899-8930 Email: threshold-crypto@nist.gov All comments are subject to release under the Freedom of Information Act (FOIA).This publication is available free of charge from: https://doi.org/10.6028/NIST.IR.8214NISTIR 8214 T HRESHOLD SCHEMES FOR CRYPTOGRAPHIC PRIMITIVES Reports on Computer Systems Technology The Information Technology Laboratory (ITL) at the National Institute of Standards and Technology (NIST) promotes the U.S. economy and public welfare by providing technical leadership for the Nation’s measurement and standards infrastructure. ITL develops tests, test methods, reference data, proof of concept implementations, and technical analyses to advance the development and productive use of information technology. ITL’s responsi- bilities include the development of management, administrative, technical, and physical standards and guidelines for the cost-effective security and privacy of other than national security-related information in federal information systems. Abstract The Computer Security Division at the National Institute of Standards and Technology is interested in promoting the security of implementations of cryptographic primitives. This se- curity depends not only on the theoretical properties of the primitives but also on the ability to withstand attacks on their implementations. It is thus important to mitigate breakdowns that result from differences between ideal and real implementations of cryptographic algorithms. This document overviews the possibility of implementing cryptographic primitives using threshold sc