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How polynomial based encryption schemes such as NTRU encode messages in to polynomials? Is there a generic conversion?

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  • $\begingroup$ My first guess would be using a random message and deriving a symmetric key from it by hashing (e.g. using HKDF). $\endgroup$ Mar 25 '16 at 10:14
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In NTRUEncrypt, a raw message m of octet string of length l octets is encoded through the following steps:

  1. Padded it with a random salt of b byte and a few extra information to form the actual octet string M that is to be encrypted.

  2. This M byte string is then converted to a binary string Mbin using octect-string-to-binary-string-primitive (OS2BSP).

  3. In NTRUEncrypt, the message is actually a ternary polynomial, so for every 3 bits in Mbin, use a binary to ternary mapping as follows to convert it into a ternary string Mtrin.

    • {0, 0, 0} -> {0, 0}
    • {0, 0, 1} -> {0, 1}
    • {0, 1, 0} -> {0, -1}
    • {0, 1, 1} -> {1, 0}
    • {1, 0, 0} -> {1, 1}
    • {1, 0, 1} -> {1, -1}
    • {1, 1, 0} -> {-1, 0}
    • {1, 1, 1} -> {-1, 1}
  4. Finally the message polynomial m(x) is to take each element in Mtrin as the corresponding coefficient.

See section 8 for more details of conversion, and section 10.2.2 for encryption procedure. https://github.com/NTRUOpenSourceProject/ntru-crypto/blob/master/doc/EESS1-v3.1.pdf

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