We present a new post-quantum Public Key Encryption scheme (PKE) named Supersingular Isogeny Lollipop Based Encryption or SILBE. SILBE is obtained by leveraging the generalised lollipop attack of Castryck and Vercauteren on the M-SIDH Key exchange by Fouotsa, Moriya and Petit. Doing so, we can in fact make SILBE a post-quantum secure Updatable Public Key Encryption scheme (UPKE). SILBE is in fact the first isogeny-based UPKE which is not based on group actions. Hence, SILBE overcomes the limitations highlighted by Eaton, Jao, Komlo and Mokrani at SAC’21 regarding the design of an SIDH-style UPKE. This is possible by leveraging both the Deuring Correspondence and Kani’s Lemma, two central concepts in Isogeny-Based Cryptography.

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SILBE: An Updatable Public Key Encryption Scheme from Lollipop Attacks

  • Max Duparc,
  • Tako Boris Fouotsa,
  • Serge Vaudenay

摘要

We present a new post-quantum Public Key Encryption scheme (PKE) named Supersingular Isogeny Lollipop Based Encryption or SILBE. SILBE is obtained by leveraging the generalised lollipop attack of Castryck and Vercauteren on the M-SIDH Key exchange by Fouotsa, Moriya and Petit. Doing so, we can in fact make SILBE a post-quantum secure Updatable Public Key Encryption scheme (UPKE). SILBE is in fact the first isogeny-based UPKE which is not based on group actions. Hence, SILBE overcomes the limitations highlighted by Eaton, Jao, Komlo and Mokrani at SAC’21 regarding the design of an SIDH-style UPKE. This is possible by leveraging both the Deuring Correspondence and Kani’s Lemma, two central concepts in Isogeny-Based Cryptography.