TY - GEN
T1 - Equivalent keys of a nonlinear filter generator using a power residue symbol
AU - Kodera, Yuta
AU - Taketa, Yuki
AU - Kusaka, Takuya
AU - Nogami, Yasuyuki
AU - Uehara, Satoshi
N1 - Funding Information:
Acknowledgment. This work was partly supported by a JSPS KAKENHI Grant-in-Aid for Scientific Research Challenging Research (Pioneering) 19H05579.
Publisher Copyright:
© Springer Nature Switzerland AG 2020.
PY - 2020
Y1 - 2020
N2 - The existence of equivalent keys for a secret key is an inseparable topic in cryptography. Especially for pseudorandom number generators for cryptographic applications, equivalent keys are not only a specific pair of keys that generate the same sequence but includes the one that gives simply the phase-shifted sequence. In this paper, the authors especially focus on a kind of nonlinear filter generator (NLFG) defined by using a power residue calculation over an odd characteristic. Generally speaking, an evaluation of NLFGs has conducted by the randomness of the sequence itself and the security of keys. Though the previous evaluations of the randomness of the target NLFG are studied and proven theoretically, the security aspects as a cryptosystem still have not discussed. Therefore, this paper would like to begin a new security evaluation by focusing on the existence of equivalent keys for the NLFG. As a result, the authors first show that sequences generated by the NLFG are classified into several types of sequences depending on the choice of a certain parameter. Owing to this, it is found that there exist equivalent keys concerning the parameter corresponding to the above. At the same time, we show that the equivalent keys are possible to eliminate by giving the restriction on the corresponding parameter adequately.
AB - The existence of equivalent keys for a secret key is an inseparable topic in cryptography. Especially for pseudorandom number generators for cryptographic applications, equivalent keys are not only a specific pair of keys that generate the same sequence but includes the one that gives simply the phase-shifted sequence. In this paper, the authors especially focus on a kind of nonlinear filter generator (NLFG) defined by using a power residue calculation over an odd characteristic. Generally speaking, an evaluation of NLFGs has conducted by the randomness of the sequence itself and the security of keys. Though the previous evaluations of the randomness of the target NLFG are studied and proven theoretically, the security aspects as a cryptosystem still have not discussed. Therefore, this paper would like to begin a new security evaluation by focusing on the existence of equivalent keys for the NLFG. As a result, the authors first show that sequences generated by the NLFG are classified into several types of sequences depending on the choice of a certain parameter. Owing to this, it is found that there exist equivalent keys concerning the parameter corresponding to the above. At the same time, we show that the equivalent keys are possible to eliminate by giving the restriction on the corresponding parameter adequately.
KW - Equivalent keys
KW - Multi-value NTU sequence
KW - Nonlinear filter generator
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U2 - 10.1007/978-3-030-58208-1_2
DO - 10.1007/978-3-030-58208-1_2
M3 - Conference contribution
AN - SCOPUS:85091067002
SN - 9783030582074
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 23
EP - 36
BT - Advances in Information and Computer Security - 15th International Workshop on Security, IWSEC 2020, Proceedings
A2 - Aoki, Kazumaro
A2 - Kanaoka, Akira
PB - Springer Science and Business Media Deutschland GmbH
T2 - 15th International Workshop on Security, IWSEC 2020
Y2 - 2 September 2020 through 4 September 2020
ER -