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- W4221157326 abstract "<div> The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and Adleman [19] and now called the RSA public key cryptosystem in their honor. Later, a few authors gave a simply extension of RSA over algebraic numbers field( see [20]- [22]), but they require that the ring of algebraic integers is Euclidean ring, this requirement is much more stronger than the class number one condition. In this paper, we introduce a high dimensional form of RSA by making use of the ring of algebraic integers of an algebraic number field and the lattice theory. We give an attainable algorithm (see Algorithm I below) of which is significant both from the theoretical and practical point of view. Our main purpose in this paper is to show that the high dimensional RSA is a lattice based on public key cryptosystem indeed, of which would be considered as a new number in the family of post-quantum cryptography(see [17] and [18]). On the other hand, we give a matrix expression for any algebraic number fields (see Theorem 2.7 below), which is a new result even in the sense of classical algebraic number theory.</div>" @default.
- W4221157326 created "2022-04-03" @default.
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- W4221157326 date "2022-02-11" @default.
- W4221157326 modified "2023-10-18" @default.
- W4221157326 title "On the High Dimensional RSA Algorithm—A Public Key Cryptosystem Based on Lattice and Algebraic Number Theory" @default.
- W4221157326 doi "https://doi.org/10.36227/techrxiv.19142642.v1" @default.
- W4221157326 hasPublicationYear "2022" @default.
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