Y. Zheng, X. M. Zhang, GAC - the Criterion for Global Avalanche Characteristics of Cryptographic Functions, Journal for Universal Computer Science, Vol. 1 (5), pp. 316-333, 1995. Home/Search Document Details and Download
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Cross-Correlation Analysis of Cryptographically Useful Boolean.. - Sarkar (2001) (Correct)
....when f = g and gives us the following Corollary 3.1 Let f be an n variable function. Then [C f (0) C f (2 n 1) H n = W 2 f (0) W 2 f (2 n 1) This result is called the Wiener Khintchine Theorem in continuous analysis and has also been obtained for Boolean functions [2, 17, 10]. Applying the inverse transform to the cross correlation vector gives the following Corollary 3.2 Let f; g be n variable functions. Then 2 n [C f;g (0) C f;g (2 n 1) W f (0)W g (0) W f (2 n 1)W g (2 n 1) H n : 3) Applying the inverse transform with g = f , gives ....
....n 2 W 2 f (u) X u2F n 2 W 2 g (u) 2 2n 2 2n = 2 4n : From this the result follows. The above provides a bound on the sum of squares of the cross correlation coecients. It generalises the bounds on sum of squares of the auto correlation coecients obtained in Theorem 2 of [17]. Theorem 3.2 Let f; g be n variable functions and E be a subspace of F n 2 . Then X w2E W f (w)W g (w) jEj X u2E C f;g (u) Proof : Using Theorem 3.1, we can write, X w2E W f (w)W g (w) X w2E X u2F n 2 C f;g (u) 1) X u2F n 2 X w2E C f;g (u) 1) If u 2 E ....
X.-M. Zhang and Y. Zheng, GAC-the criterion for global avalanche characteristics of cryptographic functions. Journal for Universal Computer Science, volume 1. No. 5, 1995, 316-333. 16
Cryptographically Resilient Functions - Zhang, Zheng (1997) (3 citations) Self-citation (Zhang Zheng) (Correct)
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X. M. Zhang and Y. Zheng, "GAC --- the criterion for global avalanche characteristics of cryptographic functions," Journal of Universal Computer Science, vol. 1, no. 5, pp. 316--333, 1995, (available at http://hgiicm.tu-graz.ac.at/).
Characterizing the Structures of Cryptographic Functions.. - Zhang, Zheng (1996) (1 citation) Self-citation (Zhang Zheng) (Correct)
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X. M. Zhang and Y. Zheng. GAC --- the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science, 1(5):316--333, 1995. (available at http://hgiicm.tu-graz.ac.at/). 23
Auto-Correlations and New Bounds on the Nonlinearity of.. - Zhang, Zheng (1996) Self-citation (Zhang Zheng) (Correct)
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Zhang, X. M., Zheng, Y.: GAC --- the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science 1 (1995) 316--
New Bounds on the Nonlinearity of Boolean Functions - Zhang, Zheng Self-citation (Zhang Zheng) (Correct)
....4 q 2 2n j j Delta 2 min ; where Delta min = minfj Delta(ff)jjff 2 V n ; ff 6= 0g. It is easy to verify that j Delta(ff)j is divisable by four. Thus Delta(ff) 6= 0 implies j Delta(ff)j = 4. From Theorem 1, N f = 2 n Gamma1 Gamma 1 2 4 q 2 2n 16j j: From Theorem 3 of [13], if f is a non bent cubic function then Delta max = 2 1 2 (n 1) where Delta max = maxfj Delta(ff)jjff 2 V n ; ff 6= 0g. By using Theorem 2 N f = 2 n Gamma1 Gamma 1 2 q 2 n 2 1 2 (n 1) Using Theorem 3, we obtain Theorem 12 of [11] if a function f on V n satisfies ....
....based on the auto correlation of a function under consideration. This opens up a possible new avenue for future research, that is to extend the results so that they take into account other factors such as linear structures, algebraic degree and global avalanche characteristics (GAC) introduced in [13]. ....
X. M. Zhang and Y. Zheng. GAC --- the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science, 1(5):316--333, 1995. (available at http://hgiicm.tu-graz.ac.at/).
New Lower Bounds on Nonlinearity and A Class of Highly.. - Zhang, Zheng Self-citation (Zhang Zheng) (Correct)
....it satisfies the propagation criterion with respect to all ff 2 Vn with 1 W h (ff) k, where W h (ff) is the Hamming weight of ff, i.e. the number of ones in ff. f(x) Phi f(x Phi ff) is also called the directional derivative of f in the direction ff. Further work on the topic can be found in [15]. To simplify our discussions, a notation indicated by is introduced: Notation 1 Let f be a function on Vn . The set of vectors in Vn with respect to which f does not satisfy the propagation criterion is denoted by . Given two sequences a = a 1 ; am ) and b = b 1 ; b m ) ....
