Cryptographic Boolean Functions and Applications

Cryptographic Boolean Functions and Applications

Volumn , Issue , 2009, Pages 1-232

  Cusick, Thomas W ^a   Stanica, Pantelimon ^a  

^a NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYPTOGRAPHY;

BUILDING BLOCKES; CRYPTOGRAPHIC ALGORITHMS; CRYPTOGRAPHIC BOOLEAN FUNCTIONS; CRYPTOGRAPHIC SYSTEMS; DIGITAL SECURITY; FUNDAMENTAL TOOLS; JOURNAL ARTICLES;

BOOLEAN FUNCTIONS;

EID: 84942052987     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-0-12-374890-4.X0001-8     Document Type: Book

References (489)

1. Adams C.M., Tavares S.E. The structured design of cryptographically good S-boxes. J Cryptology 1990, 3:27-41.
2. Adams C.M., Tavares S.E. Generation and counting of bent sequences. IEEE Trans Inform Theory 1990, 5:1170-1173.
3. Adams C.M., Tavares S.E. Generating bent sequences. Discrete Appl Math 1992, 39:155-159.
4. Advanced Encryption Standard. Federal Information Standard 197, ; 2001. http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf.
5. Advanced Encryption Standard. Third conference, attendee feedback form, . http://csrc.nist.gov/encryption/aes/round2/conf3/AES3FeedbackForm-summary.pdf.
6. Agievich S. On the representation of bent functions by bent rectangles. In: Probabilistic methods in discrete mathematics. Proc. of the fifth international Petrozavodsk conference. p. 121-35; 2002.
7. Alexi W., Chor B., Goldreich O., Schnorr C. RSA and Rabin functions: certain parts are as hard as the whole. SIAM J Comput 1988, 17:194-209.
8. Anderson R.J. Solving a class of stream ciphers. Cryptologia 1990, 14:285-288.
9. Anderson R.J. Faster attack on certain stream ciphers. Electr Lett 1993, 29:1322-1323.
10. Anderson R. Searching for the optimum correlation attack. LNCS 1995, vol. 1008:137-143. Springer, Berlin.
11. Anderson R. On Fibonacci keystream generators. LNCS 1995, vol. 1008:346-352. Springer, Berlin.
12. Armknecht F. Improving fast algebraic attacks. LNCS 2004, vol. 3017:65-82. Springer, Berlin.
13. Armknecht F., Carlet C., Gaborit P., Kuenzli S., Meier W., Ruatta O. Efficient computation of algebraic immunity for algebraic and fast algebraic attacks. LNCS 2006, vol. 4004:147-164. Springer, Berlin.
14. Asratian A.S., Denley T.M.J., Häggkvist R. Bipartite graphs and their applications 1998, Cambridge University Press.
15. Augot D, Biryukov A, Canteaut A, Cid C, Courtois N, De Cannière C et al. D.STVL.2-AES security report. ECRYPT report, ; January 2006. http://www.ecrypt.eu.org/documents/D.STVL.2-1.0.pdf.
16. Babbage S. On the relevance of the strict avalanche criterion. Electr Lett 1990, 26(7):461-462.
17. Bakhtiari S, Safavi-Naini R, Pieprzyk JP. Cryptographic hash functions: a survey, Preprint 95-9. Department of Computer Science, The University of Wollongong; 1995.
18. Bauer C., Gottlöb E.J. Results of an automated attack on the running key cipher. Cryptologia 2005, 29:248-254.
19. Beale M., Monaghan M.F. Encryption using random Boolean functions. Proc. IMA conference on crypt. and coding. Cirencester 1986, 219-230. Oxford University Press.
20. Beauchamp K.G. Walsh functions and their applications 1975, Academic Press, New York.
21. Bellare M, Rogaway P. Introduction to modern cryptography (lecture notes), ; 2006. http://www-cse.ucsd.edu/users/mihir/cse207/classnotes.html.
22. Bending TD. Bent functions, SDP designs and their automorphism groups. Ph.D. thesis. University of London; 1993.
23. Bennett C.H., Brassard G., Robert J.-M. How to reduce your enemy's information. LNCS 1986, vol. 218:468-476. Springer, Berlin.
24. Bennett C.H., Brassard G., Robert J.-M. Privacy amplification by public discussion. SIAM J Comput 1988, 17:210-229.
25. Berlekamp E.R. Factoring polynomials over finite fields. Bell System Tech J 1967, 1853-1859.
26. Berlekamp E.R. Algebraic coding theory 1968, McGraw-Hill, New York.
27. Berlekamp E.R. Factoring polynomials over large finite fields. Math Comput 1970, 24:713-735.
28. Bernasconi A., Codenotti B. Spectral analysis of Boolean functions as a graph eigenvalue problem. IEEE Trans Comput 1999, 48:345-351.
29. Bernasconi A, Codenotti B. On Boolean functions associated to bipartite Cayley graphs. In: Workshop on Boolean problems, Freiberg; 2000, p. 167-174.
30. Bernasconi A, Codenotti B, Simon J. On the Fourier analysis of Boolean functions, preprint, 1-24, ; 1996. http://www.imc.pi.cnr.it/~codenotti/ps_files/fourier.ps.
31. Bernasconi A., Codenotti B., VanderKam J.M. A characterization of bent functions in terms of strongly regular graphs. IEEE Trans Comput 2001, 50:984-985.
32. Bernstein DJ. Which eSTREAM ciphers have been broken? manuscript; 2008.
33. Beth T., Piper F. The stop-and-go generator. LNCS 1985, vol. 209:88-92. Springer, Berlin.
34. Betke U., Wills J.M. Untere Schranken für zwei diophantische Approximations-Funktionen. Monatsh Math 1972, 76:214-217.
35. Biggs N. Algebraic graph theory 1993, Cambridge University Press. 2nd ed.
36. Biham E., Biryukov A., Shamir A. Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials. LNCS 1999, vol. 1592:12-23. Springer, Berlin.
37. Biham E., Shamir A. Differential cryptanalysis of DES-like cryptosystems. LNCS 1991, vol. 537:2-21. Springer, Berlin.
38. Biham E., Shamir A. Differential cryptanalysis of the Data Encryption Standard 1993, Springer.
39. Biss D.K. A lower bound on the number of functions satisfying the strict avalanche criterion. Discrete Math 1998, 185:29-39.
40. Black J, Rogaway P. A suggestion for handling arbitrary-length messages with the CBC MAC, Comments to NIST concerning AES modes of operation, . http://csrc.nist.gov/groups/ST/toolkit/BCM/workshops.html.
41. Blackburn S.R. The linear complexity of the self-shrinking generator. IEEE Trans Inform Theory 1999, 45:2073-2077.
42. Blöcher U., Dichtl M. Fish: a fast software stream cipher. LNCS 1994, vol. 809:41-44. Springer, Berlin.
43. Blum L., Blum M., Shub M. A simple unpredictable pseudo-random number generator. SIAM J Comput 1986, 15:364-383.
44. Blum M, Micali S. How to generate cryptographically strong sequences of pseudo-random bits. In: Proc. 23rd IEEE symposium on foundations of computer science; 1982, p. 112-17.
45. Blum M., Micali S. How to generate cryptographically strong sequences of pseudo-random bits. SIAM J Comput 1984, 13:850-864.
46. Boole G The laws of thought. Reprint of the 1854 original. With an introduction by John Corcoran. Great Books in Philosophy 2003, Prometheus Books, Amherst, NY.
47. Braeken A., Preneel B. On the algebraic immunity of symmetric Boolean functions. LNCS 2005, vol. 3797:35-48. Springer, Berlin.
48. Brands S., Gill R. Cryptography, statistics and pseudo-randomness (part I). Prob Math Stat 1995, 15:101-114.
49. Brickell EF, Denning DE, Kent ST, Mahler DP, Tuchman W. SKIPJACK review. Interim report, July 28; 1993. 8 p.
50. Brynielsson L. Below the unicity distance. In: Workshop on stream ciphers, Karlsruhe; 1989.
51. Buchberger B. Introduction to Groebner bases, logic of computation (Marktoberdorf, 1995). NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci. 1997, vol. 157:35-66. Springer, Berlin.
52. Cameron P. Random strongly regular graphs?. Electronic Notes in Discrete Mathematics 2001, vol. 10. Elsevier, Amsterdam. J. Nesetril, M. Noy, O. Serra (Eds.).
53. Camion P., Carlet C., Charpin P., Sendrier N. On correlation-immune functions. LNCS 1992, vol. 576:86-100. Springer, Berlin.
54. Campbell K.W., Wiener M.J. DES is not a group. LNCS 1992, vol. 740:512-520. Springer, Berlin.
55. Canright D. A very compact S-box for AES. LNCS 2005, vol. 3659:441-455. Springer, Berlin.
56. Canright D. A very compact Rijndael S-box, Naval Postgraduate School Technical Report: NPS-MA-05-001; 2005.
57. Canteaut A. Open problems related to algebraic attacks on stream ciphers. LNCS 2006, vol. 3969:120-134. Springer, Berlin.
58. Canteaut A., Carlet C., Charpin P., Fontaine C. Propagation characteristics and correlation-immunity of highly nonlinear Boolean functions. LNCS 2000, vol. 1807:507-522. Springer, Berlin.
