从 JavaCard 中的私钥计算 ECC 公钥

Question

With Java Card APIs, which "support" Elliptic curves, how do I compute a public key given a known secret key.

Following a DH shared secret negotiation I'm interested in deriving common shared keys. According to TR-03111 and X9.63 the shared secret from the DH ECC key agreement should not be used but, according to my understanding, the affine representation of the x-coordinate (The x component of the public key associated with the shared secret as a private key) is to be used.

With BigInteger arithmetic or ECPoint.multiply() this easy, but no such APIs exist in Java Card.

Answer 1

This multiplication isn't directly available for Java Card. Basically Java Card hides low level operations for you.

However, if you have a relatively new Java Card you may get away with this by using a KeyAgreement instance created using ALG_EC_SVDP_DH_PLAIN_XY . What you can do is to create a ECPublicKey where the public key point is simply set to point G. This base point G is part of the domain parameters. The private key should of course be set to your value.

Then all it comes down to is to perform a key agreement; the result of the agreement will be the points X and Y of the public key.

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Note that support of any algorithm constant depends on the card implementation. The constant will be there - if the implemented API is new enough - but the algorithm may not be implemented.