Two kinds of contemporary developments in cryptography are examined. Widening applications of teleprocessing have given rise to a need for new types of cryptographic systems, which minimize the need for secure key distribution channels and supply the equivalent of a written signature. This paper suggests ways to solve these currently open problems. It also discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing.

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New Directions in Cryptography

Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Quantum Computation and Quantum Information

An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: (1) Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intented recipient. Only he can decipher the message, since only he knows the corresponding decryption key. (2) A message can be “signed” using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed encryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in “electronic mail” and “electronic funds transfer” systems. A message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n, of two large secret primer numbers p and q. Decryption is similar; only a different, secret, power d is used, where e * d ≡ 1(mod (p - 1) * (q - 1)). The security of the system rests in part on the difficulty of factoring the published divisor, n.

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A method for obtaining digital signatures and public-key cryptosystems

From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Handbook of Applied Cryptography

PROBLEM TO BE SOLVED: To solve the problem, wherein it is impossible for an electronic content information provider to provide commercially secure and effective method, for a configurable general-purpose electronic commercial transaction/distribution control system. SOLUTION: In this system, having at least one protected processing environment for safely controlling at least one portion of decoding of digital information, a secure content distribution method comprises a process for encapsulating digital information in one or more digital containers; a process for encrypting at least a portion of digital information; a process for associating at least partially secure control information for managing interactions with encrypted digital information and/or digital container; a process for delivering one or more digital containers to a digital information user; and a process for using a protected processing environment, for safely controlling at least a portion of the decoding of the digital information. COPYRIGHT: (C)2006,JPO&NCIPI

https://apps.dtic.mil/dtic/tr/fulltext/u2/a423264.pdf

Systems and Methods for Secure Transaction Management and Electronic Rights Protection

Wyner's results for discrete memoryless wire-tap channels are extended to the Gaussian wire-tap channel. It is shown that the secrecy capacity Cs is the difference between the capacities of the main and wire.tap channels. It is further shown that Rd= Cs is the upper boundary of the achievable rate-equivocation region.

The Gaussian wire-tap channel

A cryptographic system is described which is secure if and only if computing logarithms over GF(p) is infeasible. Previously published algorithms for computing this function require O(p^{1/2}) complexity in both time and space. An improved algorithm is derived which requires O =(\log^{2} p) complexity if p - 1 has only small prime factors. Such values of p must be avoided in the cryptosystem. Constructive uses for the new algorithm are also described.

An improved algorithm for computing logarithms over GF(p) and its cryptographic significance (Corresp.)

A cryptographic system is described which is secure if and only if computing logarithms over GF(p) is infeasible. Previously published algorithms for computing this function require O(P’/~) complexity in both time and space. An improved algorithm is derived which requires O(log2 p) complexity if p 1 has only small prime factors. Such values of p must be avoided in the cryptosystem. Constructive uses for the new algorithm are also described.

An Improved Algorithm for Computing Logarithms over GF(p) and Its Cryptographic Significance

The knapsack problem is an NP-complete combinatorial problem that is strongly believed to be computationally difficult to solve in general. Specific instances of this problem that appear very difficult to solve unless one possesses "trapdoor information" used in the design of the problem are demonstrated. Because only the designer can easily solve problems, others can send him information hidden in the solution to the problems without fear that an eavesdropper will be able to extract the information. This approach differs from usual cryptographic systems in that a secret key is not needed. Conversely, only the designer can generate signatures for messages, but anyone can easily check their authenticity.

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Martin E. Hellman

Papers

New Directions in Cryptography

The Gaussian wire-tap channel

An improved algorithm for computing logarithms over GF(p) and its cryptographic significance (Corresp.)

An Improved Algorithm for Computing Logarithms over GF(p) and Its Cryptographic Significance

Hiding information and signatures in trapdoor knapsacks