59. Canteaut A, Daum H, Dobbertin H, Leander G. Normal and nonnormal bent functions. In: Coding and cryptography-WCC 2003, INRIA. p. 91-100.
60. Canteaut A., Daum H., Dobbertin H., Leander G. Finding nonnormal bent functions. Discrete Appl Math 2006, 154:202-218.
61. Canteaut A., Trabbia M. Improved fast correlation attacks using parity check equations of weight 4 and 5. LNCS 2000, vol. 1807:573-588. Springer, Berlin.
62. Cao D. Bounds on eigenvalues and chromatic numbers. Linear Alg Appl 1998, 270:1-13.
63. Carlet C. A transformation on Boolean functions, its consequences on some problems related to Reed-Muller codes. LNCS 1991, vol. 473:42-50. Springer, Berlin.
64. Carlet C. Partially-bent functions. Des Codes Cryptogr 1993, 3:135-145.
65. Carlet C. Two new classes of bent functions. LNCS 1994, vol. 765:77-101. Springer, Berlin.
66. Carlet C. Generalized partial spreads. IEEE Trans Inform Theory 1995, 41:1482-1487.
67. Carlet C. A construction of bent functions. Finite Fields Appl 1996, 233:47-58.
68. Carlet C. Recent results on binary bent functions. J Combin Inform System Sci 2000, 25:133-149.
69. Carlet C. Private communication; 1997.
70. Carlet C. More correlation-immune and resilient functions over Galois fields and Galois rings. LNCS 1997, vol. 1233:422-433. Springer, Berlin.
71. Carlet C. Sur le critère de propagation de degré l et d'ordre k. C R Acad Sci Paris Sr I Math 1998, 326:891-896.
72. Carlet C. On the propagation criterion of degree l and order k. LNCS 1998, vol. 1403:462-474. Springer, Berlin.
73. Carlet C. On cryptographic propagation criteria for Boolean functions. Inform Comput 1999, 151:32-56.
74. Carlet C. On the divisibility properties and nonlinearity of resilient functions. C R Acad Sci Paris Sr I Math 2000, 331:917-922.
75. Carlet C. A larger class of cryptographic Boolean functions via a study of the Maiorana-McFarland construction. LNCS 2002, vol. 2442:549-564. Springer, Berlin.
76. Carlet C. On the coset weight divisibility and nonlinearity of resilient and correlation-immune functions. Discrete math. theor. comput. sci. 2002, 131-144. Springer, London.
77. Carlet C. On the complexity of cryptographic Boolean functions. Finite fields with applications to coding theory, cryptography and related areas, Oaxaca, 2001 2002, 53-69. Springer, Berlin.
78. Carlet C. On the degree, nonlinearity, algebraic thickness, and nonnormality of Boolean functions, with developments on symmetric functions. IEEE Trans Inform Theory 2004, 50:2178-2185.
79. Carlet C. On the secondary constructions of resilient and bent functions. Progr. Comput. Sci. Appl. Logic 2004, vol. 2:3-28. Birkhäuser, Basel.
80. Carlet C. On the confusion and diffusion properties of Maiorana-McFarland's and extended Maiorana-McFarland's functions. J Complexity 2004, 20:182-204.
81. Carlet C. Improving the algebraic immunity of resilient and nonlinear functions and constructing bent functions, . http://eprint.iacr.org/2004/276.
82. Carlet C. Boolean functions for cryptography and error correcting codes. Available at . http://www.rocg.inria.fr/secret/Claude.Carlet/pubs.html.
83. Carlet C., Charpin P., Zinoviev V. Codes bent functions and permutations suitable for DES-like cryptosystems. Des Codes Cryptogr 1998, 15:125-156.
84. Carlet C., Dalai D.K., Gupta K.C., Maitra S. Algebraic immunity for cryptographically significant Boolean functions: analysis and construction. IEEE Trans Inform Theory 2006, 52:3105-3121.
85. Carlet C., Ding C. Highly nonlinear mappings. J Complexity 2004, 20:205-244.
86. Carlet C., Dobbertin H., Leander G. Normal extensions of bent functions. IEEE Trans Inform Theory 2004, 50:2880-2885.
87. Carlet C., Dubuc S. On generalized bent and q-ary perfect nonlinear functions. Finite fields and applications, Augsburg, 1999 2001, 81-94. Springer, Berlin.
88. Carlet C., Gouget A. An upper bound on the number of m-resilient Boolean functions. LNCS 2002, vol. 2501:484-496. Springer, Berlin.
89. Carlet C., Guillot P. A characterization of binary bent functions. J Combin Theory A 1996, 76:328-335.
90. Carlet C., Guillot P. An alternate characterization of the bentness of binary functions with uniqueness. Des Codes Cryptogr 1998, 14:133-140.
91. Carlet C, Guillot P Bent, resilient functions and the numerical normal form. DIMACS ser. discrete math. theoret. comput. sci. 2001, vol. 56:87-96. Amer. Math. Soc., Providence, RI.
92. Carlet C, Klapper A. Upper bounds on the number of resilient functions and of bent functions. In: Proc. 23rd symposium on inform. theory in the Benelux; 2002. p. 307-14.
93. Carlet C., Prouff E. On a new notion of nonlinearity relevant to multioutput pseudo-random generators. LNCS 2004, vol. 3006:291-305. Springer, Berlin.
94. Carlet C., Prouff E. Vectorial functions and covering sequences. LNCS 2004, vol. 2948:215-248. Springer, Berlin.
95. Carlet C., Sarkar P. Spectral domain analysis of correlation immune and resilient Boolean functions. Finite Fields Appl 2002, 8:120-130.
96. Carlet C., Tarannikov Y. Covering sequences of Boolean functions and their cryptographic significance. Des Codes Cryptogr 2002, 25:263-279.
97. Chabaud F., Vaudenay S. Links between differential and linear cryptanalysis. LNCS 1995, vol. 950:363-374. Springer, Berlin.
98. Chambers W.G. Clock-controlled shift registers in binary sequence generators. IEE Proc E 1988, 135:17-24.
99. Chambers W.G., Gollmann D. Lock-in effect in cascades of clock controlled shift-registers. LNCS 1988, vol. 330:331-343. Springer, Berlin.
100. Chambers W.G., Jennings S.M. Linear equivalence of certain BRM shift-register sequences. Electr Lett 1984, 20:1018-1019.
101. Charnes C., Pieprzyk J.P. Linear nonequivalence versus nonlinearity. LNCS 1993, vol. 718:156-164. Springer, Berlin.
102. Charnes C., Rötteler M., Beth T. On homogeneous bent functions. LNCS 2001, vol. 2227:249-259. Springer, Berlin.
103. Charnes C., Rötteler M., Beth T. Homogeneous bent functions, invariants and designs. Des Codes Cryptogr 2002, 26:139-154.
104. Charpin P. Normal Boolean functions. J Complexity 2004, 20:245-265.
105. Charpin P., Pasalic E. On propagation characteristics of resilient functions. LNCS 2003, vol. 2595:175-195. Springer, Berlin.
106. Chee S., Lee S., Kim K. Semi-bent functions. LNCS 1995, vol. 917:107-118. Springer, Berlin.
107. Chee S., Lee S., Kim K., Kim D. Correlation immune functions with controllable nonlinearity. ETRI J 1997, 19:389-401.
108. Chee S., Lee S., Lee D., Sung S.H. On the correlation immune functions and their nonlinearity. LNCS 1996, vol. 1123:232-243. Springer, Berlin.
109. Chepyzhov V., Johansson T., Smeets B. A simple algorithm for fast correlation attacks on stream ciphers. LNCS 2001, vol. 1978:181-195. Springer, Berlin.
110. Chepyzhov V., Smeets B. On a fast correlation attack on certain stream ciphers. LNCS 1992, vol. 547:176-185. Springer, Berlin.
111. Chor B, Goldreich O, Håstad J, Friedman J, Rudich S, Smolensky R. The bit extraction problem or t-resilient functions. In: Proc. 26th IEEE symposium on foundations of computer science; 1985, p. 396-407.
112. Chowla S., Herstein I.N., Moore K. On recursions connected with symmetric groups I. Canadian J Math 1951, 3:328-334.
113. Cid C., Murphy S., Robshaw M. An algebraic framework for cipher embeddings. LNCS 2005, vol. 3796:278-289. Springer, Berlin.
114. Cid C., Murphy S., Robshaw M. Algebraic aspects of the Advanced Encryption Standard 2006, Springer, Berlin.
115. Clark A., Golić J.D., Dawson E. A comparison of fast correlation attacks. LNCS 1997, vol. 1039:145-157. Springer, Berlin.
116. Clark J.A., Jacob J.L., Maitra S., Stănică P. Almost Boolean functions: the design of Boolean functions by spectral inversion. Comput Intelligence 2004, 20:450-462.
117. CRC handbook of combinatorial design 1996, CRC Press, Boca Raton. C.J. Colbourn, J. Dinitz (Eds.).
118. Coppersmith D. The Data Encryption Standard (DES) and its strength against attacks. IBM J Res Develop 1994, 38:243-250.
119. Coppersmith D., Krawczyk H., Mansour Y. The shrinking generator. LNCS 1994, vol. 773:22-39. Springer, Berlin.
120. Coppersmith D., Winograd S. Matrix multiplication via arithmetic progressions. J Symbolic Comput 1990, 9:251-280.
121. Courtois N. Higher order correlation attacks, XL algorithm and cryptanalysis of Toyocrypt, . http://eprint.iacr.org/2002/087.