....and can be balanced by a linear translte. Hence the new highly nonlinear functions are more useful in practice. Further research includes the investigation of other nonlinear characteristics of this class of functions, including but not limited to algebraic degree, global avalanche characteristics [15], and correlation immunity [12] Acknowledgment The first author was supported by a Queen Elizabeth II Research Fellowship (223 23 1001) Part of the second author s work was completed while on sabbatical at the University of Tokyo. He would like to extend his thanks to Professor Hideki Imai for ....
X. M. Zhang and Y. Zheng. GAC --- the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science, 1(5):316-- 333, 1995. (available at http://hgiicm.tu-graz.ac.at/).
Characterizing the Structures of Cryptographic Functions.. - Zhang, al. (1996) (1 citation) Self-citation (Zhang Zheng) (Correct)
....by Webster and Tavares [15, 16] is equivalent to the propagation criterion of degree 1 and that the perfect nonlinearity studied by Meier and Staffelbach [6] is equivalent to the propagation criterion of degree n where n is the number of the coordinates of the function. In a relevant development [18], the authors have recently identified various limitations of the SAC and the propagation criterion. In particular, we have found that the two criteria are primarily focused on local avalanche characteristics of cryptographic functions, which would limit their usability in certain cryptographic ....
X. M. Zhang and Y. Zheng. GAC --- the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science, 1(5):316--333, 1995. (available at http://hgiicm.tu-graz.ac.at/).
Auto-Correlations and New Bounds on the Nonlinearity of.. - Zhang, Zheng (1996) Self-citation (Zhang Zheng) (Correct)
....2 min ; where Delta min = minfj Delta(ff)jjff 2 Vn ; ff 6= 0g. It is easy to verify that j Delta(ff)j is divisible by four. Thus Delta(ff) 6= 0 implies j Delta(ff)j 4. From Theorem 7, N f 2 n Gamma1 Gamma 1 2 4 p 2 2n 16j j: Now we consider another example. From Theorem 3 of [12], if f is a non bent cubic function then Delta max 2 1 2 (n 1) where Delta max = maxfj Delta(ff)jjff 2 Vn ; ff 6= 0g. Applying Theorem 10 in this paper, we have N f 2 n Gamma1 Gamma 1 2 q 2 n 2 1 2 (n 1) On the other hand, from Theorem 14 in this paper, we obtain Theorem ....
....based on the auto correlation of a function under consideration. This opens up a possible new avenue for future research, that is to extend the results so that they take into account other factors such as linear structures, algebraic degree and global avalanche characteristics (GAC) introduced in [12]. Acknowledgments: We would like to thank the anonymous referees for Eurocrypt 96 whose comments helped in improving the presentation of this paper. ....
Zhang, X. M., Zheng, Y.: GAC --- the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science 1 (1995) 316--
Cryptographically Resilient Functions - Zhang, Zheng (1997) (3 citations) Self-citation (Zhang Zheng) (Correct)
....on Vn . Then N f = min i=0; 2 n 1 Gamma1 d(f; i ) is called the nonlinearity of f . It is well known that the nonlinearity of f on Vn satisfies N f 2 n Gamma1 Gamma 2 1 2 n Gamma1 . An extensive investigation of highly nonlinear balanced functions has been carried out in [8] [9], 10] Algebraic degree and nonlinearity can also be defined for mappings or tuples of functions. Let F = f 1 ; fm ) be a function from Vn to Vm (where each f i is a function on Vn ) The algebraic degree of F , denoted by deg(F ) is defined as the minimum among the algebraic degrees of ....
X. M. Zhang and Y. Zheng, "GAC --- the criterion for global avalanche characteristics of cryptographic functions," Journal of Universal Computer Science, vol. 1, no. 5, pp. 316--333, 1995, (available at http://hgiicm.tu-graz.ac.at/).
Classification of Boolean Functions of 6 Variables.. - Braeken, Borissov, .. (2004) (Correct)
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Y. Zheng, X. M. Zhang, GAC - the Criterion for Global Avalanche Characteristics of Cryptographic Functions, Journal for Universal Computer Science, Vol. 1 (5), pp. 316-333, 1995.
Patterson-Wiedemann Construction Revisited - Gangopadhyay, Keskar, Maitra (2003) (Correct)
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X. M. Zhang and Y. Zheng. GAC - the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science, 1(5):316-333, 1995.
Minimum Distance between Bent and 1-resilient Boolean Functions - Maity, Maitra (2003) (Correct)
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X. M. Zhang and Y. Zheng. GAC - the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science, 1(5):316-333, 1995.
Highly Nonlinear Balanced Boolean Functions with very good.. - Maitra (2000) (1 citation) (Correct)
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X. M. Zhang and Y. Zheng. GAC - the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science, 1(5):316-333, 1995.
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