This paper introduces a new group signature scheme and a companion identity escrow scheme that are provably secure under the strong RSA assumption and the decisional Diffie-Hellman assumption. The group signature scheme allows members to sign messages anonymously on behalf of the group, while the identity escrow scheme enables the group manager to reveal the signer's identity in case of disputes. The proposed scheme is more efficient than existing schemes, particularly in terms of the registration protocol (JOIN), which is an order of magnitude faster and statistically zero-knowledge with respect to the group member's secrets. The security of the scheme is proven under the strong RSA assumption, while the non-interactive variant relies on the Fiat-Shamir heuristic in the random oracle model. The paper also discusses the construction of the identity escrow scheme from the group signature scheme and provides a detailed analysis of its security properties, including coalition-resistance, unforgeability, anonymity, unlinkability, exculpability, traceability, and coalition-resistance.This paper introduces a new group signature scheme and a companion identity escrow scheme that are provably secure under the strong RSA assumption and the decisional Diffie-Hellman assumption. The group signature scheme allows members to sign messages anonymously on behalf of the group, while the identity escrow scheme enables the group manager to reveal the signer's identity in case of disputes. The proposed scheme is more efficient than existing schemes, particularly in terms of the registration protocol (JOIN), which is an order of magnitude faster and statistically zero-knowledge with respect to the group member's secrets. The security of the scheme is proven under the strong RSA assumption, while the non-interactive variant relies on the Fiat-Shamir heuristic in the random oracle model. The paper also discusses the construction of the identity escrow scheme from the group signature scheme and provides a detailed analysis of its security properties, including coalition-resistance, unforgeability, anonymity, unlinkability, exculpability, traceability, and coalition-resistance.