On using RSA with low exponent in a public key network
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A new elliptic curve based analogue of RSA
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
New Public-Key Schemes Based on Elliptic Curves over the Ring Zn
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Partial known plaintext attack on Koyama scheme
Information Processing Letters
Partial known plaintext attack on Koyama scheme
Information Processing Letters
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This paper proposes fast RSA-type public-key schemes based on singular cubic curves y2 + axy = x3 over the ring Zn. The x and y coordinates of a 2 log n-bit long plaintext/ciphertext are transformed to a log n-bit long shadow plaintext/ciphertext by isomorphic mapping. Decryption is carried out by exponentiating this shorter shadow ciphertext over Zn. The decryption speed of the proposed schemes is about 2.0 times faster than that of the RSA scheme for a K-bit long message if [K/log n] is even. We prove that breaking each of the proposed schemes is computationally equivalent to breaking the RSA scheme in one-to-one communication circumstances. We also prove that the proposed schemes have the same security as the RSA scheme against the Hastad attack when linearly related plaintexts are encrypted i n broadcast applications.