On algebraic immunity of trace inverse functions on finite fields of characteristic two

Feng, Xun‐Li; Gong, Guang

doi:10.1007/s11424-016-5208-z

Cited by 2 publications

(3 citation statements)

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“…Theorem 3 [ 18 ] Let Tr ( λx –1 ) be the trace inverse function over finite fields

F_{2^{n}}

, where n ≥ 2,

λ \in {double-struckF}_{2^{n}}

and λ ≠ 0. We have

A I (Tr (λ x^{‐ 1})) = ⌊ \sqrt{n} ⌋ + ⌈\frac{n}{⌊ \sqrt{n} ⌋}⌉ ‐ 2 = ⌈ 2 \sqrt{n} ⌉ ‐ 2

where AI (Tr( λx –1 )) denotes the algebraic immunity of Tr( λx –1 ).…”

Section: Two Spectra Attacks On the Stream Cipher Based On Guessmentioning

confidence: 99%

“…In Ref. [ 18 ], Feng and Gong proved that the trace inverse function over finite fields with characteristic two is not a Boolean function with the optimal algebraic immunity.…”

Section: Two Spectra Attacks On the Stream Cipher Based On Guessing T...mentioning

confidence: 99%

“…Theorem 3 [18] Let Tr(λx −1 ) be the trace inverse function over finite fields F 2 n , where n ≥ 2, λ ∈ F 2 n and λ ̸ = 0. We have…”

Section: Tr(smentioning

confidence: 99%

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Security Analysis of A Stream Cipher with Proven Properties

Gao

Li²

2021

Chinese J of Electronics

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Si and Ding proposed a stream cipher with two keys (the first and the second key) and an expected security strength. To further measure the security, we analyze the stream cipher by considering the selective discrete Fourier spectra attack and the fast selective discrete Fourier spectra attack. The two attacks reveal a fact that the second key is more important than the first key, that is, if the second key is leaked out, the first key can be obtained with a lower time complexity than that of the expected security. In addition, we analyze the ability of the stream cipher to resist the guess‐and‐determine attack. The results show an attacker is able to gain the two keys with an exponentially improved time complexity and a polynomial data complexity. It implies that we need a securer permutation over finite fields to design a new binary additive stream cipher to achieve the expected security level.

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“…Theorem 3 [ 18 ] Let Tr ( λx –1 ) be the trace inverse function over finite fields

F_{2^{n}}

, where n ≥ 2,

λ \in {double-struckF}_{2^{n}}

and λ ≠ 0. We have

A I (Tr (λ x^{‐ 1})) = ⌊ \sqrt{n} ⌋ + ⌈\frac{n}{⌊ \sqrt{n} ⌋}⌉ ‐ 2 = ⌈ 2 \sqrt{n} ⌉ ‐ 2

where AI (Tr( λx –1 )) denotes the algebraic immunity of Tr( λx –1 ).…”

Section: Two Spectra Attacks On the Stream Cipher Based On Guessmentioning

confidence: 99%

“…In Ref. [ 18 ], Feng and Gong proved that the trace inverse function over finite fields with characteristic two is not a Boolean function with the optimal algebraic immunity.…”

Section: Two Spectra Attacks On the Stream Cipher Based On Guessing T...mentioning

confidence: 99%