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The present document gives an overview of the current understanding and best practice in academia and industry about quantum-safe cryptography (QSC). It focuses on identifying and assessing cryptographic primitives that have been proposed for efficient key establishment and authentication applications, and which may be suitable for standardization by ETSI and subsequent use by industry to develop quantum-safe solutions for real-world applications.

QSC is a rapidly growing area of research. There are already academic conference series such as PQC and workshops have been established by ETSI/IQC [i.1] and NIST. The European Commission has recently granted funding to two QSC projects under the Horizon 2020 framework: SAFEcrypto [i.2] and PQCrypto [i.3] and [i.4]. The present document draws on all these research efforts.

The present document will cover three main areas. Clauses 4 and 5 discuss the types of primitives being considered and describe an assessment framework; clauses 6 to 10 discuss some representative cryptographic primitives; and clause 11 gives a preliminary discussion of key sizes.