Elliptic curve isogeny based key agreement protocol

Abstract

An electronic key pre-distribution device (110) for configuring multiple network nodes (210, 211) with local key information is provided. The key pre-distribution device comprises applies at least a first hash function (147) and a second hash function (148) to a digital identifier of a network node. The first and second hash functions map the digital identifier to a first public point (141; H1(ID)) and a second public point (142; H2(ID)) on a first elliptic curve (131) and second elliptic curve (132). A first and second secret isogeny (135) is applied to the first and second public elliptic curve point (141, 142), to obtain a first private elliptic curve point (151) and second private elliptic curve point (152) being part of private key material (155) for the network node (210).

1 . A key distribution device comprising
 a storage circuit or storage media,
 wherein the storage circuit or storage media is arranged to store information representing a first isogeny and a second isogeny, 
 wherein the first isogeny is for a first elliptic curve, 
 wherein the second isogeny is for a second elliptic curve, 
 wherein the first isogeny and the second isogeny are each arranged to receive a point on an elliptic curve and to produce a point on an elliptic curve as output, 
 wherein the first elliptic curve is different than the second elliptic curve; 
   a processor circuit,
 wherein the processor circuit is arranged to obtain a digital identifier for a network node, 
 wherein the processor circuit is arranged to apply a first hash function to the digital identifier to obtain a first public point, 
 wherein the processor circuit is arranged to apply a second hash function to the digital identifier to obtain a second public point,
 wherein the first public point is on the first elliptic curve, 
 wherein the second public point is on the second elliptic curve, 
 wherein the first public point and the second public point are a portion of a public key material, 
 
 wherein the processor circuit is arranged to apply the first isogeny to the first public point to obtain a first private point, 
 wherein the processor circuit is arranged to apply the second isogeny to the second public point to obtain a second private point, 
 wherein the first private point and the second private point are a portion of a private key material for the network node; and 
   a communication interface circuit, wherein the communication interface circuit is arranged to configure a network node with the first private point and the second private point.   
     
     
         2 . The key distribution device as in  claim 1 ,
 wherein the first isogeny is a mapping from the first elliptic curve to the second elliptic curve,   wherein the second isogeny is a dual of the first isogeny.   
     
     
         3 . The key distribution device as in  claim 1 , wherein the first elliptic curve is defined by a different formula than the second elliptic curve. 
     
     
         4 . The key distribution device as in  claim 1 ,
 wherein the first isogeny maps from the first elliptic curve to the first elliptic curve,   wherein the second isogeny maps from the second elliptic curve to the second elliptic curve,   wherein the first isogeny comprises an elliptic curve scalar multiplication of a first input point on the first elliptic curve with a first secret integer,   wherein the second isogeny comprises an elliptic curve scalar multiplication of a second input point input point on the second elliptic curve to the second elliptic curve with a second secret integer,   wherein the information comprises the secret integer.   
     
     
         5 . An method for key distribution comprising:
 storing information,
 wherein the information comprises a first isogeny for a first elliptic curve and a second isogeny for a second elliptic curve, 
 wherein the first isogeny and the second isogeny are arranged to receive a point on an elliptic curve and to produce a point on an elliptic curve as output, 
 wherein the first elliptic curve is different than the second elliptic curve; 
   obtaining a digital identifier for a network node;   applying at least a first hash function to the digital identifier to obtain a first public point;   applying a second hash function to the digital identifier to the digital identifier to obtain a second public point,   wherein the first public point is on the a first elliptic curve,   wherein the second public point is on the second elliptic curve,   wherein the first public point and the second public point are a portion of a public key material;   applying the first isogeny to the first public point to obtain a first private point;   applying the second isogeny to the second public point to obtain a second private point,   wherein the first private point and the second private point are a portion is of a private key material; and   configuring the network node with the first private point and the second private point.   
     
     
         6 . A computer program stored on a non-transitory medium, wherein the computer program when executed on a processor performs the method as claimed in  claim 5 .