122. Courtois N, Bard G. Algebraic cryptanalysis of the Data Encryption Standard, . http://eprint.iacr.org/2006/402.
123. Courtois N., Meier W. Algebraic attacks on stream ciphers with linear feedback. LNCS 2003, vol. 2656:345-359. Springer, Berlin.
124. Courtois N., Pieprzyk J.P. Cryptanalysis of block ciphers with overdefined systems of equations. LNCS 2002, vol. 2501:267-287. Springer, Berlin.
125. Courtois N, Meier W. Algebraic attacks on stream ciphers with linear feedback (extended version of [123]), . http://www.cryptosystem.net/stream/.
126. Cusick T.W. Boolean functions satisfying a higher order strict avalanche criterion. LNCS 1994, vol. 765:102-117. Springer, Berlin.
127. Cusick T.W. Bounds on the number of functions satisfying the strict avalanche criterion. Inform Process Lett 1996, 57:261-263.
128. Cusick T.W. On constructing balanced correlation immune functions. Springer ser. discrete math. theor. comput. sci. 1999, 184-190. Springer, London.
129. Cusick T.W., Ding C., Renvall A. Stream ciphers and number theory. North-Holland mathematical library 1998, vol. 55. North-Holland/Elsevier, Amsterdam.
130. Cusick T.W., Stănică P. Bounds on the number of functions satisfying the strict avalanche criterion. Inform Process Lett 1996, 60:215-219.
131. Cusick T.W., Stănică P. Fast evaluation, weights and nonlinearity of rotation-symmetric functions. Discrete Math 2002, 258:289-301.
132. Cvetkovic D.M., Doob M., Sachs H. Spectra of graphs 1979, Academic Press.
133. Daemen J., Rijmen V. The Design of Rijndael. AES-the Advanced Encryption Standard. Information security and cryptography 2002, Springer, Berlin.
134. Dalai D.K., Maitra S., Sarkar P. Basic theory in construction of Boolean functions with maximum possible annihilator immunity. Des Codes Cryptogr 2006, 40:41-58.
135. Dalai DK, Maitra S. Reducing the number of homogeneous linear equations in finding annihilators, . http://eprint.iacr.org/2006/032.
136. Data Encryption Standard. National Bureau of Standards, Federal Information Standard 46, USA; 1977.
137. Daum M, Dobbertin H, Leander G. An algorithm for checking normality of Boolean functions. Coding and cryptography-WCC 2003, INRIA, p. 133-42.
138. Davidoff G., Sarnak P., Valette A. Elementary number theory, group theory and Ramanujan graphs 2003, Cambridge University Press.
139. Davio M., Desmedt Y., Quisquater J.-J. Propagation characteristics of the DES. LNCS 1985, vol. 209:62-73. Springer, Berlin.
140. Davis J.A., Jedwab J. A survey of Hadamard difference sets. Groups, difference sets and the monster 1996, 145-156. de Gruyter, Berlin-New York.
141. Dawson E. Cryptanalysis of summation generator. LNCS 1993, vol. 718:209-215. Springer, Berlin.
142. Dawson E., Clark A. Divide and conquer attacks on certain classes of stream ciphers. Cryptologia 1994, 18:25-40.
143. Dawson E., Nielsen L. Automated cryptanalysis of XOR plaintext strings. Cryptologia 1996, 20:165-181.
144. de Bruijn N.G. A combinatorial problem. Nederl Akad Wetensch Proc 1946, 49:758-764. or Indagationes Math 1946;8:461-7.
145. de Cannière C., Biryukov A., Preneel B. An introduction to block cipher cryptanalysis. Proc IEEE 2006, 94:346-356.
146. de Cannière C, Preneel B. Trivium specifications. http://www.ecrypt.eu.org/stream/p3ciphers/trivium/trivium_p3.pdf.
147. Delsarte P. Four fundamental parameters of a code and their combinatorial significance. Inform Control 1973, 23:407-438.
148. Denisov O.V. An asymptotic formula for the number of correlation immune of order k Boolean functions. Discrete Math Appl 1992, 2:407-426. [translation of Russian article in Diskretnaya Matematika 3 (1991), 25-46].
149. Denisov O.V. A local limit theorem for the distribution of a part of the spectrum of a random binary function. Discrete Math Appl 2000, 12:87-101. [translation of Russian article in Diskretnaya Matematika 12 (2000), 82-95].
150. Diffie W., Hellman M. New directions in cryptography. IEEE Trans Inform Theory 1976, 22:644-654.
151. Dillon J.F. A survey of bent functions. NSA Technical Journal-unclassified 1972, 191-215.
152. Dillon JF. Elementary Hadamard difference sets. Ph.D. thesis. University of Maryland; 1974.
153. Dillon J.F. Elementary Hadamard difference sets. 6th Southeastern conf. on combinatorics, graph theory & computing 1975, 237-249.
154. Dillon JF. Private communication; 1997.
155. Dillon J.F., Dobbertin H. New cyclic difference sets with Singer parameters. Finite Fields Appl 2004, 10:342-389.
156. Ding C., Xiao G., Shan W. The stability theory of stream ciphers. LNCS 1991, vol. 561. Springer, Berlin.
157. Dobbertin H. Construction of bent functions and balanced Boolean functions with high nonlinearity. LNCS 1995, vol. 1008:61-74. Springer, Berlin.
158. Dobbertin H., Leander G. A survey of some recent results on bent functions. LNCS 2005, vol. 3486:1-29. Springer, Berlin.
159. Dobbertin H, Leander G. Cryptographer's toolkit for construction of 8-bit bent functions, . http://eprint.iacr.org/2005/089.
160. Dubuc S. Etude des propriétés de dégénérescence et de normalité des fonctions booléennes et construction de fonctions q-aires parfaitement nonlinéaires. Ph.D. thesis. Université de Caen; 2001.
161. eCRYPT-European Network of Excellence for Cryptology, . http://www.ecrypt.eu.org/index.html.
162. Erdös P, Kleitman DJ, Rothschild BL. Asymptotic enumeration of Kn-free graphs. In: Colloquio Internazionale sulle Teorie Combinatorie (Rome, 1976), Tomo II, 19-27. Atti dei Convegni Lincei, No. 17, Accad. Naz. Lincei.
163. Evertse J.-H. Linear structures in block ciphers. LNCS 1988, vol. 304:249-266. Springer, Berlin.
164. Faugère J.-C. A new efficient algorithm for computing Gröbner bases (F4). J Pure Appl Alg 1999, 139:61-88.
165. Fedorova M., Tarannikov Y. On the constructing of highly nonlinear resilient Boolean functions by means of special matrices. LNCS 2001, vol. 2247:254-266. Springer, Berlin.
166. Feistel H. Cryptography and computer privacy. Scientific American 1973, 228:15-23.
167. Ferguson N., Kelsey J., Lucks S., Schneier B., Stay M., Wagner D., et al. Improved cryptanalysis of Rijndael. LNCS 2001, vol. 1978:213-230. Springer, Berlin.
168. Ferguson N., Schroeppel R., Whiting D. A simple algebraic representation of Rijndael. LNCS 2001, vol. 2259:149-165. Springer, Berlin.
169. Filiol E., Fontaine C. Highly nonlinear balanced Boolean functions with a good correlation immunity. LNCS 1998, vol. 1403:475-488. Springer, Berlin.
170. FIPS 113. Computer data authentication. Federal Information Processing Standards Publication 113, National Bureau of Standards. Springfield, Virginia; 1994.
171. Fischer J.-B., Stern J. An efficient pseudo-random generator provably as secure as syndrome decoding. LNCS 1996, vol. 1070:245-255. Springer, Berlin.
172. Forré R. The strict avalanche criterion: spectral properties of Boolean functions and an extended definition. LNCS 1990, vol. 403:450-468. Springer, Berlin.
173. Forré R. A fast correlation attack on nonlinearly feedforward filtered shift-register sequences. LNCS 1990, vol. 434:586-595. Springer, Berlin.
174. Forré R. Methods and instruments for designing S-boxes. J Cryptology 1990, 2:115-130.
175. Fredricksen H. The lexicographically least de Bruijn cycle. J Combin Theory A 1970, 9:1-5.
176. Fredricksen H. A class of nonlinear de Bruijn cycles. J Combin Theory A 1975, 19:192-199.
177. Fredricksen H. A survey of full length nonlinear shift register cycle algorithms. SIAM Review 1982, 24:195-221.
178. Fredricksen H., Kessler I.J. An algorithm for generating necklaces of beads in two colors. Discrete Math 1986, 61:181-188.
179. Fredricksen H., Maiorana J. Necklaces of beads in k colors and k-ary de Bruijn sequences. Discrete Math 1978, 23:207-210.
180. Friedman J. On the bit extraction problem. In: Proc. 33rd IEEE symposium on foundations of computer science; 1992. p. 314-19.
181. Gallager R.G. Low-density parity-check codes 1963, MIT Press, Cambridge, MA.
182. Garey M.R., Johnson D.S. Computers and intractability: a guide to the theory of NP-completeness 1979, W. H. Freeman, San Francisco.
183. Geffe P.R. How to protect data with ciphers that are really hard to break. Electronics 1973, 46:99-101.
184. Gennaro R. An improved pseduo-random generator based on discrete log. LNCS 2000, vol. 1880:469-481. Springer, Berlin.
