Hi Xuelei -

Great analysis.

Some comments in line.

On 8/10/2017 3:10 PM, Xuelei Fan wrote:

I want to extend the comment a little bit.

1. The background
A elliptic curve is determined by either an equation of form
     y^2 = x^3 + ax + b            (1) [Weierstrass form]
     y^2 + xy = x^3 + ax^2 + b.    (2)

However, some other forms may also be used.  For example:
     y^2 = x(x-1)(x-r)             (3)
     By^2 = x^3 + Ax^2 + x         (4) [RFC 7748, Montgomery curve]
     x^2 + y^2 = 1 + dx^2y^2       (5) [RFC 7748, Edwards curve]

In general, any elliptic curve can be written in Weierstrass form (1) or (2). That's, Montgomery curve and Edwards curve can be expressed in Weierstrass form.

2. Where we are now?
In JDK, an elliptic curve is defined in the Weierstrass form ((1)/(2)). See java.security.spec.EllipticCurve:

    EllipticCurve​(ECField field, BigInteger a, BigInteger b)

In theory, the existing APIs can be used for RFC 7748, by converting the Montgomery curve and Edwards curve to the Weierstrass form. However, the conversion can be misleading and complicate the implementation significantly. For example, before using a point Weierstrass form (x, y), the implementation need to convert it to Montgomery curve (x', -) so as to use the fully potential of RFC 7748. The curves returned in public APIs need to use (x, y), while the implementation need to use (x', y'). It's very confusing and the compatibility impact could be significant. For example:

    public something(ECPublicKey ecPublicKey)  {
       // Problem: If no other information, it is unclear
       // whether the ecPublicKey can be used for a particular
       // signature verification or not when the RFC 7748/8032
       // get supported.

       // Problem: an old application may use ecPublicKey for
       // the old style operation, even the ecPublicKey is supposed
       // to be x25519.  It's not easy to control the behavior in
       // legacy application code, and may introduce unexpected
       // security issues.

    public KeyAgreement getKeyAgreement(AlgorithmParameterSpec aps) {
       // Problem: the code bellow should be comment in the current
       // code.  However, the ECParameterSpec may not be able to use
       // for the old style "EC" key agreement.
       // JDK crypto provider can take special action to avoid this
       // issue in the JCA/JCE implementation.  But it cannot be
       // granted other provider can do this as well, and old
       // provider may run into problems as well.
       if (aps instance of ECParameterSpec) {
           return KeyAgreement.getInstance("EC");

What's the problem with ECPublicKey/ECPrivateKey/ECKey? It's mainly about the ECParameterSpec:

     ECParameterSpec ECKey.getParams​()

and ECParameterSpec is using java.security.spec.EllipticCurve. This design makes it pretty confusing to use ECPublicKey/ECPrivateKey/ECKey for RFC 7748 (Edwards curve form and Montgomery curve form).

Can EllipticCurve be extended to support more forms? The java.security.spec.EllipticCurve defines two methods to get the coefficients of Weierstrass form.
     public BigInteger getA()
     public BigInteger getB()

The 'A' and 'B' may not exist in other forms, for example the (3)(4)(5) forms above. While, the spec might be able to be updated by throwing UnsupportedOperationException for getA() and getB() for the (3)(4)(5) forms, and define new extended classes for new forms, like:
     public MCEllipticCurve extends EllipticCurve   // Montgomery curve
     public EDEllipticCurve extends EllipticCurve   // Edwards curve

Instead of converting, I was thinking about mapping. E.g. Montgomery A and B matches the A and B of the curve. But the "x" of the Montgomery point is just the "x" of the ECPoint with the "y" left as null. For Edwards, it looks like you would map "d" to A. For [3] I'd map "r" to A. I'd leave B as null for both- no reason to throw an unsupported exception as the code generally has a clue about what types of keys they're dealing with (or we provide a marker so they can figure it out).

The conversion in and out for points is a conversion from little endian to big endian and vice versa, but that only has to be done if you're importing or exporting a parameter set and that's an implementation issue not an API issue.

