A TENSOR-THEORETIC ENHANCEMENT TO THE HILL CIPHER SYSTEM

The Hill matrix algorithm[3], published in 1929, is known for being the first purely algebraic cryptographic system and for starting the entire field of algebraic cryptology. In this paper, an operator derived from ring isomorphism theory is adapted for use in the Hill system which greatly increases the block size that a matrix can encrypt; specifically, a k×k invertible matrix over Z _n represents an invertible matrix of order k ³, which produces ciphertext blocks k ²-times as long as the original matrix could. This enhancement increases the Hill system's security considerably.     

AN EXTENSION OF HILL CIPHER USING GENERALISED INVERSES AND mth RESIDUE MODULO n

Hill Cipher is a symmetric polyalphabetic block cipher that enciphers a string of letters into another string of the same length using the linear transformation y=xK. In deciphering, the determinant value must be less than 26 and relatively prime to 26 so that the matrix K of the linear transformation is invertible in modulo 26. The Affine Hill cipher extends the concept of Hill cipher by using the non-linear transformation y=xK+b. In this paper, we extend this concept to encrypt a plaintext of blocksize m to a ciphertext of blocksize n≥m using (a) affine transformation and (b) polynomial transformation to make this cipher more secure. Here the matrix K of the transformation need not be a square matrix. To enable decryption, we state the conditions to be satisfied by K which are as follows. Case (a): (i) For affine transformation, the generalised inverse K ⁺ of the matrix K corresponding to the transformation should satisfy the equation KK ⁺=I in modulo p where p is a chosen prime p>26. For m=n, K ⁺ is the usual inverse of the matrix K. Case(b): (i) For polynomial transformation, the generalised inverse K ⁺ should satisfy the above condition, (ii) If r is the degree of the polynomial, then choose those values of s≤r such that the sth root of modulo p exists for all elements in Z _p . In other words, choose those values of s that are relatively prime to Φ(p).     

HOW STATISTICS LED THE GERMANS TO BELIEVE ENIGMA SECURE AND WHY THEY WERE WRONG: NEGLECTING THE PRACTICAL MATHEMATICS OF CIPHER MACHINES

Only in 1974 did German intelligence and cryptologists admit that the Enigma cipher machine was not, and had not been, a secure system. Throughout World War II, German experts relied on a theoretical statistical security that took neither wartime operational reality nor their opponents' years of attention and attack into account. They ignored the far more important operational weaknesses and human errors that actually provided enemy cryptanalysts with their most valuable entries into the cipher system.     

A STATISTICAL ATTACK ON THE RUNNING KEY CIPHER

The frequencies of n-graphs, groups of n letters, for n as large as 6 are compiled and used to launch a statistical attack on a running key cipher. Programs written in C++ make the calculations possible. The results of the attack for various values of n are analyzed.     

RESULTS OF AN AUTOMATED ATTACK ON THE RUNNING KEY CIPHER

ABSTRACT

The running key cipher uses meaningful text as the key. Since the message also consists of meaningful text, the result is obtained by combining valid words. Automated attacks can find all such combinations that yield a given ciphertext. The results of these attacks are presented in this paper.     

HOW TO USE THE GERMAN ENIGMA CIPHER MACHINE: A PHOTOGRAPHIC ESSAY

Abstract

Alexander von Kryha (1891–1955) dedicated at least 15 years of his life to encryption machines of his own development. His machines competed with the Enigma in the 1920s and with Hagelin's machines in the 1950s, but they were much too weak cryptographically to succeed. It is the tragedy of Alexander von Kryha that he made a huge effort in marketing his machines, but did not realize that he was dealing with one of the poorest designs ever. In 1955 Kryha committed suicide, while his company went bankrupt.     

