Re: IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION

From	Peter Pearson <pkpearson@nowhere.invalid>
Newsgroups	sci.crypt
Subject	Re: IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION
Date	2021-10-02 15:34 +0000
Message-ID	<irrcgkFam13U1@mid.individual.net> (permalink)
References	<sj4sts$1fie$1@gioia.aioe.org> <irop5nFpr0vU1@mid.individual.net> <sj9p51$5mq$1@gioia.aioe.org>

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On Sat, 2 Oct 2021 09:08:16 -0500, 711 Spooky Mart <711@spooky.mart> wrote:
> On 10/1/21 10:52 AM, Peter Pearson wrote:
>> On Thu, 30 Sep 2021 12:43:16 -0500, 711 Spooky Mart <711@spooky.mart> wrote:
>>>
>>> https://eprint.iacr.org/2014/335
[snip]
>> 
>> As best I can tell (the presentation is awfully muddled), the
>> public key is a multiplier "Sara" and a modulus "Bra", and message M is
>> encrypted as
>> 
>>   e = (M * Sara) mod Bra
>> 
>> while the private key is another multiplier "Sbr" and another modulus "B",
>> and ciphertext is decrypted as
>> 
>>   d = (e * Sbr) mod B.
>> 
>> This algorithm is so far from being cryptographically sound that
>> I'm afraid I must be missing some big, obvious, April-fools-day
>> joke.
>
[snip]
>
> The cryptosystem is based on the DH idea of hidden subgroup membership,
> then the trap door is a combination of factoring composites (easy to do)
> combined with exponentiation and addition of exponents (hard to do).
> Prime numbers are not required for key generation. The exponentiation
> and addition obfuscate the subgroup relationship between the numbers so
> that discrete logarithm can't be computed with the usual algorithms. How
> would one prove this is less hard than factoring RSA/Rabin semiprimes?

Is my description of the encryption and decryption processes wrong?
I took those two lines straight from the paper, but maybe I missed
some explanation about how this wasn't the real algorithm.

If my description of the algorithm is wrong, please present the
correct algorithm.  

If my description is correct, please provide sample values for
e, Sara, and Bra, and I will either tell you what M is, or
demonstrate that there is no unique decryption of e.

-- 
To email me, substitute nowhere->runbox, invalid->com.

Thread

IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION 711 Spooky Mart <711@spooky.mart> - 2021-09-30 12:43 -0500
  Re: IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION Peter Pearson <pkpearson@nowhere.invalid> - 2021-10-01 15:52 +0000
    Re: IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION 711 Spooky Mart <711@spooky.mart> - 2021-10-02 05:41 -0500
    Re: IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION 711 Spooky Mart <711@spooky.mart> - 2021-10-02 09:08 -0500
      Re: IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION Peter Pearson <pkpearson@nowhere.invalid> - 2021-10-02 15:34 +0000
        Re: [BORKED] IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION 711 Spooky Mart <711@spooky.mart> - 2021-10-04 16:25 -0500
          Re: [BORKED] IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION Peter Pearson <pkpearson@nowhere.invalid> - 2021-10-05 15:20 +0000
            Re: [BORKED] IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION 711 Spooky Mart <711@spooky.mart> - 2021-10-05 14:26 -0500
              Re: [BORKED] IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION Peter Pearson <pkpearson@nowhere.invalid> - 2021-10-05 20:32 +0000

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