The 3-volume-set LNCS 12696 - 12698 constitutes the refereed proceedings of the 40thAnnual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2021, which was held in Zagreb, Croatia, during October 17-21, 2021.The 78 full papers included in these proceedings were accepted from a total of 400 submissions. They were organized in topical sections as follows:Part I: Best papers; public-key cryptography; isogenies; post-quantum cryptography; lattices; homomorphic encryption; symmetric cryptanalysis;Part II: Symmetric designs; real-world cryptanalysis; implementation issues; masking and secret-sharing; leakage, faults and tampering; quantum constructions and proofs; multiparty computation;Part III: Garbled circuits; indistinguishability obfuscation; non-malleable commitments; zero-knowledge proofs; property-preserving hash functions and ORAM; blockchain; privacy and law enforcement.