Signature schemes based on the strong RSA assumption
CCS '99 Proceedings of the 6th ACM conference on Computer and communications security
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Statistical Zero Knowledge Protocols to Prove Modular Polynomial Relations
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
The Gap-Problems: A New Class of Problems for the Security of Cryptographic Schemes
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
Logics for Reasoning about Cryptographic Constructions
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A composable cryptographic library with nested operations
Proceedings of the 10th ACM conference on Computer and communications security
A probabilistic polynomial-time process calculus for the analysis of cryptographic protocols
Theoretical Computer Science
Reconciling Two Views of Cryptography (The Computational Soundness of Formal Encryption)
Journal of Cryptology
Note: A simple transitive signature scheme for directed trees
Theoretical Computer Science
The Group of Signed Quadratic Residues and Applications
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Journal of Cryptology
Collision-free accumulators and fail-stop signature schemes without trees
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Adaptive security of symbolic encryption
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
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Rivest (TCC 2004) explored the notion of a pseudo-free group from cryptographic perspective. He made the conjecture that the RSA group $\mathbb{Z}_{N}^{*}$ is a plausible pseudo-free group. Daniele Micciancio proved that (to appear in Journal of Cryptology), under strong RSA assumption, $\mathbb{Z}_{N}^{*}$ is pseudo-free. The proof uses the fact that N is the product of two safe primes, and elements are sampled uniformly at random from the subgroup QR N of quadratic residues. He asked whether the proof can be carried over if elements are sampled uniformly at random from the whole of $\mathbb{Z}_{N}^{*}$. In this article, we show that one can sample uniformly at random from the subgroup $QR_{N}^{+}$ of signed quadratic residues to prove that $\mathbb{Z}_{N}^{*}$ is pseudo-free. Consequently, we believe one can show $\mathbb{Z}_{N}^{*}$ pseudo-free where elements are sampled from $QR_{N} \cup QR_{N}^{+}$, thus enlarging the set from which elements are sampled.