[cryptography] Supersingular Isogeny DH

Marcel tiepelt at dev-nu11.de
Thu Jul 9 02:25:23 EDT 2015


Hello,

taken the key exchange protocol De Feo, Jao and Plot in
https://eprint.iacr.org/2011/506.pdf

The public parameter are:
Elliptic curve E over finite field F_q, Torsion subgroup <P_A, Q_A> =
E[l_A] of E(F_q)

The Parameter for the key exchange for Alice are:
two random numbers m_A, n_A to compute the isogeny with kernel:
K_A := [m_A] P_A + [n_A] Q_A

So my question is, why do i need to random values m_A and n_A to compute
the torsiongroup E[l_A] and respectively the kernel K_A ?

Why does is not suffice to use only 1 point to generate E[l_A] and
Kernel K_A ?

Regards,

Marcel


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