ارائه کران بالا برای احتمال مشخصه‌های تفاضلی پنج ساختار رمز قالبی دارای امنیت اثبات‌پذیر

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه جامع امام حسین(ع)

2 دانشگاه جامع امام حسین ع

چکیده

رمزهای قالبی نقش مهم در تأمین امنیت اطلاعات و ارتباطات و پدافند الکترونیکی و سایبری دارند. یک رمز قالبی امن می‌بایست در برابر حملات شناخته‌شده مانند حمله تفاضلی امن باشد. در سال 2008 کیم و همکاران هفت ساختار رمز قالبی با ویژگی امنیت اثبات‌پذیر در برابر حمله تفاضلی ارائه کردند که از آن‌ها برای طراحی برخی رمزهای قالبی استفاده شده است. در این مقاله کران بالای مشخصه‌های تفاضلی با تعداد دورهای مختلف، برای پنج ساختار از ساختارهای ذکرشده ارائه می‌شود. برای این کار از روش تحلیل تفاضلی خودکار مبتنی بر برنامه‌ریزی خطی برای شمارش حداقل تعداد تابع­های دور فعال استفاده شده است. این روش به‌طور رسمی توسط موها و همکارانش در سال 2011 ارائه شد و تاکنون برای تحلیل و ارزیابی رمزهای قالبی متعددی به‌کار گرفته شده است. بدین ترتیب نشان داده می­شود مشخصه‌های تفاضلی پنج دوری از ساختارهای ذکرشده، کران بالای  دارند که در مقایسه با کران‌های تفاضلی ارائه‌شده توسط کیم و همکاران مورد تأیید هستند. منظور از p، مشخصه تفاضلی تابع دور مورد استفاده در این ساختارها است.

کلیدواژه‌ها


عنوان مقاله [English]

Upper Bounds for the Probability of Differential Characteristics of Five Block Cipher Constructions Functions

نویسندگان [English]

  • J. Alizadeh 1
  • Gh. Jamshidian 2
  • A. Gaeini 2
  • A. Mirghadri 2
1 دانشکده فاوا
2 IHU
چکیده [English]

Block ciphers have the main role in the communication and information security and also electronic and cyber defense. A secure block cipher must be resistant against the known attacks, such as the differential cryptanalysis. Kim et al. presented seven block cipher constructions with provable security against          differential cryptanalysis in 2008, which can be used to design the block ciphers. In this paper, for five of the seven mentioned block cipher constructions, the upper bounds on the probability of differential       characteristics have been presented. This has been done using an automated differential cryptanalysis     approach based on linear programming. This approach formally introduced by Mouha et al. in 2011, was used for the analysis of several block ciphers.  Using the Mouha et al.’s approach, it is shown that the      five-round differential characteristics of the constructions have the upper bound p < sup>4 which are approvable in comparison with the upper bounds of the differentials obtained by Kim et al. where p is the differential probability of the round function used in the constructions.
 

کلیدواژه‌ها [English]

  • Block Cipher
  • Differential Characteristic
  • Differential
  • Security Bound
  • Mixed Integer Linear Programming
 