185. Gilbert E.N., Riordan J. Symmetry types of periodic sequences. Illinois J Math 1961, 5:657-665.
186. Gladman B. A specification for Rijndael, the AES algorithm, . http://www.techheap.com/cryptography/encryption/spec.v36.pdf.
187. Gligor VD, Donescu P. Fast encryption and authentication: XCBC Encryption and XECB Authentication Modes, Submission to NIST, . http://csrc.nist.gov/CryptoToolkit/modes/proposedmodes/index.html.
188. Godsil C.D. Problems in algebraic combinatorics. Elec J Combin 1995, # F1.
189. Golić J.D. On the security of shift register based keystream generators. LNCS 1994, vol. 809:90-100. Springer, Berlin.
190. Golić J.D. Intrinsic statistical weakness of keystream generators. LNCS 1995, vol. 917:91-103. Springer, Berlin.
191. Golić J.D. Linear cryptanalysis of stream ciphers. LNCS 1995, vol. 1008:154-169. Springer, Berlin.
192. Golić J.D. On the security of nonlinear filter generators. LNCS 1997, vol. 1039:173-188. Springer, Berlin.
193. Golić J.D. Correlation analysis of the shrinking generator. LNCS 2001, vol. 2139:440-457. Springer, Berlin.
194. Golić J.D. Vectorial Boolean functions and induced algebraic equations. IEEE Trans Inform Theory 2006, 52:528-537.
195. Golić J.D. Embedding probabilities for the alternating step generator. IEEE Trans Inform Theory 2005, 51:2543-2553.
196. Golić J.D., Menicocci R. Edit distance correlation attack on the alternating step generator. LNCS 1997, vol. 1294:499-512. Springer, Berlin.
197. Golić J.D., Menicocci R. Edit probability correlation attacks on stop/go clocked keystream generators. J Cryptology 2003, 16:41-68.
198. Golić J.D., Menicocci R. Correlation analysis of the alternating step generator. Des Codes Cryptogr 2004, 31:51-74.
199. Golić J.D., Mihaljević M.J. A generalized correlation attack on a class of stream ciphers based on the Levenshtein distance. J Cryptology 1991, 3:201-212.
200. Golić JD, Morgari G. Vectorial fast correlation attacks, . http://eprint.iacr.org/2004/247.
201. Golić J.D., O'Connor L. Embedding and probabilistic correlation attacks on clock-controlled shift registers. LNCS 1995, vol. 950:230-243. Springer, Berlin.
202. Golić J.D., Petrović S.V. A generalized correlation attack with a probabilistic constrained edit distance. LNCS 1993, vol. 658:472-476. Springer, Berlin.
203. Golić J.D., Petrović S.V. Correlation attacks on clock-controlled shift registers in keystream generators. IEEE Trans Comput 1996, 45:482-486.
204. Golić J.D., Salmasizadeh M., Dawson E. Fast correlation attacks on the summation generator. J Cryptology 2000, 13:245-262.
205. Golić J.D., Salmasizadeh M., Simpson L., Dawson E. Fast correlation attacks on nonlinear filter generators. Inform Process Lett 1997, 64:37-42.
206. Gollmann D. Pseudo random properties of cascade connections of clock controlled shift registers. LNCS 1985, vol. 209:93-98. Springer, Berlin.
207. Gollmann D. Correlation analysis of cascaded sequences. 1986 IMA conference 1989, 289-297. Clarendon Press, Oxford.
208. Gollmann D. Transition matrices of clock-controlled shift registers. Cryptography and coding III. 1991 IMA conference 1993, 197-210. Clarendon Press, Oxford.
209. Gollmann D., Chambers W.G. Clock-controlled shift registers: a review. IEEE J Selected Areas Communications 1989, 7:525-533.
210. Gollmann D., Chambers W.G. A cryptanalysis of stepk,m cascades. LNCS 1990, vol. 434:680-687. Springer, Berlin.
211. Golomb S.W. Shift register sequences 1967, Holden-Day, San Francisco, revised edition Laguna Hills, CA: Aegean Park Press; 1982.
212. Gopalakrishnan K., Stinson D.R. A short proof of the non-existence of certain cryptographic functions. J Combin Math Combin Comput 1996, 20:129-137.
213. Gordon B., Mills W.H., Welch L.R. Some new difference sets. Canadian J Math 1962, 14:614-625.
214. Göttfert R., Niederreiter H. On the linear complexity of products of shift-register sequences. LNCS 1994, vol. 765:151-158. Springer, Berlin.
215. Günther C.G. Alternating step generators controlled by de Bruijn sequences. LNCS 1988, vol. 304:5-14. Springer, Berlin.
216. Gupta KC, Sarkar P. Computing partial Walsh transform from the algebraic normal form of a Boolean function, preprint, ; 2006. http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-25.ps.
217. Haemers WH. Eigenvalue techniques in design and graph theory. Ph.D. thesis. Eindhoven University of Technology; 1979 (also found in Math. Centre Tract 121, Mathematical Centre, Amsterdam, 1980).
218. Hall M. Combinatorial theory 1967, Blaisdell, Waltham, MA.
219. Hall P., Dowling G. Approximate string matching. Computing Surveys 1980, 12:381-402.
220. Hardy G.H., Wright E.M. An introduction to the theory of numbers 1960, Clarendon Press, Oxford. 4th ed.
221. Håstad J., Schrift A., Shamir A. The discrete logarithm modulo a composite hides O(n) bits. J Computer System Sci 1993, 47:376-404.
222. Hauge E.R., Mykkeltveit J. The analysis of de Bruijn sequences of non-extremal weight. Discrete Math 1998, 189:133-147.
223. Hedayat A.S., Sloane N.J.A., Stufken J. Orthogonal arrays: theory and applications. Springer series in statistics 1999, Springer, New York.
224. Hell M., Johansson T. Two new attacks on the self-shrinking generator. IEEE Trans Inform Theory 2006, 52:3837-3843.
225. Herlestam T. On functions of linear shift register sequences. LNCS 1986, vol. 219:119-129. Springer, Berlin.
226. Hoffman A.J. On eigenvalues and colorings of graphs. Graph theory and its applications 1970, 78-91. Academic Press. B. Harris (Ed.).
227. Hou X.-D. New constructions of bent functions. J Combin Inform System Sci 2000, 25:173-189.
228. Hou X.-D. On the norm and covering radius of the first-order Reed-Muller codes. IEEE Trans Inform Theory 1997, 43:1025-1027.
229. Hou X.-D. Cubic bent functions. Discrete Math 1998, 189:149-161.
230. Hou X.-D., Langevin P. Results on bent functions. J Combin Theory A 1997, 80:232-246.
231. Huang T, You K-H. Strongly regular graphs associated with bent functions. In: Proc. 7th internat. symp. parallel architect., algo. and networks; 2004. p. 380-4.
232. Huynh D.T. A superexponential lower bound for Gröbner bases and Church-Rosser commutative Thue systems. Inform Control 1986, 68:196-206.
233. Impagliazzo R, Naor M. Efficient cryptographic schemes provably as secure as subset sum. In: Proc. 30th IEEE symposium on foundations of computer science; 1989. p. 236-41.
234. ISO/IEC 9797. Data cryptographic techniques-data integrity mechanism using a cryptographic check function employing a block cipher algorithm; 1989.
235. ISO/IEC 9797-1. Information technology-security techniques-data integrity, mechanism using a cryptographic check function employing a block cipher algorithm. International Organization for Standards, Geneva, Switzerland; 1999.
236. Iwata T, Kurosawa K. OMAC: One-key CBC MAC, submitted for consideration to NIST (available at: ); 2002. http://csrc.nist.gov/CryptoToolkit/modes/proposedmodes/ProposedModesPage.html.
237. Jakobsen T., Knudsen L. The interpolation attack on block ciphers. LNCS 1997, vol. 1267:28-40. Springer, Berlin.
238. Jennings S.M. Multiplexed sequences: some properties of the minimum polynomial. LNCS 1983, vol. 149:189-206. Springer, Berlin.
239. Johansson T. Reduced complexity correlation attacks on two clock controlled generators. LNCS 1998, vol. 1514:342-356. Springer, Berlin.
240. Johansson T., Jönsson F. Improved fast correlation attacks on stream ciphers via convolutional codes. LNCS 1999, vol. 1592:347-362. Springer, Berlin.
241. Johansson T., Jönsson F. Fast correlation attacks based on turbo code techniques. LNCS 1999, vol. 1666:181-197. Springer, Berlin.
242. Johansson T., Jönsson F. Fast correlation attacks through reconstruction of linear polynomials. LNCS 2000, vol. 1880:300-315. Springer, Berlin.
243. Jørgensen L.K., Klin M. Switching of edges in strongly regular graphs. I. A family of partial difference sets on 100 vertices. Electronic J Combin 2003, 10. # R17.
244. Jungnickel D., Pott A. Difference sets: an introduction. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 1999, vol. 542:259-295. Kluwer Acad. Publ., Dordrecht.
245. Junod P. On the complexity of Matsui's attack. LNCS 2001, vol. 2259:199-211. Springer, Berlin.
246. Junod P. Statistical cryptanalysis of block ciphers. Ph.D. thesis 3179. École Polytechnique Fédérale de Lausanne, Switzerland; 2004.
