A key-exchange system based on imaginary quadratic fields
Journal of Cryptology
A course in computational algebraic number theory
A course in computational algebraic number theory
REACT: Rapid Enhanced-Security Asymmetric Cryptosystem Transform
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Faster Generation of NICE-Schnorr-Type Signatures
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
An IND-CCA2 Public-Key Cryptosystem with Fast Decryption
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Efficient Implementation of Cryptosystems Based on Non-maximal Imaginary Quadratic Orders
SAC '99 Proceedings of the 6th Annual International Workshop on Selected Areas in Cryptography
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
An Efficient NICE-Schnorr-Type Signature Scheme
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Chosen-Ciphertext Security for Any One-Way Cryptosystem
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
NICE - New Ideal Coset Encryption
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Designs, Codes and Cryptography
Efficient Undeniable Signature Schemes Based on Ideal Arithmetic in Quadratic Orders
Designs, Codes and Cryptography
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
An adaptation of the NICE cryptosystem to real quadratic orders
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Factoring pq2 with Quadratic Forms: Nice Cryptanalyses
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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We describe the first polynomial time chosen-plaintext total break of the NICE family of cryptosystems based on ideal arithmetic in imaginary quadratic orders, introduced in the late 90's by Hartmann, Paulus and Takagi [HPT99]. The singular interest of these encryption schemes is their natural quadratic decryption time procedure that consists essentially in applying Euclid's algorithm. The only current specific cryptanalysis of these schemes is Jaulmes and Joux's chosen-ciphertext attack to recover the secret key [JJ00]. Originally, Hartmann et al. claimed that the security against a total break attack relies only on the difficulty of factoring the public discriminant $\Delta_q=-pq^2$, although the public key was also composed of a specific element of the class group of the order of discriminant Δ q , which is crucial to reach the quadratic decryption complexity. In this article, we propose a drastic cryptanalysis which factors Δ q (and hence recovers the secret key), only given this element, in cubic time in the security parameter. As a result, performing our cryptanalysis on a cryptographic example takes less than a second on a standard PC.