  [1]      J. Daemen and V. Rijmen, “The design of Rijndael: AES-the advanced encryption standard,” Springer Science & Business Media, 2013.##
  [2]       T. Shirai, K. Shibutani, T. Akishita, S. Moriai, and T. Iwata, “The 128-bit blockcipher CLEFIA,” in International workshop on fast software encryption, Springer, pp. 181-195, 2007.##
  [3]      A. Bogdanov et al., “PRESENT: An                    ultra-lightweight block cipher,” in International Workshop on Cryptographic Hardware and Embedded Systems, Springer, pp. 450-466, 2007.##
  [4]      D. Hong et al., “HIGHT: A new block cipher suitable for low-resource device,” in International Workshop on Cryptographic Hardware and Embedded Systems, Springer, pp. 46-59, 2006.##
  [5]      F. Abed, C. Forler, and S. Lucks, “General classification of the authenticated encryption schemes for the CAESAR competition,” Computer Science Review, vol. 22, pp. 13-26, 2016.##
  [6]      L. Bassham, Ç. Çalık, K. McKay, N. Mouha, and M. Sönmez Turan, “Profiles for the Lightweight Cryptography Standardization Process (Retired Draft),” National Institute of Standards and Technology, 2017.##
  [7]      E. Biham and A. Shamir, “Differential cryptanalysis of DES-like cryptosystems,” Journal of CRYPTOLOGY, vol. 4, no. 1, pp. 3-72, 1991.##
  [8]      M. Matsui, “Linear cryptanalysis method for DES cipher,” in Workshop on the Theory and Application of of Cryptographic Techniques, Springer, pp.      386-397, 1993.##
  [9]      J. H. Cheon, M. Kim, K. Kim, L. Jung-Yeun, and S. Kang, “Improved impossible differential cryptanalysis of Rijndael and Crypton,” in International Conference on Information Security and Cryptology, Springer, pp. 39-49, 2001.##
[10]      A. Bogdanov and M. Wang, “Zero correlation linear cryptanalysis with reduced data complexity,” in International Workshop on Fast Software Encryption, Springer, pp. 29-48, 2012.##
[11]      J. Borghoff, L. R. Knudsen, and M. Stolpe, “Bivium as a mixed-integer linear programming problem,” in IMA International Conference on Cryptography and Coding, Springer, pp. 133-152, 2009.##
[12]      N. Mouha, Q. Wang, D. Gu, and B. Preneel, “Differential and linear cryptanalysis using mixed-integer linear programming,” in International Conference on Information Security and Cryptology, Springer, pp. 57-76, 2011.##
[13]      S. Sadeghi and N. Bagheri, “Security analysis of SIMECK block cipher against related-key impossible differential,” Information Processing Letters, vol. 147, pp. 14-21, 2019.##
[14]      S. Sadeghi, T. Mohammadi, and N. Bagheri, “Cryptanalysis of reduced round SKINNY block cipher,” IACR Transactions on Symmetric Cryptology, pp. 124-162, 2018.##
[15]      L. Sun, W. Wang, and M. Wang, “More accurate differential properties of LED64 and Midori64,” 2018.##
[16]      W. Bi, X. Dong, Z. Li, R. Zong, and X. Wang, “MILP-aided cube-attack-like cryptanalysis on Keccak Keyed modes,” Designs, Codes and Cryptography, vol. 87, no. 6, pp. 1271-1296, 2019.##
[17]      B. Zhu, X. Dong, and H. Yu, “MILP-based differential attack on round-reduced GIFT,” in Cryptographers’ Track at the RSA Conference, Springer, pp. 372-390, 2019.##
[18]      S. SADEGHI and N. BAGHERI, “Linear Cryptanalysis of Reduced-round Versions of MORUS,” 2016.##
[19]      M. Sajadieh and M. Vaziri, “Using MILP in Analysis of Feistel Structures and Improving Type II GFS by Switching Mechanism,” in International Conference on Cryptology in India, Springer, pp. 265-281, 2018.##
[20]      M. A. Abdelraheem, J. Alizadeh, H. A. Alkhzaimi, M. R. Aref, N. Bagheri, and P. Gauravaram, “Improved linear cryptanalysis of reduced-round SIMON-32 and SIMON-48,” in International Conference on Cryptology in India, Springer, pp. 153-179, 2015.##
[21]      J. Kim, C. Lee, J. Sung, S. Hong, S. Lee, and J. Lim, “Seven new block cipher structures with provable security against differential cryptanalysis,” IEICE transactions on fundamentals of electronics, Communications and computer sciences, vol. 91, no. 1, pp. 3047-3058, 2008.##
[22]      M. Matsui, “New block encryption algorithm MISTY,” in International Workshop on Fast Software Encryption, Springer, pp. 54-68, 1997.##
[23]      S. Sun et al., “Towards finding the best characteristics of some bit-oriented block ciphers and automatic enumeration of (related-key) differential and linear characteristics with predefined properties,” IACRCryptology ePrint Archive, vol. 747, p. 2014, 2014.##
[24]      S. Sun, L. Hu, P. Wang, K. Qiao, X. Ma, and L. Song, “Automatic security evaluation and (related-key) differential char