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→Introduction: the cryptosystem "new hope" is always capitalized. In fact it is often written as "NewHope" but in the context here, using a space seems more appropirate |
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In 2014, Peikert presented a key-transport scheme<ref>{{Cite journal|last=Peikert|first=Chris|date=2014-01-01|title=Lattice Cryptography for the Internet|journal=Cryptology ePrint Archive |url=https://eprint.iacr.org/2014/070}}</ref> following the same basic idea of Ding's, where the new idea of sending an additional 1-bit signal for rounding in Ding's construction is also used.
The "
For somewhat greater than 128 [[bits of security]], Singh presents a set of parameters which have 6956-bit public keys for the Peikert's scheme.<ref name=":1">{{Cite journal|last=Singh|first=Vikram|date=2015|title=A Practical Key Exchange for the Internet using Lattice Cryptography|journal=Cryptology ePrint Archive |url=http://eprint.iacr.org/2015/138}}</ref> The corresponding private key would be roughly 14,000 bits. An RLWE version of the classic MQV variant of a Diffie–Hellman key exchange was later published by Zhang et al. in 2014. The security of both key exchanges is directly related to the problem of finding approximate short vectors in an ideal lattice. This article will closely follow the RLWE work of Ding in "A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem".<ref name=":0">{{Cite book|url=https://eprint.iacr.org/2012/688.pdf|title=A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem|last1=Ding|first1=Jintai|last2=Xie|first2=Xiang|last3=Lin|first3=Xiaodong|year=2012}}</ref> For this presentation a typical polynomial is expressed as:
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