LEX算法的输出位置分析

LEX算法是进入eSTREAM计划第三阶段的一个候选算法,该算法的基本思想是从AES算法中输出一部分中间状态作为LEX算法的密钥流。研究输出位置对LEX算法的安全性影响,考察输出位置在奇数轮和偶数轮相同的情况下LEX算法的安全性,利用猜测决定攻击对该LEX算法进行分析,在已知236.3字节的密钥流序列的条件下,仅需要281.4轮LEX加密就可完全恢复128比特初始密钥,远远小于对LEX算法的现有分析结果。该结果表明,现有LEX算法的输出位置的选择是合理的。     

THE MEMORIA TECHNICA CIPHER

A comprehensive analysis of the ciphers invented by Charles L. Dodgson (Lewis Carroll) and how he used them indicate that his Memoria Technica (1875), a variant of a mnemonic scheme first proposed by Richard Grey in 1730, is properly viewed as Dodgson's fifth cipher system. He used his Memoria Technica cipher as a tool in work that was never published, a projected book whose working title was “Logarithms by Lightning: A Mathematical Curiosity.” The logarithms project, a joint work with his colleague, Robert Edward Baynes, is examined in detail.     

MA4210 ALPHANUMERIC POCKET CIPHER

Abstract

Vigenère ciphers can be broken, if the key length is known. In trying to break the Vigenère cipher, Charles Babbage and Friedrich Wilhelm Kasiski found the length of the key by searching for periodical repetitions in the ciphertext to split the cipher into multiple Caesar ciphers. William Friedman's, “index of coincidence,” also requires an adequate length of the ciphertext to retrieve the key length. Both methods lack, if the ciphertext is short or does not include repetitions and no other effective linguistic solution to break short Vigenère ciphers is known. Massively decreasing the solution space by logic, reverse digram frequency, and language properties allows breaking short and long Vigenère ciphers with and without repetitions.     

A RECONSTRUCTION OF THE KEY TO BEALE CIPHER NUMBER TWO

A reconstruction of the key used to encrypt B2 (Beale Cipher Number 2) reveals greater statistical anomalies in Bl than previously reported by Gillogly [8]. The 1885 pamphlet versions of the ciphers are used in this analysis. Several explanations of these anomalies are discussed. The application of artificial intelligence techniques to automated cryptanalysis of the Beale Ciphers is discussed.     

THE TWO-MESSAGE PROBLEM IN CIPHER TEXT AUTOKEY. PART II

This is Part II of a two-part paper on the problem of the title. In this part the analysis of the two-message problem started in Part I is completed. In addition a brief discussion is given of a computer-assisted solution. A list of twelve two-message problems involving several types of conditions is attached for the benefit of the reader.     

CRYPTOLOGY AND THE LAW

Abstract

Skipjack is a block cipher designed by the NSA for use in US government phones, and commercial mobile and wireless products by AT&;T. Among its initial implementations in hardware were the Clipper chip and Fortezza PC cards, which have since influenced the private communications market to be compatible with this technology. For instance, the Fortezza card comes in PCMCIA interface and is a very easy plug-n-play device to add on to mobile and wireless systems to provide encryption for wireless transmissions. Initially classified when it was first proposed, Skipjack was declassified in 1998, and it sparked numerous security analyses from security researchers worldwide because it provides insight into the state-of-the-art security design techniques used by a highly secretive government intelligence agency such as the NSA. In this paper, commemorating a decade since Skipjack's public revelation, we revisit the security of Skipjack, in particular its resistance to advanced differential-style distinguishers. In contrast to previous work that considered conventional and impossible differential distinguishers, we concentrate our attention on the more recent advanced differential-style and related-key distinguishers that were most likely not considered in the original design objectives of the NSA. In particular, we construct first-known related-key impossible differential, rectangle and related-key rectangle distinguishers of Skipjack. Our related-key attacks (i.e., related-key miss-in-the-middle and related-key rectangle attacks) are better than all the previous related-key attacks on Skipjack. Finally, we characterize the strength of Skipjack against all these attacks and motivate reasons why, influenced by the Skipjack structure, some attacks fare better. What is intriguing about Skipjack is its simple key schedule and a structure that is a cross between conventional Feistel design principles and the unconventional use of different round types. This work complements past results on the security analysis of Skipjack and is hoped to provide further insight into the security of an NSA-designed block cipher; the only one publicly known to date.     

