Unstructured Inversions of New Hope

Introduced as a new protocol implemented in “Chrome Canary” for the Google Inc. Chrome browser, “New Hope” is engineered as a postquantum key exchange for the TLS 1.2 protocol. The structure of the exchange is a combination of elliptic curve enhancements along with revised lattice-based cryptography. New Hope incorporates the key-encapsulation mechanism of Peikert which itself is a modified Ring-LWE scheme. The search space used to introduce the closest-vector problem is generated by an intersection of a tesseract and hexadecachoron, or the l∞-ball and l1-ball respectively. This intersection results in the 24-cell V of lattice D4̃. With respect to the density of the Voronoi cell V, the proposed mitigation against backdoor attacks proposed by the authors of New Hope may not withstand such attempts if enabled by a quantum computer capable of implementing Grover’s search algorithm.