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An accumulator based on bilinear pairings was proposed at CT-RSA'05. Here, it is first demonstrated that the security model proposed by Lan Nguyen does lead to a cryptographic accumulator that is not collision resistant. Secondly, it is shown that collision-resistance can be provided by updating the adversary model appropriately. Finally, an improvement on Nguyen's identity escrow scheme, with membership revocation based on the accumulator, by removing the trusted third party is proposed.