247. Kam J.B., Davida G.I. Structured design of substitution-permutation encryption networks. IEEE Trans Comput 1979, 28(10):747-753.
248. Kahn D. The codebreakers 1967, Macmillan, New York.
249. Kavut S., Maitra S., Yücel M.D. Enumeration of 9-variable rotation symmetric Boolean functions having nonlinearity >240. LNCS 2006, vol. 4329:266-279. Springer, Berlin.
250. Kavut S., Maitra S., Yücel M.D. Search for Boolean functions with excellent profiles in the rotation symmetric class. IEEE Trans Inform Theory 2007, 53:1743-1751.
251. Kavut S., Yücel D. Generalized rotation symmetric and dihedral symmetric boolean functions-9 variable Boolean functions with nonlinearity 242. LNCS 2007, vol. 4851:321-329. Springer, Berlin.
252. Kesava Menon P. Difference sets in Abelian groups. Proc AMS 1960, 11:368-377.
253. Key E.L. An analysis of the structure and complexity of nonlinear binary sequence generators. IEEE Trans Inform Theory 1976, 22:732-736.
254. Kharaghani H., Tayfeh-Rezaie B. A Hadamard matrix of order 428. J Combin Designs 2005, 13:435-440.
255. Khoo K., Gong G., Stinson D.R. A new characterization of semi-bent and bent functions on finite fields. Des Codes Cryptogr 2006, 38:279-295.
256. Kim K., Matsumoto T., Imai H. A recursive construction method of S-boxes satisfying strict avalanche criteria. LNCS 1991, vol. 537:564-574. Springer, Berlin.
257. Kim K. Construction of DES-like S-boxes based on Boolean functions satisfying the SAC. LNCS 1993, vol. 739:59-72. Springer, Berlin.
258. Kipnis A., Shamir A. Cryptanalysis of the HFE public key cryptosystem by relinearization. LNCS 1999, vol. 1666:19-30. Springer, Berlin.
259. Klapper A., Goresky M. Cryptanalysis based on 2-adic rational approximation. LNCS 1995, vol. 963:262-273. Springer, Berlin.
260. Kleiman E. The XL and XSL attacks on Baby Rijndael. Master of Science Thesis. Iowa State University, ; 2005. http://orion.math.iastate.edu/dept/thesisarchive/MS/EKleimanMSSS05.pdf.
261. Knuth D.E. The art of computer programming, vol. 2: Seminumerical algorithms 1981, Addison-Wesley, Reading, MA. 2nd ed.
262. Krause M. BDD-based cryptanalysis of keystream generators. LNCS 2002, vol. 2332:222-237. Springer, Berlin.
263. Krawczyk H. The shrinking generator: some practical considerations. LNCS 1994, vol. 809:45-46. Springer, Berlin.
264. Kumar P.V., Scholtz R.A., Welch L.R. Generalized bent functions and their properties. J Combin Theory A 1985, 40:90-107.
265. Kurosawa K., Satoh T. Design of SAC/PC(l) of order k Boolean functions and three other cryptographic criteria. LNCS 1997, vol. 1233:434-449. Springer, Berlin.
266. Lachaud G., Wolfmann J. Sommes de Kloosterman Courbes elliptique et codes cyclique en characteristique 2. C R Acad Sci Paris, Série 1 1987, 305:881-883.
267. Lai X. On the design and security of block ciphers. ETH Series in Information Processing 1992, vol. 1. Hartung-Gorre Verlag, Kostanz.
268. Lai X. Additive and linear structures of cryptographic functions. LNCS 1995, vol. 1008:75-85. Springer, Berlin.
269. Langevin P, Leander G, Rabizzoni P, Véron P, Zanotti J-P. The number of bent functions with 8 variables, . http://langevin.univ-tln.fr/project/quartics.
270. Langevin P, Rabizzoni P, Véron P, Zanotti J-P. On the number of bent functions with 8 variables. In: Boolean functions: cryptography and applications, proceedings-BFCA'06. 2006. p. 125-35.
271. Leander NG. Normality of bent functions, monomial and binomial bent functions. Ph.D. thesis. Ruhr Universität Bochum; 2004.
272. Lechner R.J. Harmonic analysis of switching functions. Recent developments in switching theory 1971, Academic Press, New York. A. Mukhopadhyay (Ed.).
273. Lee D.H., Kim J., Hong J., Han J.W., Moon D. Algebraic attacks on summation generators. LNCS 2004, vol. 3017:34-48. Springer, Berlin.
274. Lee S., Chee S., Park S., Park S. Conditional correlation attack on nonlinear filter generators. LNCS 1996, vol. 1163:360-367. Springer, Berlin.
275. Lempel A., Cohn M. Maximal families of bent sequences. IEEE Trans Inform Theory 1982, 28:865-868.
276. Lempel A., Weinberger M.J. Self-complementary normal bases in finite fields. SIAM J Discrete Math 1988, 1:193-198.
277. Defending secrets, sharing data: new locks and keys for electronic information 1993, DIANE Publishing Company. B. Leonard (Ed.).
278. Lidl R., Niederreiter H. Introduction to finite fields and their applications 1986, Cambridge University Press, Cambridge.
279. Lloyd S. Counting functions satisfying a higher order strict avalanche criterion. LNCS 1990, vol. 434:63-74. Springer, Berlin.
280. Lloyd S. Properties of binary functions. LNCS 1991, vol. 473:124-139. Springer, Berlin.
281. Lloyd S. Characterizing and counting functions satisfying the strict avalanche criterion of order (n-3). Cryptography and coding II 1992, 165-172. Clarendon Press, Oxford. C. Mitchell (Ed.).
282. Lloyd S. Counting binary functions with certain cryptographic properties. J Cryptology 1992, 5:107-131.
283. Lloyd S. Balance uncorrelatedness and the strict avalanche criterion. Discrete Appl Math 1993, 41:223-233.
284. Löhlein B. Attacks based on conditional correlations against the nonlinear filter generator, . http://eprint.iacr.org/2003/020.
285. Long D.L., Wigderson A. The discrete logarithm hides O(logn) bits. SIAM J Comput 1988, 17:363-372.
286. Machale D. George Boole: his life and work (profiles of genius series) 1985, Boole Press.
287. MacWilliams F.J., Sloane N.J.A. The theory of error-correcting codes 1978, North-Holland Publishing Company, Amsterdam.
288. Maiorana JA. A class of bent functions. R41 Technical paper. August 1970.
289. Maitra S. Highly nonlinear balanced Boolean functions with very good autocorrelation property. Electron. Notes Discrete Math. 2001, vol. 6. Elsevier, Amsterdam, 10 pages.
290. Maitra S. Highly nonlinear balanced Boolean functions with good local and global avalanche characteristics. Inform Process Lett 2002, 83:281-286.
291. Maitra S. On nonlinearity and autocorrelation properties of correlation immune Boolean functions. JISE J Inf Sci Eng 2004, 20:305-323.
292. Maitra S., Pasalic E. Further constructions of resilient Boolean functions with very high nonlinearity. Discrete Math. Theor. Comput. Sci. 2002, 265-280. Springer, London.
293. Maitra S., Pasalic E. Further constructions of resilient Boolean functions with very high nonlinearity. IEEE Trans Inform Theory 2002, 48:1825-1834.
294. Maitra S., Sarkar P. Highly nonlinear resilient functions optimizing Siegenthaler's inequality. LNCS 1999, vol. 1666:198-215. Springer, Berlin.
295. Maitra S., Sarkar P. Hamming weights of correlation immune Boolean functions. Inform Process Lett 1999, 71:149-153.
296. Maitra S., Sarkar P. Characterization of symmetric bent functions-an elementary proof. J Combin Math Combin Comput 2002, 43:227-230.
297. Maitra S., Sarkar P. Maximum nonlinearity of symmetric Boolean functions on odd number of variables. IEEE Trans Inform Theory 2002, 48:2626-2630.
298. Maitra S., Sarkar P. Cryptographically significant Boolean functions with five valued Walsh spectra. Theoret Comput Sci 2002, 276:133-146.
299. Maitra S., Sarkar P. Modifications of Patterson-Wiedemann functions for cryptographic applications. IEEE Trans Inform Theory 2002, 48:278-284.
300. Massey J.L. Shift-register synthesis and BCH decoding. IEEE Trans Inform Theory 1969, 15:122-127.
301. Massey J.L., Serconek S. A Fourier transform approach to the linear complexity of nonlinearly filtered sequences. LNCS 1994, vol. 839:332-340. Springer, Berlin.
302. Massey J.L., Serconek S. Linear complexity of periodic sequences: a general theory. LNCS 1996, vol. 1109:358-371. Springer, Berlin.
303. Matsui M., Yamagishi A. A new method for known plaintext attack of FEAL cipher. LNCS 1993, vol. 658:81-91. Springer, Berlin.
304. Matsui M. Linear cryptanalysis method for DES cipher. LNCS 1994, vol. 765:386-397. Springer, Berlin.
305. Matsui M. On correlation between the order of S-boxes and the strength of DES. LNCS 1995, vol. 950:366-375. Springer, Berlin.
306. Maximov A, Hell M, Maitra S. Plateaued rotation symmetric Boolean functions on odd number of variables. In: First Workshop on Boolean Functions: cryptography and applications (BFCA05), 2005, Rouen, France (also available at ). http://www.eprint.iacr.org/2004/144.ps.
