Una evidencia robusta de que el algoritmo DES fortalecido con una permutación inicial variable es eficiente
A Robust Evidence of the DES Algorithm Strengthened by a Variable Initial Permutation being Efficient
Rolando Flores Carapia, Víctor Manuel Silva García, Cornelio Yáñez Márquez y Oscar Camacho Nieto
Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico Nacional, México rfcarapia@yahoo.com , vsilvag@ipn.mx, www.cidetec.ipn.mx
]]> Centro de Investigación en Computación, Instituto Politécnico Nacional, México cyanez@cic.ipn.mx, oscarc@cic.ipn.mx, www.cornelio.org.mx , www.cic.ipn.mx
Artículo recibido el 15/12/2010.
Aceptado el 24/10/2011.
Resumen
Utilizando el Teorema JV se puede asociar un numero de tamaño 1089 a una permutación de 64 posiciones en 63 pasos, este resultado se aplicó para reforzar DES mediante una permutación inicial variable, con lo cual se incrementa la complejidad computacional del algoritmo, ya que cada permutación trabaja como una llave. Sin embargo, aun queda pendiente saber cómo actúan la permutación inicial variable y la llave de 56 bits, con relación a la complejidad computacional del algoritmo. En esta investigación, se dará luz al problema anterior, en el sentido de que se propondrá un esquema de Monte Carlo usando el modelo del "Birthday" para el cálculo de probabilidades.
Palabras clave: Teorema JV, modelo birthday, DES, modelo de decisión de Monte Carlo, permutación variable.
Abstract
]]> By using the JV Theorem, it is possible to associate a number of size 1089 to a 64 position permutation in 63 steps. This result has been applied to strengthening the DES algorithm by using a variable initial permutation, increasing the computational complexity of the algorithm, given that each permutation works as a key. However, it still remains to be seen how the variable initial permutation and the 56 bit key work regarding the computational complexity of the algorithm. In the current work, the former question is addressed by proposing a Monte Carlo scheme using the Birthday model for the probability calculation.Keywords. JV theorem, birthday model, DES, Monte Carlo decision model, variable permutation.
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Referencias
1. Bailey, D.H. (2011). A Compendium of BBP-Type Formulas for Mathematical Constants. Retrieved from http://crd.lbl.gov/~dhbailey/dhbpapers/bbp-formulas.pdf. [ Links ]
2. Bailey, D.H., Plouffe, S.M., Borwein, P.B., & Borwein, J.M. (1997). The Quest for Pi. The Mathematical Intelligencer, 19(1), 50–56. [ Links ]
]]>3. Biham, E. & Shamir, A. (1993). Differential cryptanalysis of the full 16-round DES. Advances in Cryptology-CRYPTO' 92. Lecture Notes inComputer Science, 740, 487–496. [ Links ]
4. Daemen, J. & Rijmen, V. (2001). Advances Encryption Standard (AES), FIPS 197. [ Links ]
5. Data Encryption Standard (DES), FIPS PUB 46-2, 1993. [ Links ]
6. Data Encryption Standard (DES), FIPS PUB 46-3, 1999. [ Links ]
7. Elgamal, T. (1985). A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, 31(4), 469–472. [ Links ]
]]>8. Gentle, J.E. (2003). Random Number Generation and Monte Carlo Methods (2nd ed.). New York: Springer. [ Links ]
9. Gómez, A. (2006). Enciclopedia de la Seguridad Informatica. Alfaomega: Mexico. [ Links ]
10. Matsui, M. (1994). Linear Cryptanalysis Method for DES cipher. Advances in Cryptology-EUROCRYPT'93. Lecture Notes in Computer Science, 765, 386–397. [ Links ]
11. Rivest, R.L., Shamir, A., & Adleman, L. (1978). A method for obtaining digital signatures and Public-key cryptosystems. Communications of the ACM, 21(2), 120–126. [ Links ]
12. Rosen, K.H. (2003). Discrete Mathematics and its Applications (5th ed.). Boston: McGraw Hill. [ Links ]
]]>13. Silva, V.M., Flores, G.R., López, I., & Rentería, C. (2010). Algorithm for Strengthening Some Cryptographic Systems. Journal of Applied Mathematical Sciences, 4(20), 967–976. [ Links ]
14. Spivak, M. (1997). Calculus: Cálculo Infinitesimal (2nd ed.). Barcelona: Reverté [ Links ].
15. Stinson, D.R. (2002). Cryptography: Theory and practice (2nd ed.). Boca Raton: Chapman & Hall/ CRC. [ Links ]
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