Formalization of the Data Encryption Standard

Hiroyuki Okazaki; Yasunari Shidama

doi:10.2478/v10037-012-0016-y

.blurhash-client-img { display: none !important; }

Formalization of the Data Encryption Standard

Formalized Mathematics

Volume 20 (2012): Issue 2 (June 2012)

By: Hiroyuki Okazaki and Yasunari Shidama

Open Access

|Feb 2013

Abstract

In this article we formalize DES (the Data Encryption Standard), that was the most widely used symmetric cryptosystem in the world. DES is a block cipher which was selected by the National Bureau of Standards as an official Federal Information Processing Standard for the United States in 1976 [15].

References

[1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
Search in Google Scholar
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
Search in Google Scholar
[3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
Search in Google Scholar
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
Search in Google Scholar
[5] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
Search in Google Scholar
[6] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. FormalizedMathematics, 1(3):529-536, 1990.
Search in Google Scholar
[7] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
Search in Google Scholar
[8] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
Search in Google Scholar
[9] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
Search in Google Scholar
[10] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
Search in Google Scholar
[11] Czesław Bylinski. Some properties of restrictions of finite sequences. Formalized Mathematics, 5(2):241-245, 1996.
Search in Google Scholar
[12] Shunichi Kobayashi and Kui Jia. A theory of Boolean valued functions and partitions. Formalized Mathematics, 7(2):249-254, 1998.
Search in Google Scholar
[13] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.
Search in Google Scholar
[14] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.
Search in Google Scholar
[15] U.S. Department of Commerce/National Institute of Standards and Technology. Fips pub 46-3, data encryption standard (DES). http://csrc.nist.gov/publications/fips/-fips46-3/fips46-3.pdf. Federal Information Processing Standars Publication, 1999.
Search in Google Scholar
[16] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
Search in Google Scholar
[17] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
Search in Google Scholar
[18] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.
Search in Google Scholar
[19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
Search in Google Scholar
[20] Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.
Search in Google Scholar
[21] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
Search in Google Scholar
[22] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Search in Google Scholar