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I am a little confused about why it is believed to be secure against quantum attacks, couldn't the hash function be attacked? Yes, the attacker could attack the hash function, for example, by trying to find a second preimage (and there are known Merkle Signature Schemes where we can show that forging a signature can be reduced to the second preimage ...


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Yes, a stateless hashbased signature method called Sphincs was recently proposed. It works by having a moderately large Merkle tree (similar to what D.W. suggested), but instead of using Lamport or Winternitz one time signatures at the bottom, it uses a hash based few-time signature method; this allows an occasional collision at the very bottom of the tree. ...


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The inventors of the Supersingular Isogeny Key Exchange, Defeo, Jao and Plut have posted some code on GITHUB at: https://github.com/defeo/ss-isogeny-software/ There is also a paper on implementation of this key exchange by some people from the University of Waterloo. Their paper is "Efficient Implementations of A Quantum-Resistant Key-Exchange Protocol on ...


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Since the time you asked your question some new algorithms have shown great promise. The first set of algorithms are based on the Learning with Errors Problem in over polynomial rings. See http://www.cc.gatech.edu/~cpeikert/pubs/suite.pdf There is also an elliptic curve scheme based around supersingular elliptic curve isogenies. There's a Wikipedia ...


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There is a very easy way to get Perfect Forward Secrecy with the Post Quantum Security of NTRU (if you believe NTRU is secure). However it requires TWO exchanges of information. During Exchange 1 both parties generate and exchange ephemeral NTRU keys. During Exchange 2 both parties generate random numbers and encrypt their random numbers with the other ...


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The Wikipedia Article on Post Quantum Cryptography has the following to say about symmetric algorithm quantum resistance: Symmetric Key Quantum Resistance[edit] Provided one uses sufficiently large key sizes, the symmetric key cryptographic systems like AES and SNOW 3G are already resistant to attack by a quantum computer.[20] Further, key management ...


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Two approaches to Post Quantum Key Exchange that have acceptable bandwidth requirements are the NTRU/Ring-LWE lattice designs and the ECC Isogeny Key exchange you mention. Since the UK spy agency published an attack on a lattice based scheme they had designed, there has been an active discussion between Dan Bernstein and the Lattice Cryptographers over the ...


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The Supersingular Elliptic Curve Isogeny Key Exchange that you refer to was first published in 2011 by DeFeo, Jao, and Plut. It builds on but is quite distinct from earlier work by Rostovetsev and Stolbunov in 2006. As a Post Quantum/Quantum Safe replacement for Elliptic Curve Diffie-Hellman (ECDH) it has several good properties: The number of bits that ...



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