307. Mayhew G.L. Weight class distributions of de Bruijn sequences. Discrete Math 1994, 126:425-429.
308. Mayhew G.L. Further results on de Bruijn weight classes. Discrete Math 2001, 232:171-173.
309. Mayr E.W., Meyer A. The complexity of the word problem for commutative semigroups and polynomial ideals. Adv Math 1982, 46:305-329.
310. McFarland R. A discrete Fourier theory for binary functions. R41 Technical paper; June 1971.
311. McFarland R. A family of difference sets in non-cyclic groups. J Combin Theory A 1973, 15:1-10.
312. McGrew D, Viega J. The Galois/counter mode of operation (GCM), submission to NIST modes of operation process, January 15; 2004.
313. McGrew D., Viega J. The security and performance of the Galois/counter mode (GCM) of operation. LNCS 2004, vol. 3348:343-355. Springer, Berlin.
314. McKay B.D., Spence E. Classification of regular two-graphs on 36 and 38 vertices. Australas J Combin 2001, 24:293-300.
315. Meier W., Pasalic E., Carlet C. Algebraic attacks and decomposition of Boolean functions. LNCS 2004, vol. 3027:474-491. Springer, Berlin.
316. Meier W., Staffelbach O. Fast correlation attacks on certain stream ciphers. LNCS 1989, vol. 330:301-314. Springer, Berlin.
317. Meier W., Staffelbach O. Fast correlation attacks on certain stream ciphers. J Cryptology 1988-89, 1:159-176.
318. Meier W., Staffelbach O. Nonlinearity criteria for cryptographic functions. LNCS 1990, vol. 434:549-562. Springer, Berlin.
319. Meier W., Staffelbach O. Correlation properties of combiners with memory in stream ciphers. LNCS 1991, vol. 473:204-213. Springer, Berlin.
320. Meier W., Staffelbach O. Correlation properties of combiners with memory in stream ciphers. J Cryptology 1992, 5:67-86.
321. Meier W., Staffelbach O. The self-shrinking generator. LNCS 1995, vol. 950:205-214. Springer, Berlin.
322. Menezes A.J., Van Oorschot P.C., Vanstone S.A. Handbook of applied cryptography 1997, CRC Press, Boca Raton.
323. Meng Q, Yang M, Zhang H, Cui J Discrete Math 2008, 308:5576-5584.
324. Meng Q., Zhang H., Yang M., Cui J. On the degree of homogeneous bent functions. Discrete Appl Math 2007, 155:665-669.
325. Menicocci R. Short Gollmann generators may be insecure. Codes and cyphers, cryptography and coding IV. 1993 IMA conference 1995, 281-297. Formara, Southend-on-Sea.
326. Mihaljević M.J. An approach to the initial state reconstruction of a clock-controlled shift register based on a novel distance measure. LNCS 1993, vol. 718:349-356. Springer, Berlin.
327. Mihaljević M.J. A faster cryptanalysis of the self-shrinking generator. LNCS 1996, vol. 1172:182-189. Springer, Berlin.
328. Mihaljević M.J., Fossorier M., Imai H. A low complexity and high performance algorithm for the fast correlation attack. LNCS 2001, vol. 1978:196-212. Springer, Berlin.
329. Mihaljević M.J., Fossorier M., Imai H. Fast correlation attack algorithm with list decoding and an application. LNCS 2002, vol. 2355:196-210. Springer, Berlin.
330. Mihaljević M.J., Golić J.D. A fast iterative algorithm for a shift register initial state reconstruction given the noisy output sequence. LNCS 1990, vol. 453:165-175. Springer, Berlin.
331. Mihaljević M.J., Golić J.D. A comparison of cryptanalytic principles based on iterative error-correction. LNCS 1992, vol. 547:527-531. Springer, Berlin.
332. Mihaljević M.J., Golić J.D. Convergence of a Bayesian iterative error-correction procedure on a noisy shift register sequence. LNCS 1993, vol. 658:124-137. Springer, Berlin.
333. Miranovich K. Spectral analysis of Boolean functions under nonuniformity of arguments, . http://eprint.iacr.org/2002/021.
334. Mitchell C. Enumerating Boolean functions of cryptographic significance. J Cryptology 1990, 2:155-170.
335. Modes of Operation. Workshop 1 (October 20, 2000), Baltimore, Maryland, USA, . http://csrc.nist.gov/CryptoToolkit/modes/.
336. Modes of Operation. Workshop 2 (August 24, 2001), Goleta, California, USA, . http://csrc.nist.gov/CryptoToolkit/modes/.
337. Monnerat J., Vaudenay S. On some weak extensions of AES and BES. LNCS 2004, vol. 3269:414-426. Springer, Berlin.
338. Moriai S., Shimoyama T., Kaneko T. Higher order differential attack using chosen higher order differences. LNCS 1999, vol. 1556:106-117. Springer, Berlin.
339. Murphy S., Robshaw M.J. Esential algebraic structures within the AES. LNCS 2002, vol. 2442:1-16. Springer, Berlin.
340. Murphy S, Robshaw MJ. Comments on the security of the AES and the XSL technique, September 26; 2002. http://www.isg.rhul.ac.uk/~mrobshaw/rijndael/xslnote.pdf.
341. Neumann PM A lemma that is not Burnside's. Math Scientist 1979, 4:133-141.
342. NIST. Modes of operations for symmetric block ciphers (available at: ). http://csrc.nist.gov/CryptoToolkit/modes/.
343. NIST. Request for AES proposals, . http://csrc.nist.gov/CryptoToolkit/aes/pre-round1/aes_.9709.htm.
344. Nyberg K. Construction of bent functions and difference sets. LNCS 1991, vol. 473:151-160. Springer, Berlin.
345. Nyberg K. Perfect nonlinear S-boxes. LNCS 1992, vol. 547:378-386. Springer, Berlin.
346. Nyberg K. On the construction of highly nonlinear permutations. LNCS 1992, vol. 658:92-98. Springer, Berlin.
347. Nyberg K. New bent mapping suitable for fast implementation. LNCS 1994, vol. 809:179-184. Springer, Berlin.
348. Nyberg K. S-boxes and round functions with controllable linearity and differential uniformity. LNCS 1995, vol. 1008:111-130. Springer, Berlin.
349. O'Connor L. An upper bound on the number of functions satisfying the strict avalanche criterion. Inform Process Lett 1994, 52:325-327.
350. O'Connor L., Klapper A. Algebraic nonlinearity and its application to cryptography. J Cryptology 1994, 7:213-227.
351. O'Connor JJ, Robertson EF. George Boole, . http://www.history.mcs.st-andrews.ac.uk/Biographies/Boole.html.
352. Olsen J.D., Scholtz R.A., Welch L.R. Bent-function sequences. IEEE Trans Inform Theory 1982, 28:858-864.
353. Oswald E, Daemen J, Rijmen V. AES-The state of the art of Rijndael's security. Technical report (October 30, 2002), . http://www.citeseerx.ist.psu.edu/viewdoc/summary%3Fdoi%3D10.1.1.3.164.
354. Park S.-J., Lee S.-J., Goh S.-C. On the security of the Gollmann cascades. LNCS 1995, vol. 963:148-156. Springer, Berlin.
355. Park S.M., Lee S., Sung S.H., Kim K. Improving bounds for the number of correlation immune Boolean functions. Inform Process Lett 1997, 61:209-212.
356. Pasalic E., Johansson T., Maitra S., Sarkar P. New constructions of resilient and correlation immune Boolean functions achieving upper bounds on nonlinearity. Electronic notes in discrete mathematics 2001, vol. 6. Elsevier Ltd, Amsterdam.
357. Pasalic E., Maitra S. Linear codes in generalized construction of resilient functions with very high nonlinearity. IEEE Trans Inform Theory 2002, 48:2182-2191.
358. Patarin J. Hidden fields equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms. LNCS 1996, vol. 1070:33-48. Springer, Berlin.
359. Patel S., Sundaram G.S. An efficient discrete log pseudo-random generator. LNCS 1998, vol. 1462:304-317. Springer, Berlin.
360. 15, 16) Reed-Muller code is at least 16276. IEEE Trans Inform Theory 1983, 29:354-356. see also the correction in IEEE Trans Inform Theory 36 (1990), 443.
361. Penzhorn W.T. Correlation atttacks on stream ciphers: computing low-weight parity checks based on error-correcting codes. LNCS 1997, vol. 1039:159-172. Springer, Berlin.
362. Peralta R. Simultaneous security of bits in the discrete log. LNCS 1986, vol. 219:62-72. Springer, Berlin.
363. Pieprzyk J.P. Nonlinearity of exponent permutations. LNCS 1990, vol. 434:80-92. Springer, Berlin.
364. Pieprzyk J.P. On bent permutations. Finite Fields, Coding Theory and Adv. in Communications and Computing 1993, vol. 141:173-181. Marcel Decker, New York. G.L. Mullen, P.J.-S. Shiue (Eds.).
365. Pieprzyk J.P., Qu C.X. Fast hashing and rotation-symmetric functions. J Universal Computer Science 1999, 5:20-31.
366. Piret G-F. Block ciphers: security proofs, cryptanalysis, design, and fault attacks. Ph.D. thesis. Université Catholique de Louvain, 2005.
