A RSA-type cryptosystem based on quartic polynomials
RSA cryptosystem was introduced by Rivest. Shamir, and Adlernan 111 1978. Common users of RSA cryptosystem are currently using 1024-bit keys. They are recommended to use 2048-bit keys in 20 I I and 3072-bit key in 2031. However, increasing the bit of keys will decrease the efficiency and increase...
Saved in:
| 主要作者: | |
|---|---|
| 格式: | Thesis |
| 語言: | English |
| 出版: |
2011
|
| 主題: | |
| 在線閱讀: | http://psasir.upm.edu.my/id/eprint/84971/1/IPM%202011%2019%20ir.pdf |
| 標簽: |
添加標簽
沒有標簽, 成為第一個標記此記錄!
|
| id |
my-upm-ir.84971 |
|---|---|
| record_format |
uketd_dc |
| spelling |
my-upm-ir.849712021-12-31T03:08:12Z A RSA-type cryptosystem based on quartic polynomials 2011-04 Wong, Tze Jin RSA cryptosystem was introduced by Rivest. Shamir, and Adlernan 111 1978. Common users of RSA cryptosystem are currently using 1024-bit keys. They are recommended to use 2048-bit keys in 20 I I and 3072-bit key in 2031. However, increasing the bit of keys will decrease the efficiency and increase the cost. Therefore, the aim of this study is to analyze and implement a new cryptosystem which is more secure than RSA, LUC and LUC3 cryptosystem for same bit of keys. This cryptosystem which is called LUC.j() cryptosystem is derived 11'0111 a fourth and sixth order Lucas sequence and is based on quartic polynomial. In this research, numerous mathematical attacks will be analyzed with the cryptosystem and compared with RSA. LUC. and LUC3 cryptosystems, The numerous mathematical attacks arc Has tads attack. GCD attack, garbage-man-in the- middle (I) attack. chosen plaintext attack. garbage-man-in-the-middle (II) attack. common modulus attack. Wiener's attack. Lentras attack and faults based attack. Most of these attacks have shown that the LUCU1 cryptosystem is secure than RSA, LUe and LUC3 cryptosystems. The other attacks have shown that they are in the same security level. This is because these attacks do not result from a weakness of cryptosystem but rather from a bad implementation. The efficiency of the cryptosystem is the ability to compute e-th term of the fourth and sixth order of Lucas sequence in a reasonable period of time. Therefore. instate of computing Ve sequentially. a new algorithm will be presented to compute Vc in less away of time by omitting some terms in the calculations. By using this algorithm, the time for computations will be decreased. As a conclusion, this cryptosystem has the potential to replace the RSA cryptosystem in the future. Quartic fields Polynomials Cryptography 2011-04 Thesis http://psasir.upm.edu.my/id/eprint/84971/ http://psasir.upm.edu.my/id/eprint/84971/1/IPM%202011%2019%20ir.pdf text en public doctoral Universiti Putra Malaysia Quartic fields Polynomials Cryptography Mohd. Said, Mohamad Rushdan |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English |
| advisor |
Mohd. Said, Mohamad Rushdan |
| topic |
Quartic fields Polynomials Cryptography |
| spellingShingle |
Quartic fields Polynomials Cryptography Wong, Tze Jin A RSA-type cryptosystem based on quartic polynomials |
| description |
RSA cryptosystem was introduced by Rivest. Shamir, and Adlernan 111 1978.
Common users of RSA cryptosystem are currently using 1024-bit keys. They are
recommended to use 2048-bit keys in 20 I I and 3072-bit key in 2031. However,
increasing the bit of keys will decrease the efficiency and increase the cost.
Therefore, the aim of this study is to analyze and implement a new cryptosystem
which is more secure than RSA, LUC and LUC3 cryptosystem for same bit of keys.
This cryptosystem which is called LUC.j() cryptosystem is derived 11'0111 a fourth and
sixth order Lucas sequence and is based on quartic polynomial.
In this research, numerous mathematical attacks will be analyzed with the
cryptosystem and compared with RSA. LUC. and LUC3 cryptosystems, The
numerous mathematical attacks arc Has tads attack. GCD attack, garbage-man-in the-
middle (I) attack. chosen plaintext attack. garbage-man-in-the-middle (II) attack.
common modulus attack. Wiener's attack. Lentras attack and faults based attack. Most of these attacks have shown that the LUCU1 cryptosystem is secure than RSA,
LUe and LUC3 cryptosystems. The other attacks have shown that they are in the
same security level. This is because these attacks do not result from a weakness of
cryptosystem but rather from a bad implementation.
The efficiency of the cryptosystem is the ability to compute e-th term of the fourth
and sixth order of Lucas sequence in a reasonable period of time. Therefore. instate
of computing Ve sequentially. a new algorithm will be presented to compute Vc in
less away of time by omitting some terms in the calculations. By using this
algorithm, the time for computations will be decreased. As a conclusion, this
cryptosystem has the potential to replace the RSA cryptosystem in the future. |
| format |
Thesis |
| qualification_level |
Doctorate |
| author |
Wong, Tze Jin |
| author_facet |
Wong, Tze Jin |
| author_sort |
Wong, Tze Jin |
| title |
A RSA-type cryptosystem based on quartic polynomials |
| title_short |
A RSA-type cryptosystem based on quartic polynomials |
| title_full |
A RSA-type cryptosystem based on quartic polynomials |
| title_fullStr |
A RSA-type cryptosystem based on quartic polynomials |
| title_full_unstemmed |
A RSA-type cryptosystem based on quartic polynomials |
| title_sort |
rsa-type cryptosystem based on quartic polynomials |
| granting_institution |
Universiti Putra Malaysia |
| publishDate |
2011 |
| url |
http://psasir.upm.edu.my/id/eprint/84971/1/IPM%202011%2019%20ir.pdf |
| _version_ |
1747813507371368448 |