SILBE: An Updatable Public Key Encryption Scheme from Lollipop Attacks

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 generalized lollipop attack of Castryck and Vercauteren on the M-SIDH Key exchange by Fouotsa, Moriya and Petit. Doing so, we can in fact make of SILBE a post-quantum secure Updatable Public Key Encryption scheme (UPKE). SILBE is the first isogeny-based UPKE which is not based on group actions. In its core, SILBE extensively uses both the Deuring Correspondence and Kani’s Lemma, two central concepts in Isogeny-Based Cryptography.