[Cryptography] Simple provably secure stream cipher

[Bill Cox]

On Sat, Jun 6, 2015 at 12:04 AM, Bill Cox <waywardgeek at gmail.com> wrote:

> For any prime p suitable for Diffie-Hellman key agreement with group
> generator g = 2, simply generate the binary digits of fraction(2^n/p),
> where n is a shared secret.  XOR these digits over the message stream for
> both encryption and decryption.
>
> I'm ignoring issues such as the need for a unique nonce, and maliability
> defense.  The standard fixes apply.  The ability to determine n is
> trivially equivalent to solving the discrete log problem.
>
> Is this well known?  I'm pretty much finding that everything seems to be
> already known in crypto...
>
> Bill
>


Sorry!  While true that we cannot recover n, as that is DLP equivalent,
this is not a secure stream cipher at all, as only log(p) bits is enough to
determine the rest of the pattern forever.  Specifically, this is _not_
suitable as a stream cipher.  It does seem to make a pretty nice PRNG,
though too slow for practical use.

On Sat, Jun 6, 2015 at 12:04 AM, Bill Cox <waywardgeek at gmail.com> wrote:

> For any prime p suitable for Diffie-Hellman key agreement with group
> generator g = 2, simply generate the binary digits of fraction(2^n/p),
> where n is a shared secret.  XOR these digits over the message stream for
> both encryption and decryption.
>
> I'm ignoring issues such as the need for a unique nonce, and maliability
> defense.  The standard fixes apply.  The ability to determine n is
> trivially equivalent to solving the discrete log problem.
>
> Is this well known?  I'm pretty much finding that everything seems to be
> already known in crypto...
>
> Bill
>
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