A key-exchange system based on imaginary quadratic fields
Journal of Cryptology
Handbook of Applied Cryptography
Handbook of Applied Cryptography
A World Wide Number Field Sieve Factoring Record: On to 512 Bits
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Open problems in number theoretic complexity, II
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
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
On the Security of Cryptosystems with Quadratic Decryption: The Nicest Cryptanalysis
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
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
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
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Recently, a novel public-key cryptosystem constructed on number fields is presented. The prominent theoretical property of the public-key cryptosystem is a quadratic decryption bit complexity of the public key, which consists of only simple fast arithmetical operations. We call the cryptosystem NICE (New Ideal Coset Encryption). In this paper, we consider practical aspects of the NICE cryptosystem. Our implementation in software shows that the decryption time of NICE is comparably as fast as the encryption time of the RSA cryptosystem with e = 216+1. To show if existing smart cards can be used, we implemented the NICE cryptosystem using a smart card designed for the RSA cryptosystem. Our result shows that the decryption time of NICE is comparably as fast as the decryption time of RSA cryptosystem but not so fast as in software implementation. We discuss the reasons for this and indicate requirements for smartcard designers to achieve fast implementation on smartcards.