![](bga.png)
no polynomial time algorithm can discover the
original signer of σ using the component σ
1
alone.
This ensures that no group of size below t can find
the original signer of a signature σ
1
. Additionally, in
verifiable secret sharing of discrete logarithms, no set
of t − 1 or fewer users can obtain the secret l from σ
2
in polynomial time with non-negligible probability.
Hence l cannot be obtained to find the original signer
of σ
1
, unless a group of at least t users cooperate.
Hence, threshold anonymity holds for the signature
(σ
1
,σ
2
) and theorem 2 holds.
8 CONCLUSIONS AND OPEN
PROBLEMS
Step out ring signatures, introduced in (Klonowski
et al., 2008), had security flaws. We identified those
flaws present in the scheme and fixed them in order
to make it secure. We have introduced the new con-
cept of the Threshold discernible ring signature using
the corrected version of the step out ring signature.
Our scheme is proved secure under DDH assumption.
The problem of finding a scheme which is secure in
the standard model and formulating step out ring sig-
natures using bilinear groups remain open.
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