A New RSA-Type Scheme Based on Singular Cubic Curves (y-αx)(y-βx)<cd02261.gif>x3(mod n)

Hidenori KUWAKADO; Kenji KOYAMA

A New RSA-Type Scheme Based on Singular Cubic Curves (y-αx)(y-βx)x³(mod n)

Hidenori KUWAKADO, Kenji KOYAMA

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This paper proposes a new RSA-type scheme over non-singular parts of singular cubic curves E_n(α,β):(y-αx)(y-βx)x³(mod n). In usual one-to-one communication, we prove that breaking the proposed scheme is not easier than breaking the RSA scheme for the whole ciphertexts. If encryption key e is larger than 19 for 512 bits modulus n, then the proposed scheme is secure against the Hastad attack in broadcast applications. A plaintext of two blocks, i.e., x and y coordinates in E_n(α,β), is encrypted to a ciphertext of three blocks, where the size of one block is log₂n bits. The decryption speed ofthe proposed scheme is as fast as that of the RSA scheme for the even block plaintext.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.1 pp.49-53

Publication Date: 1996/01/25

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Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)

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Hidenori KUWAKADO, Kenji KOYAMA, "A New RSA-Type Scheme Based on Singular Cubic Curves (y-αx)(y-βx)x3(mod n)" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 1, pp. 49-53, January 1996, doi: .
Abstract: This paper proposes a new RSA-type scheme over non-singular parts of singular cubic curves E_n(α,β):(y-αx)(y-βx)x³(mod n). In usual one-to-one communication, we prove that breaking the proposed scheme is not easier than breaking the RSA scheme for the whole ciphertexts. If encryption key e is larger than 19 for 512 bits modulus n, then the proposed scheme is secure against the Hastad attack in broadcast applications. A plaintext of two blocks, i.e., x and y coordinates in E_n(α,β), is encrypted to a ciphertext of three blocks, where the size of one block is log₂n bits. The decryption speed ofthe proposed scheme is as fast as that of the RSA scheme for the even block plaintext.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e79-a_1_49/_p

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@ARTICLE{e79-a_1_49,
author={Hidenori KUWAKADO, Kenji KOYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New RSA-Type Scheme Based on Singular Cubic Curves (y-αx)(y-βx)x3(mod n)},
year={1996},
volume={E79-A},
number={1},
pages={49-53},
abstract={This paper proposes a new RSA-type scheme over non-singular parts of singular cubic curves E_n(α,β):(y-αx)(y-βx)x³(mod n). In usual one-to-one communication, we prove that breaking the proposed scheme is not easier than breaking the RSA scheme for the whole ciphertexts. If encryption key e is larger than 19 for 512 bits modulus n, then the proposed scheme is secure against the Hastad attack in broadcast applications. A plaintext of two blocks, i.e., x and y coordinates in E_n(α,β), is encrypted to a ciphertext of three blocks, where the size of one block is log₂n bits. The decryption speed ofthe proposed scheme is as fast as that of the RSA scheme for the even block plaintext.},
keywords={},
doi={},
ISSN={},
month={January},}

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TY - JOUR
TI - A New RSA-Type Scheme Based on Singular Cubic Curves (y-αx)(y-βx)x3(mod n)
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 49
EP - 53
AU - Hidenori KUWAKADO
AU - Kenji KOYAMA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 1996
AB - This paper proposes a new RSA-type scheme over non-singular parts of singular cubic curves E_n(α,β):(y-αx)(y-βx)x³(mod n). In usual one-to-one communication, we prove that breaking the proposed scheme is not easier than breaking the RSA scheme for the whole ciphertexts. If encryption key e is larger than 19 for 512 bits modulus n, then the proposed scheme is secure against the Hastad attack in broadcast applications. A plaintext of two blocks, i.e., x and y coordinates in E_n(α,β), is encrypted to a ciphertext of three blocks, where the size of one block is log₂n bits. The decryption speed ofthe proposed scheme is as fast as that of the RSA scheme for the even block plaintext.
ER -