FROM THE ARCHIVES: CODETALKERS NOT WANTED

Abstract

The Hill Cipher, also known as matrix encryption, uses matrices to encipher and decipher text. Various attacks, such as those found by Jack Levine [2 Levine , J. 1961 . “Some Applications of High-Speed Computers to the Case n = 2 of Algebraic Cryptography,” Mathematics of Computation , 15 ( 75 ). [Google Scholar] 3 Levine , J. 1961 . “Some Elementary Cryptanalysis of Algebraic Cryptography,” American Mathematical Monthly , 68 ( 5 ): 411 – 418 .[Taylor &; Francis Online] , [Google Scholar] 5 Levine , J. and R. Chandler . 1989 . “The Hill Cryptographic System with Unknown Cipher Alphabet but Known Plaintext,” Cryptologia , 13 ( 1 ): 1 – 28 .[Taylor &; Francis Online] , [Google Scholar]], have been published for this system. This article reviews a few previous results and presents a powerful new attack in which the rows of the matrix can be determined independent of one another, greatly reducing the amount of time needed for decipherment.     

INFORMATION THEORETIC APPROACH TO SECURE LSFR CIPHERS

To break a normal LFSR cipher, a cryptanalyst needs only 2n bits of corresponding plain and ciphertext, where n is the number of stages of the shift register.[l] In this paper, a method of substituting completely random characters into the ciphertext and therefore preventing the encipherment of a full 2n-length sequence (under its proper key) will be discussed. Due to the high redundancy of English, a cipher containing several completely random characters will still be readable.     

一次一密加密系统设计与实现

文中在VC 6.0环境下设计并实现了一次一密文件加密系统。针对文件加密的特点:在文件的头部和尾部有相同或类似关于文件类型的信息,为了防止这部分信息对文件加密产生的影响,提出了相应的加密方法,并通过穷举法和分析破译法对加密有效性进行验证。同时设计并实现安全的随机密钥产生系统,通过特定算法,使密钥序列更接近随机序列。用户可以输入密钥序号系统自动采用相应密钥进行文件加密,也可以自定义密钥,密钥定期更新,以保证系统具有较高的安全性。     

THE MATRIX CIPHER OF C. L. DODGSON

A diary entry of Charles L. Dodgson, better known as Lewis Carroll, indicates that he invented two polyalphabetic ciphers in 1858. He published neither of them. In this paper we present one, a matrix based cipher, and show that it is equivalent to a Variant Beaufort cipher using a non-standard arithmetic. This is placed in historical perspective not only from the point of view of cryptography but also in regard to the state of mathematics in England in the middle of the nineteenth century. The authors have written a computer program that can be used to explore this and similar ciphers.     

THE QUADRATIC RESIDUE CIPHER AND SOME NOTES ON IMPLEMENTATION

Although of similar age, the Quadratic Residue Cipher (QRC) has been neglected compared with the publicity received by other public key cryptosystems, notably the RSA cipher. This paper attempts to redress the balance somewhat, explaining in expository form the principle of the QRC, the advantages it offers over RSA and some experiences gained as a result of using the cipher.     

THE HAND-HELD CALCULATOR AS A CRYPTOGRAPHIC MACHINE

The degree of sophistication available in today's programmable personal calculators may be used to provide a practical field cipher capability of significant power. Procedures are presented for key management, key generator cycling alarm, cipher-type selection to match cryptanalytic threat level, and key length options as an answer to key-search attacks. Three basic cipher procedures are presented with special emphasis given to the inherent power of transposition techniques. Four cryptogram examples are included to demonstrate four of the levels of available security offered by the system.     

用VC++如何实现表结构的动态操作

本文结合数据模型增加一列新属性再检索出一条记录的具体编程,介绍了ＶＣ＋＋环境下对数据库表的两种动态操作方法,并且介绍了一些数据库表的设计方法。     

THE APPLICATION OF KEY DEPENDENT AND VARIABLE ROTOR SETS TO GENERALIZED ROTOR CRYPTOGRAPHIC SYSTEMS

The structure and utilization of the “Generalized Rotor” (GR) cryptographic operator for the construction of cryptographic systems and mixers of pseudo-random streams has been discussed previously [1,2]. This article discusses the creation of key dependent rotors for rotor systems and their cryptographic application. Generation of key dependent rotor sets from an original fixed “basis” rotor set is discussed and is shown to allow the creation and management of readily changed rotor sets. The use of such frequently changed rotor sets adds materially to cryptographic security of systems utilizing these sets. The generation and application of “variable” rotor sets to substitution-permutation block codes is shown to add appreciable crypt analytic difficulties to these codes at a small processing cost and at a moderate memory cost to the encryption/decryption operation.