367. Pommerening K. Fourier analysis of Boolean maps-a tutorial, manuscript, 2005 (available at: ). http://www.staff.uni-mainz.de/pommeren/Kryptologie/Bitblock/A_Nonlin/Fourier.pdf.
368. Preneel B. Analysis and design of cryptographic hash functions. Ph.D. thesis. Katholieke Universiteit Leuven, Belgium; 1993.
369. Preneel B, Biryukov A, de Cannière C, Örs SB, Oswald E, van Rompay B et al. Final report of European project IST-1999 12324. New European Schemes for Signatures, Integrity, and Encryption, . https://www.cosic.esat.kuleuven.be/nessie/.
370. Preneel B., Govaerts R., Vandewalle J. Boolean functions satisfying higher order propagation criteria. LNCS 1992, vol. 547:141-152. Springer, Berlin.
371. Preneel B., Van Leekwijck W., Van Linden L., Govaerts R., Vandewalle J. Propagation characteristics of Boolean functions. LNCS 1991, vol. 473:161-173. Springer, Berlin.
372. Prömel H.J., Schickinger T., Steger A. A note on triangle-free and bipartite graphs. Discrete Math 2002, 257:531-540.
373. Qu C., Seberry J., Pieprzyk J.P. On the symmetric property of homogeneous Boolean functions. LNCS 1999, vol. 1587:26-35. Springer, Berlin.
374. Qu C., Seberry J., Pieprzyk J.P. Homogeneous bent functions. Discrete Appl Math 2000, 102:133-139.
375. Ralston A. De Bruijn sequences-a model example of the interaction of discrete mathematics and computer science. Math Mag 1982, 55:131-143.
376. Rao C.R. Factorial experiments derivable from combinatorial arrangements of arrays. J Roy Statist Soc 1947, 9:128-139.
377. Ritter T. A variable size core for block cipher cryptography, cipher blocks of arbitrary size with good data diffusion (available at: ). http://www.ciphersbyritter.com/VSBCCORE.HTM.
378. Rivest R.L. The RC5 encryption algorithm. LNCS 1995, vol. 1008:86-96. Springer, Berlin.
379. Rivest RL. Block encryption algorithm with data dependent rotation. US patent #5, 724, 428, issued on March 3, 1998.
380. Rivest RL, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems. MIT Memo MIT/LCS/TM-82; 1977.
381. Rivest R.L., Shamir A., Adleman L. A method for obtaining digital signatures and public key cryptosystems. Comm ACM 1978, 21:120-126.
382. Rodier F. Sur la non-linéarité des fonctions booléennes. Acta Arithmetica 2004, 115:1-22.
383. Rodier F. Asymptotic nonlinearity of Boolean functions. Coding and cryptography-WCC 2003, INRIA, p. 397-405.
384. Rosen K. Elementary number theory and its applications 2000, Pearson Addison Wesley. 4th ed.
385. Rothaus O.S. On bent functions. J Combin Theory A 1976, 20:300-305.
386. Rotman J. An introduction to the theory of groups 1995, Springer.
387. Rueppel R.A. Correlation immunity and the summation generator. LNCS 1986, vol. 218:260-272. Springer, Berlin.
388. Rueppel RA Analysis and design of stream ciphers. Springer communications and control engineering series 1986, Springer, Berlin.
389. Rueppel R.A. Stream ciphers. Contemporary cryptology: the science of information integrity 1992, 65-134. IEEE Press, Chapter 2 in [427].
390. Rueppel R.A., Staffelbach O.J. Products of linear recurring sequences with maximum complexity. IEEE Trans Inform Theory 1987, 33:124-131.
391. Ruskey F., Sawada J. An efficient algorithm for generating necklaces with fixed density. SIAM J Comput 1999, 29:671-684.
392. Sağdic{ogonek}oğlu S. Cryptological viewpoint of Boolean functions. Ph.D. thesis. The Middle East Technical University; 2003.
393. Sakthivel G. Differential cryptanalysis of substitution permutation networks and Rijndael-like ciphers. Master's project report, Rochester Institute of Technology, Department of Computer Science; 2005.
394. Sarkar P. A note on the spectral characterization of Boolean functions. Inform Process Lett 2000, 74:191-195.
395. Sarkar P., Maitra S. Nonlinearity bounds and constructions of resilient Boolean functions. LNCS 2000, vol. 1880:515-532. Springer, Berlin.
396. Sarkar P., Maitra S. Construction of nonlinear Boolean functions with important cryptographic properties. LNCS 2000, vol. 1807:485-506. Springer, Berlin.
397. Sarkar P., Maitra S. Cross-correlation analysis of cryptographically useful Boolean functions and S-boxes. Theory Comput Syst 2002, 35:39-57.
398. Sarkar P., Maitra S. Construction of nonlinear resilient Boolean functions using 'small' affine functions. IEEE Trans Inform Theory 2004, 50:2185-2193.
399. Savard J. The Advanced Encryption Standard (Rijndael), . http://www.quadibloc.com/crypto/co040401.htm.
400. Savicky P. On the bent Boolean functions that are symmetric. European J Combin 1994, 15:407-410.
401. Schneeweiss W.G. Boolean functions with engineering applications and computer programs 1989, Springer.
402. Schneider M. A note on the construction and upper bounds of correlation-immune functions. LNCS 1997, vol. 1355:295-306. Springer, Berlin.
403. Schneider M. On the construction and upper bounds of balanced and correlation-immune functions. Selected Areas Crypt 1997, 73-87.
404. Schneier B. Applied cryptography 1996, John Wiley & Sons. 2nd ed.
405. Schnorr CP. The multiplicative complexity of Boolean functions. In: Applied algebra, algebr. algorithms and error-correcting codes, Italy; 1988.
406. Seberry J., Xia T., Pieprzyk J.P. Construction of cubic homogeneous Boolean bent functions. Australas J Combin 2000, 22:233-245.
407. Seberry J., Zhang X.-M. Highly nonlinear 0-1 balanced Boolean functions satisfying strict avalanche criterion. LNCS 1993, vol. 718:145-155. Springer, Berlin.
408. Seberry J., Zhang X.-M., Zheng Y. On construction and nonlinearity of correlation immune functions. LNCS 1994, vol. 765:181-199. Springer, Berlin.
409. Seberry J., Zhang X.-M., Zheng Y. Improving the strict avalanche characteristics of cryptographic functions. Inform Process Lett 1994, 50:37-41.
410. Seberry J., Zhang X.-M., Zheng Y. Nonlinearly balanced functions and their propagation characteristics. LNCS 1994, vol. 773:49-60. Springer, Berlin.
411. Seberry J., Zhang X.-M., Zheng Y. Relationships among nonlinearity criteria. LNCS 1995, vol. 950:389-398. Springer, Berlin.
412. Seberry J., Zhang X.-M., Zheng Y. Nonlinearity and propagation characteristics of balanced Boolean functions. Inform Comput 1995, 119:1-13.
413. Segers AJM. Algebraic attacks from a Gröbner basis perspective. Master's Thesis. Technische Universiteit Eindhoven, Netherlands; 2004.
414. Selmer E.S. Linear recurrence relations over finite fields, 1965 Cambridge University lecture notes 1966, Dept. of Math., University of Bergen, Bergen, Norway.
415. Selmer E.S. From the memoirs of a Norwegian cryptologist. LNCS 1994, vol. 765:142-150. Springer, Berlin.
416. Shamir A., Patarin J., Courtois N., Klimov A. Efficient algorithms for solving overdefined systems of multivariate polynomial equations. LNCS 2000, vol. 1807:392-407. Springer, Berlin.
417. Shannon C.E. A mathematical theory of communication. Bell System Tech J 1948, 27:379-423. 623-56.
418. Shannon C.E. Communication theory of secrecy systems. Bell System Tech J 1949, 28:656-715.
419. Claude Elwood Shannon: collected papers 1993, IEEE Press, NY, (with a profile of Shannon by Anthony Liversidge). N.J.A. Sloane, A.D. Wyner (Eds.).
420. Shoup V. A computational introduction to number theory and algebra 2005, Cambridge University Press.
421. Shrikhande S.S. The uniqueness of the L2 association scheme. Ann Math Statist 1959, 30:781-798.
422. Siegenthaler T. Correlation immunity of nonlinear combining functions for cryptographic applications. IEEE Trans Inform Theory 1984, 30:776-780.
423. Siegenthaler T. Decrypting a class of stream ciphers using ciphertext only. IEEE Trans Comput 1985, 34:81-85.
424. Siegenthaler T. Cryptanalysts representation of nonlinearly filtered ML sequences. LNCS 1986, vol. 219:103-110. Springer, Berlin.
425. Siegenthaler T. Design of combiners to prevent divide and conquer attacks. LNCS 1986, vol. 218:273-279. Springer, Berlin.
426. Simon M.K., Omura J.K., Scholtz R.A., Levitt B.K. Spread spectrum communications 1985, vol. 1. Computer Science Press, Rockville, MD.
427. Contemporary cryptology: the science of information integrity 1992, IEEE Press. G.J. Simmons (Ed.).
428. Simpson L., Golić J., Dawson E. A probabilistic correlation attack on the shrinking generator. LNCS 1998, vol. 1438:147-158. Springer, Berlin.
429. Simpson L., Golić J., Salmasizadeh M., Dawson E. A fast correlation attack on multiplexer generators. Inform Process Lett 1999, 70:89-93.
