Fix ECP leakage in Add() and Double() (GH #869, PR #871)

This check-in provides the fix for leaks in ECP's Add() and Double(). The fixes were taken from Joost Renes, Craig Costello, and Lejla Batina's [Complete addition formulas for prime order elliptic curves](https://eprint.iacr.org/2015/1060.pdf).

The Pull Request includes two additional changes that were related to testing the primary fix. First, an `AuthenticatedKeyAgreementWithRolesValidate` interface was added. It allows us to test key agreement when roles are involved. Roles are "client", "server", "initiator", "recipient", etc.

Second, `SetGlobalSeed` was added to `test.cpp` to help with reproducible results. We had code in two different places that set the seed value for the random number generator. But it was sloppy and doing a poor job since results could not be reproduced under some circumstances.

1 files changed, 36 insertions, 0 deletions

diff --git a/ecp.h b/ecp.h
index f7c919aa..dc4e86b0 100644
--- a/ecp.h
+++ b/ecp.h
@@ -106,6 +106,42 @@ public:
 	bool operator==(const ECP &rhs) const

 		{return GetField() == rhs.GetField() && m_a == rhs.m_a && m_b == rhs.m_b;}

 

+protected:

+	/// \brief Addition and Double functions

+	/// \sa <A HREF="https://eprint.iacr.org/2015/1060.pdf">Complete

+	///  addition formulas for prime order elliptic curves</A>

+	class AdditionFunction

+	{

+	public:

+		explicit AdditionFunction(const ECP& ecp);

+		// Double(P)

+		Point operator()(const Point& P) const;

+		// Add(P, Q)

+		Point operator()(const Point& P, const Point& Q) const;

+

+	protected:

+		/// \brief Parameters and representation for Addition

+		/// \details Addition and Doubling will use different algorithms,

+		///  depending on the <tt>A</tt> coefficient and the representation

+		///  (Affine or Montgomery with precomputation).

+		enum Alpha {

+			/// \brief Coefficient A is 0

+			A_0=1,

+			/// \brief Coefficient A is -3

+			A_3=2,

+			/// \brief Coefficient A is arbitrary

+			A_Star=4,

+			/// \brief Representation is Montgomery

+			A_Montgomery=8

+		};

+

+		const ECP& m_ecp;

+		Alpha m_alpha;

+

+	private:

+		AdditionFunction(const AdditionFunction&);

+	};

+

 private:

 	clonable_ptr<Field> m_fieldPtr;

 	FieldElement m_a, m_b;