Isara Corporation

Edward William Eaton

Atsushi Yamada

Kassem Kalach

Gustav Michael Gutoski

Victoria De Quehen

Christopher Leonardi

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.

Obtaining keys from broadcasters in supersingular isogeny-based cryptosystems

In a general aspect, a random seed value may be used in a key encapsulation process for multiple recipients. An error vector derivation function is applied to a combination of the random seed value and an additional value, including an identifier of a recipient, to produce an error vector. A plaintext value for the recipient is obtained based on the random seed value. The error vector and the plaintext value are used in an encryption function to produce a ciphertext for the recipient. A pseudorandom function is applied to the random seed value to produce a pseudorandom function output that includes a symmetric key, and the symmetric key is used to generate an encrypted message for the recipient based on an unencrypted message. The ciphertext for the recipient and the encrypted message are provided for transmission in a communication network.

Multi-use key encapsulation processes

In a general aspect, a random seed value is used in a key encapsulation process to generate multiple ciphertexts for a recipient. The key encapsulation process includes multiple encapsulation rounds and each encapsulation round generates a respective ciphertext based on the random seed value and an additional value. The additional value includes an index indicating the encapsulation round. A symmetric key is generated based on the random seed value, and an encrypted message is generated based on the symmetric key. The ciphertexts and the encrypted message are provided for the recipient for transmission between nodes in a communication system.

Multi-round key encapsulation process

In a general aspect, a conversion scheme is used in a public key cryptosystem. In some aspects, an error vector derivation function is applied to a random value and a message value to produce an error vector. A plaintext value is generated based on the random value, the message value, and the error vector. The error vector and the plaintext value are used in an encryption function to produce a ciphertext component, and the ciphertext component is provided for transmission in a communication system.

Conversion schemes for public key cryptosystems

In a general aspect, a conversion scheme is used in a public key cryptosystem. In some aspects, a plaintext value is generated based on a message value, a constant value, and a random value. An error vector derivation function is applied to the plaintext value to produce an error vector. The plaintext value and the error vector are used in an encryption function to produce a ciphertext component, and the ciphertext component is provided for transmission in a communication network.

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Waterloo, Canada

Edward William Eaton