A New RSA-type Scheme Based on Singular Cubic Curves : y^2+axy≡x^3(mod n)

概要

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In 1991, an RSA-type scheme over elliptic curves E^^~(a^^~, b^^~):y^2≡x^3+a^^~x+b^^~(mod n), I. E. non-singularcubic curves, was presented by Koyama, Maurer, Okamoto and Vanstone. This scheme, the KMOV scheme for short, is more secure than the RSA scheme against the Hastad attack. A decryption speed of the KMOV scheme is 5.8 times slower than that of the RSA scheme. By changing the base from elliptic curves to singular cubic curves E_n(a,b):y^2+axy≡x^3+bx^2(mod n), this paper proposes a faster RSA-type scheme based on curves y^2+axy≡x^3(mod n). 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 Z_n instead of a sequential addition of the points over singular cubic curves E_n.
社団法人電子情報通信学会の論文
1995-03-27