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Supersingular isogeny Diffie–Hellman key exchange (SIDH or SIKE) is an insecure proposal for a post-quantum cryptographic algorithm to establish a secret key between two parties over an untrusted communications channel.

Jan 23, 2021 · SIKE is a key encapsulation mechanism (KEM) obtained by applying the Fujisaki-Okamoto transform (Fujisaki and Okamoto, 2011) to SIDH and suitable for use in a hybrid encryption scheme. Both schemes feature quantum resistance and offer small public keys compared to other post-quantum cryptosystems.

We show that the soundness proof for the De Feo–Jao–Plˆut iden-tification scheme (the basis for supersingular isogeny Diffie–Hellman (SIDH) signatures) contains an invalid assumption, and we provide a counterexample for this assumption—thus showing the proof of soundness is invalid.

SageMath implementation following Algorithm 2 of the paper A direct key recovery attack on SIDH. This algorithm solves the SSI-T problem in subexponential time, and does not require knowledge of the endomorphism ring of the starting curve of the protocol.

Tested with Python 3.7 and 3.8. sidh_protocol.py is an example of protocol execution on single machine, simulating both parties, Alice and Bob. server.py and client.py are the example implementation of SIDH key exchange between server (running on PC) and a …

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