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Universal Dynamic Accumulators : all parties know keys p and q. Is the original set needed to validate set membership and non membership?

I read this paper on RSA cryptographic accumulators have some questions on a few points :

"Universal Accumulators with Efficient Nonmembership Proofs"
https://www.cs.purdue.edu/homes/ninghui/papers/accumulator_acns07.pdf

I noticed this from the paper :

"Note that computing witness using auxiliary information may not apply
to all scenarios. In some applications, it is not allowed to reveal
the auxiliary information to the party who computes the accumulator,
since the auxiliary data enables her to prove arbitrary statements. In
the case when the party who computes the accumulator is trusted, it is
acceptable to give her the auxiliary information."

If an untrusted party gets the p and q that make the modulus, what does it mean that mean they can prove arbitrary statements?
Does it mean that they can prove something like : any number x is both a member and a non member of the accumulator?

Also, for parties that don’t have the p and q, then deletion is not efficient correct?
I am under the impression that p and q’s properties, and using them for the deletion is what adds the efficiency in this paper.

If you have an accumulator that you haven’t put x into, and you delete x from the accumulator even though x wasn’t in it in the first place to remove
[you can do it because you have aux: p and q]
Does that let you produce a witness that you can use to prove x is a member of the accumulator?
(Witness)**x = Original Accumulator ?
Even though x was never in the accumulator to start with?
Or will it result in an “invalid” witness, because x was never in there?

I also noticed from the paper :

"In other words, it is computationally infeasible to find both a valid
membership witness and a valid nonmembership witness for any x in Xk.
Note that this is equivalent to say that, given any set X ∈ Xk, it is
computationally infeasible to find x ∈ X with a valid nonmembership
witness or find x ∈ XkX with a valid membership witness." Is this
only computationally infeasible if you don’t know the primes p and q
which make n?

I was hoping that even if you knew p and q, that it would be computationally infeasible to find both membership and non membership witnesses that satisfy, but accumulators may not have that property. i.e. like it says, can prove arbitrary statements with p and q.

My use case, is that I wanted two parties to have access to p and q, and generator g.
One party maintains the accumulator and updates it.
They send the accumulator to the second party.
The second party uses it to check the set membership of an element x
They remove x from the accumulator using subtraction
It creates an “invalid witness” that is either
not in the group
the witness and x together don’t bilinear map to the original accumulator.
I was hopeful that I could detect if x was in an accumulator just from the inputs (Accumulator, x, g, p, q) without the original set, but I am not sure if that is possible.

It would be great because it would involve only passing around the RSA accumulator which is very small.

Is there a way of doing this?
Thanks!

Cosmos: Discussing ATOM’s potential to reach $16

Disclaimer: The findings of the following analysis are the sole opinions of the writer and should not be considered investment advice. After attaining its all-time high (ATH) in January this year, Cosmos (ATOM)’s price came under fire as it succumbed to the market-wide selling pressure. In particular, April-June saw an unhindered bear run that pulled the::Listen

Disclaimer: The findings of the following analysis are the sole opinions of the writer and should not be considered investment advice.

After attaining its all-time high (ATH) in January this year, Cosmos (ATOM)’s price came under fire as it succumbed to the market-wide selling pressure. In particular, April-June saw an unhindered bear run that pulled the coin toward its 20-month low.

While the recent price movements have marked gradual growth in the last three months, ATOM flipped the 200 EMA (green) from resistance to immediate support.

The coin currently stood at a vital juncture. A rebound from the confluence of support levels could aid the token in marking a near-term rally.

But the divergences along the indicators could pose hurdles. At press time, the alt traded at $14.4, up by 4.39% in the last 24 hours. 

ATOM 4-hour Chart

 

Source: TradingView, ATOM/USDT

The rebound from ATOM’s 20-month low in June set the stage for a consistent recovery on the charts. These bullish efforts have aided the token in finding a spot above the 200 EMA. But the price was yet to fixate a solid position above the 20 EMA (red) and 50 EMA (cyan).  

The recent ascending triangle breakout gave ATOM the much-needed push to flip the $13.4 level from resistance to support. Also, during the last two months, the price action has traced out an ascending channel (white).

With the price action bouncing back from the lower trendline of the up-channel and the 200 EMA support, it could find a bull rally provided it breaches the $14.6 resistance barrier. A close above this level would open buying opportunities with a target in the $15.3-$16 range. 

Any bullish crossovers on the 20/50 EMA would affirm an increase in near-term buying strength. But an inability of the price to break above the 50 EMA and the $14.6 barrier would likely induce a slow-moving compressed phase on the charts.

A close below the up-channel and the $13.4 baseline would hint at a selling signal.   

Rationale

 

 

Source: TradingView, ATOM/USDT

The Relative Strength Index (RSI) showed gradual recovery as it approached the midline from the oversold mark. But its lower peaks have bearishly diverged with the price action.

The Awesome Oscillator (AO) resonated with the ease in selling pressure as it closed above the zero mark. If the AO maintains its spot above this mark, it could present a buying opportunity. Nevertheless, the ADX displayed a fragile directional trend for ATOM.

Conclusion

Looking at the confluence of support levels (200 EMA, lower trendline of up-channel, $13.4 level), ATOM buyers would look for a convincing rebound. But the traders should look for entry triggers and targets discussed above to accommodate a bullish invalidation.

At last, market sentiment analysis to complement these technical factors is vital for making a profitable move.

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*This article originally appeared in AMB Crypto

Recommended: Is Cosmos Poised For a ‘Giga-Pump’?

The post Cosmos: Discussing ATOM’s potential to reach $16 appeared first on CryptosRus.

Universal Dynamic Accumulators : all parties know keys p and q. Is the original set needed to validate set membership and non membership?

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