430. Skiena S. Implementing discrete mathematics: combinatorics and graph theory with Mathematica 1990, Addison-Wesley, Reading, MA.
431. Sloane N.J.A. On single-deletion-correcting codes. Codes and designs-Ray-Chaudhuri festschrift 2002, 273-292. de Gruyter. K.T. Arasu, Á. Seress (Eds.).
432. Song B., Seberry J. Further observations on the structure of the AES algorithm. LNCS 2003, vol. 2887:223-234. Springer, Berlin.
433. Stallings W. Cryptography and network security 2006, Prentice Hall. 4th ed.
434. Stănică P. Chromos, Boolean functions and avalanche characteristics. Ph.D. thesis. State University of New York at Buffalo; 1998.
435. Stănică P. Nonlinearity, local and global avalanche characteristics of balanced Boolean functions. Discrete Math 2002, 248:181-193.
436. Stănică P. Graph eigenvalues and Walsh spectrum of Boolean functions. In: Combinatorial number theory, de Gruyter. In: Proc. of the 'Integers Conference 2005' in celebration of the 70th birthday of Ron Graham, Carrollton, Georgia, 431-42. (Appeared also in Integers-J. Combinatorial Number Theory 7(2), Art. 32).
437. Stănică P. On the nonexistence of homogeneous rotation symmetric bent Boolean functions of degree greater than two. In: Proceedings of NATO adv. stud. instit.-Boolean functions; 2008. p. 214-8.
438. Stănică P., Maitra S. A constructive count of rotation symmetric functions. Inform Process Lett 2003, 88:299-304.
439. Stănică P., Maitra S. Rotation symmetric Boolean functions-count and cryptographic properties. Discrete Appl Math 2008, 156:1567-1580. preliminary version appeared in Electronic Notes in Discrete Math 15 (2003), 141-7.
440. Stănică P., Maitra S., Clark J. Results on rotation symmetric bent and correlation immune Boolean functions. LNCS 2004, vol. 3017:161-177. Springer, Berlin.
441. Stănică P., Sung S.H. Improving the nonlinearity of certain balanced Boolean functions with good local and global avalanche characteristics. Inform Process Lett 2001, 79:167-172.
442. Stănică P., Sung S.H. Boolean functions with five controllable cryptographic properties. Des Codes Cryptogr 2004, 31:147-157.
443. Steel A. Gröbner basis timings page, ; 2004. http://magma.maths.usyd.edu.au/users/allan/gb.
444. Stinson D.R. Resilient functions and large sets of orthogonal arrays. Congr Numer 1993, 92:105-110.
445. Stinson D.R. Cryptography, theory and practice 2006, Chapman & Hall/CRC, Boca Raton. 3rd ed.
446. Strassen V. Gaussian elimination is not optimal. Numer Math 1969, 13:354-356.
447. Tarannikov Y. On resilient Boolean functions with maximal possible nonlinearity. LNCS 2000, vol. 1977:19-30. Springer, Berlin.
448. Tarannikov Y. Spectral analysis of high order correlation immune functions, preprint 2000.
449. Tarannikov Y. New constructions of resilient Boolean functions with maximal nonlinearity. LNCS 2002, vol. 2355:66-77. Springer, Berlin.
450. Tarannikov Y., Korolev P., Botev A. Autocorrelation coefficients and correlation immunity of Boolean functions. LNCS 2001, vol. 2248:460-479. Springer, Berlin.
451. Toli I., Zanoni A. Looking inside AES and BES. Proc. 18th IFIP world computer congress (TCS 2004) 2004, 23-36. Kluwer, USA. J.-J. Levy, E.W. Mayr, J.C. Mitchell (Eds.).
452. U.S. Senate, Select Committee on Intelligence. Unclassified summary: involvement of NSA in the development of the data encryption standard; 1978.
453. Vaudenay S. On the need for multipermutations: cryptanalysis of MD4 and SAFER. LNCS 1995, vol. 1008:286-297. Springer, Berlin.
454. Vazirani UV. Towards a strong communication complexity theory or generating quasi-random sequences from two communicating slightly random sources. In: Proc. 17th symposium on theory of computing; 1985. p. 366-78.
455. Vazirani UV, Vazirani VV. Efficient and secure pseudo-random number generation. In: Proc. 25th IEEE symposium on foundations of computer science; 1984. p. 458-63.
456. Vazirani U.V., Vazirani V.V. Efficient and secure pseudo-random number generation. LNCS 1985, vol. 196:193-202. Springer, Berlin.
457. Webster A.F., Tavares S.E. On the design of S-boxes. LNCS 1986, vol. 218:523-534. Springer, Berlin.
458. Weinmann R-P. Evaluating algebraic attacks on the AES. Diplomarbeit, Darmstadt University, Germany; 2004.
459. Weisstein EW. Hadamard matrix. Mathworld-a Wolfram web resource. http://mathworld.wolfram.com/HadamardMatrix.html.
460. Wiener MJ. Efficient DES key search. Technical report TR-244 (School of Computer Science, Carleton University, Ottawa, Canada), May 1994. Presented at the Rump Session of Crypto' 93.
461. Wiener M.J. Efficient DES key search-an update. CryptoBytes 1998, 3(2):6-8.
462. Wikipedia. http://en_wikipedia.org/wiki/Data_Encryption_Standard.
463. Wikipedia. http://enwikipedia.org/wiki/Linearfeedbackshiftregister.
464. Wilf H.S. The eigenvalues of a graph and its chromatic number. J London Math Soc 1967, 42:330-332.
465. Xia T., Seberry J., Pieprzyk J.P., Charnes C. Homogeneous bent functions of degree n in 2n variables do not exist for n>3. Discrete Appl Math 2004, 142:127-132.
466. Xiang Q. Recent progress in algebraic design theory. Finite Fields Appl (ten year anniversary edition) 2005, 11:622-653.
467. Xiao G.-Z., Massey J.L. A spectral characterization of correlation-immune combining functions. IEEE Trans Inform Theory 1988, 34:569-571.
468. Yang Y.X., Guo B. Further enumerating Boolean functions of cryptographic significance. J Cryptology 1995, 8:115-122.
469. Yao A. Theory and applications of trapdoor functions. In: Proc. 23rd IEEE symposium on foundations of computer science; 1982. p. 80-91.
470. Yarlagadda R., Hershey J.E. A note on the eigenvectors of Hadamard matrices of order 2n. Linear Algebra & Appl 1982, 45:43-53.
471. Yarlagadda R., Hershey J.E. Analysis and synthesis of bent sequences. IEE Proc E 1989, 136:112-123.
472. Youssef A.M., Cusick T.W., Stănică P., Tavares S.E. New bounds on the number of functions satisfying the strict avalanche criterion. Selected Areas Crypt 1996, 49-56.
473. Youssef A.M., Tavares S.E. Comment on Bounds on the number of functions satisfying the strict avalanche criterion (1996). Inform Process Lett 1996, 60:271-275.
474. Yu N.Y., Gong G. Constructions of quadratic bent functions in polynomial forms. IEEE Trans Inform Theory 2006, 52:3291-3299.
475. Zeng K., Huang M. On the linear syndrome method in cryptanalysis. LNCS 1990, vol. 403:469-478. Springer, Berlin.
476. Zeng K., Yang C.H., Rao T.R.N. On the linear consistency test (LCT) in cryptanalysis with applications. LNCS 1990, vol. 435:164-174. Springer, Berlin.
477. Zeng K., Yang C.H., Rao T.R.N. An improved linear syndrome algorithm in cryptanalysis with applications. LNCS 1991, vol. 537:34-47. Springer, Berlin.
478. Zenner E., Krause M., Lucks S. Improved cryptanalysis of the self-shrinking generator. LNCS 2001, vol. 2119:21-35. Springer, Berlin.
479. Zhang J.-Z., You Z.-S., Li Z.-L. Enumeration of binary orthogonal arrays of strength 1. Discrete Math 2001, 239:191-198.
480. Zhang X.-M., Zheng Y. Cryptographically resilient functions. IEEE Trans Inform Theory 1997, 43:1740-1747.
481. Zhao Y., Li H. On bent functions with some symmetric properties. Discrete Appl Math 2006, 154:2537-2543.
482. Zheng Y., Zhang X.-M. Improved upper bound on the nonlinearity of high order correlation immune functions. LNCS 2001, vol. 2012:262-274. Springer, Berlin.
483. Zheng Y., Zhang X.-M. New results on correlation immune functions. LNCS 2001, vol. 2015:49-63. Springer, Berlin.
484. Zheng Y., Zhang X.-M. On relationships among avalanche, nonlinearity and correlation immunity. LNCS 2000, vol. 1976:470-482. Springer, Berlin.
485. Zheng Y., Zhang X.-M. On plateaued functions. IEEE Trans Inform Theory 2001, 47:1215-1223.
486. Zheng Y., Zhang X.-M., Imai H. Restriction, terms and nonlinearity of Boolean functions. Theoret Comput Sci 1999, 226:207-223.
487. Zierler N. Linear recurring sequences. J Soc Industr Appl Math (SIAM) 1959, 7:31-48.
488. Zierler N., Mills W.H. Products of linear recurring sequences. J Algebra 1973, 27:147-157.
489. Živković M. An algorithm for the initial state reconstruction of the clock controlled shift register. IEEE Trans Inform Theory 1991, 37:1488-1490.