Isara Corporation

Christopher Leonardi

Gustav Michael Gutoski

Victoria De Quehen

Edward William Eaton

In some aspects, a key establishment protocol is executed to generate a shared secret. A first entity calculates a first image curve Erepresenting an image of an elliptic curve E under a first isogeny &#x3d5;; calculates the shared secret based on the first image curve E; receives a second image curve Eand a first pair of elliptic curve points {&#x3d5;(P), &#x3d5;(Q)} and from a second entity; obtains a basis {R, S}; calculates a third image curve Erepresenting an image of the second image curve Eunder a second isogeny &#x3c8;; calculates a third pair of elliptic curve points {&#x3c8;(R), &#x3c8;(S)}; and sends the third image curve Eand the third pair of elliptic curve points {&#x3c8;(R), &#x3c8;(S)} to the second entity, wherein the third image curve Eand the third pair of elliptic curve points {&#x3c8;(R), &#x3c8;(S)} enable the second entity to compute the shared secret.

Broadcasting in supersingular isogeny-based cryptosystems

In some aspects, a key establishment protocol is executed to generate a shared secret. A first entity calculates a first image curve Erepresenting an image of an elliptic curve E under a first isogeny &#x3d5;; calculates a first pair of elliptic curve points {&#x3d5;(P), &#x3d5;(Q)}; calculates secret integers {c, d}; sends the first image curve Eand the first pair of elliptic curve points {&#x3d5;(P), &#x3d5;(Q)} to a second entity; receives a second image curve Eand a third pair of elliptic curve points {&#x3c8;(R), &#x3c8;(S)} from the second entity; calculates a third image curve Erepresenting an image of the second image curve Eunder a second isogeny {tilde over (&#x3d5;)}, wherein the second isogeny {tilde over (&#x3d5;)}is identified based on the secret integers {c, d} and the third pair of elliptic curve points {&#x3c8;(R), &#x3c8;(S)}; and calculates the shared secret based on the third image curve E.

Growing community of inventors

Waterloo, Canada

Christopher Leonardi