Basically, all the math is BigIntegers under the hood. The curve25519 RFC specifies an implementation that's little endian, but the actual math is just math and things like the public key is really just a BigInteger.

Old code would just continue to work - since it would not be using the new curves. New code would have to look for the curve type marker (e.g. the ECField) if there was the possibility of confusion.

However, I'm not very sure of the compatibility impact (see above).

3. Where we are not now?
Using named curves is popular. There is a ECGenParameterSpec class using named curves:
     ECGenParameterSpec​ ecgp =
         new ECGenParameterSpec​(secp256r1);
     KeyPairGenerator kpg = KeyPairGenerator.getInstance("EC");
     KeyPair kp = kpg.generateKeyPair​();

     ECPublicKey pubKey = (ECPublicKey)kp.getPublic();
     String keyAlgorithm = pubKey.getAlgorithm​();  // "EC"

However, it is used for key generation only. Once the keys are generated, there is no public API to know the name of the curve in ECKey. ECKey.getAlgorithm() will return "EC" only. If it is required to known whether a key is of a named curve, the solution is not straightforward.

This ties back to "getEncoded()" representations. Under the hood, if you do a getEncoded() there's a "which name does this parameter set match up to" search which checks various tables for an OID and uses that in an X.509 SPKI output object. On input, the table lookup has to see whether or not it understands the curve OID (or the key type OID - depending).

To deal with this without having to modify the internal parameter tables I currently match keys against parameter sets that have known OIDs.

4. A general proposal
Support named curves could be a solution for #2 and #3 concerns above. For named curves, the parameters are defined explicitly. So, it is REQUIRED to have the public APIs for named curves' parameters any more. It can be something hidden in the implementation layer. The key pair generation may looks like:

    KeyPairGenerator kpg =
    KeyPair kp = kpg.generateKeyPair​();

    PublicKey pubKey = kp.getPublic();
    String keyAlgorithm = pubKey.getAlgorithm​();  // "ECWithSecp256k1"

As no explicit parameters is required, the EllipticCurve issue for Edwards curve form and Montgomery curve form in #2 is not a issue any more here.

The compatibility impact is limited as the name "ECWithSecp256k1" is not used in the past, and the Weierstrass form APIs, like ECKey/ECParameterSpec/EllipticCurve, are not necessarily to be used in this solution.

The benefits: simplify the APIs for named curves (including the Weierstrass form), and simplify the support of named curves for Edwards curve form and Montgomery curve form.

The disadvantages: no support of arbitrary curves (no surprise as this is a named curve solution), and new learn curve to use this new solution.

Right now there are 3 major APIs (JCA, PKCS11 and Microsoft CSP) and at least 4 major representational domains (Raw, PKIX, XML and JSON). In the current situation, I can take a JCA EC Public key and convert it to pretty much any of the other APIs or representations. For much of the hardware based stuff (ie, smart cards), I go straight from JCA into raw and vice versa. Assuming you left the "getEncoded()" stuff in the API and the encoding was PKIX, I'd have to encode to PKIX, decode the PKIX to extract the actual raw key or encode a PKIX blob and hope that the KeyFactory stuff actually worked.

It's not just support of arbitrary keys, but the ability to convert things without having to do multiple steps or stages.

Your solution would probably work reasonably well for TLS or IPSEC - but would not work well for anything else.

5. Can be more aggressive?
It looks amazing to support arbitrary curves for Edwards curve form and Montgomery curve form, as JDK did for Weierstrass form. However, because of the compatibility impact (see #2), a new set of algorithms names, interfaces and specs may be required. It could be overloaded if the requirements are not so strong in practice. If arbitrary curves support is strong, it can be re-considered in the future.

Per my understanding, supporting named curves and arbitrary curves can be two things, and can be considered in different stages. However, the design needs to take care of the potential conflicts between the two solutions.

As I understand it, the JEP process takes some time and right now proposed changes *might* make it into JDK10? Do you really want to do multiple JEPs to handle multiple new Edwards and Montgomery curves?

If we can hide most of this under the current EC covers, then the implementations can just implement the plugin interface and do that now.



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