Re: IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION

From	711 Spooky Mart <711@spooky.mart>
Newsgroups	sci.crypt
Subject	Re: IACR eprint: SHADOW NUMBERS PUBLIC KEY ENCRYPTION
Date	2021-10-02 05:41 -0500
Organization	Aioe.org NNTP Server
Message-ID	<sj9cue$gmm$1@gioia.aioe.org> (permalink)
References	<sj4sts$1fie$1@gioia.aioe.org> <irop5nFpr0vU1@mid.individual.net>

Show all headers | View raw

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
>>
>> This interesting, simple cryptosystem looks easy to implement in
>> software. Does anyone know of any analysis on it? How does it scan on
>> first impression?
> 
> 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.

Here's the patent:
https://patents.google.com/patent/US8811606B2/en?inventor=John+Almeida&page=2

I didn't see how it was awfully muddled. The presentation seemed very
clear and straightforward, without unnecessary and arcane verbiage. I
believe the author is Portuguese, but did well enough with his English
that I could follow his train of thought.  I was able to implement it in
Python in a few minutes from first reading.

It appears to divide up the DLP and factoring to two sets so the
attacker must solve both DLP and hidden subset composite factoring to
break it. How is it cryptographically unsound?

-- 
███████████████████████████████████
█░░░░░░░░░░░█░░░░░░░░███░░░░░░░░███
█░░███████░░█░░████░░███░░████░░███        [chan] 711
█░░░░░░░██░░█░░░░██░░███░░░░██░░███        spooky mart
██████░░██░░███░░██░░█████░░██░░███        always open
██████░░██░░███░░██░░█████░░██░░███        stay spooky
██████░░██░░█░░░░██░░░░█░░░░██░░░░█        https://bitmessage.org
██████░░██░░█░░██████░░█░░██████░░█
██████░░░░░░█░░░░░░░░░░█░░░░░░░░░░█
███████████████████████████████████

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

csiph-web