Since some ideas in cryptography are several thousands of years old, it does not make sense to try to trace the original sources for matters discussed in Chapter 1. [Ka] is an excellent over-all reference. [Ga] discusses cryptanalytic methods before the age of computers. The cryptosystem of Example 1.2 was introduced in [Hil]. [Kon] and [BeP] discuss various cryptanalytic methods for classical systems. [Zim] could be mentioned as an example of the numerous books on cryptography before the era of public keys.
Public keys were introduced in [DH], The basic knapsack system discussed in Chapter 2 is from [MeH], and complexity issues from [Br 1] and [Kar 1]. Poker by telephone, coin flipping by telephone and oblivious transfer are due to [ShRA], [Bll] and [Rab2], respectively.
The theory presented in Sections 3.2 and 3.3 is from [Sh2], [Sa3] and [Sa4], See also [Adl], The cryptosystems in Section 3.4 are (in this order) from [EvY], [Sh3], [Sh 1] and due to Graham and Shamir. [Cho] is the basic reference for dense knapsacks.
The theory presented in Chapter 4 was initiated in [RSA], [Rabl] is an early contribution. See [Ko] for the original references for Section 4.3. Section 4.4 uses ideas from [Mil] and [Del]. Theorem 4.3 is from [GMT]. See also [SchA]. [Odl] is a comprehensive treatment about discrete logarithm, and [Ang] a good summary on the complexity of number theoretic problems.
The material in Section 5.1 is from [Wil] and that in Section 5.2 from [Sa2], [SaY], [Kar2] and [Kar3]. The cryptosystems based on group theory and hiding regular languages are due to [ WaM] and [Nie], respectively. [SiS] is also a cryptosystem based on language theory, and the system based on sequential machines is due to [Ren], The cryptosystem of Section 5.4 was introduced in [McE].
The signature scheme at the end of Section 6.1 is due to [Sh4], and the material in Section 6.2 to [Bll] and [GM], The method of sharing a secret given in Section 6.3 was presented in [Mig]. The age protocol of Section 6.4 is from [Yao], The notion of oblivious transfer is due to [Rab2], Section 6.5 presents a simple protocol for the secret selling of secrets; more sophisticated techniques are contained in [BCR], Section 6.6 follows [BuP] and [NuS], The subject matter has been treated in numerous other papers, for instance, [Ben] is a comprehensive treatment with somewhat different aims. [GMR] and [GMW] are basic papers concerning zero-knowledge proofs. The first protocol in Section 6.7 is from [Dam]. Ideas from [B12] are used in the proofs of Theorems 6.2 and 6.3. A protocol for the satisfiability problem different from the one of Theorem 6.5 is given in [BCC], where the gates of the corresponding logical circuit are considered. [DMP] and [BeG] deal with non-interactive zero-knowledge proof systems. The two proof methods presented in Section 6.9 are from [FFS] (see also [FiS]) and [Sh5], Cheating schemes are discussed in [DGB],
The information theoretic viewpoint, [Shan], is not discussed in this book. The following list of references contains only works referred to in this book. Further bibliographical details are contained, for instance, in [Fl], [SP], [Br 2], [Kra], [Til] and [Wei], Cryptologia and Journal of Cryptology are periodicals devoted to cryptography. Also other journals have papers and entire issues (for instance, May 1988 issue of Proceedings of IEEE) about cryptography. CRYPTO and EUROCRYPT are annual conferences whose proceedings are usually published in Springer Lecture Notes in Computer Science. Also the standard annual conferences on theoretical computer science (STOC, FOCS, ICALP, etc.) contain many papers dealing with cryptography.
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[BI 1] M. Blum: Coin flipping by telephone. A protocol for solving impossible problems. SIGACT News, 1981, pp. 23-27
[B12] M. Blum: How to prove a theorem so no one else can claim it. Proceedings International
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[BCC] G. Brassard, D. Chaum and C. Crepeau: An introduction to minimum disclosure. Amsterdam CWI Quarterly 1 (1988) 3-17 [BCR] G. Brassard, C. Crepeau and J.-M. Robert: All-or-nothing disclosure of secrets. Lecture
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protocol. Lecture Notes in Computer Science, vol. 293. Springer, Berlin 1987, pp. 21-39 [DH] W. Diflie and M. Hellman: New directions in cryptography. IEEE Transactions on Information Theory 1T-22 (1976) 644-654 [EIG] T. El Gamal: A public key cryptosystem and signature scheme based on discrete logarithms.
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[GMW] O. Goldreich, S. Micali and A. Widgerson: How to prove all /VP-statements in zero- knowledge, and a methodology of cryptographic protocol design. Lecture Notes in Computer Science, vol. 263. Springer, Berlin 1987, pp. 171-185 [GM] S. Goldwasser and S. Micali; Probabilistic encryption. Journal of Computer and Systems
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where each c\ satisfies 0 < cf < [ log2 m] + 1. Thus, we allow the item ai to be used several times in forming the sum. However, the number of times allowed is small and never exceeds the number of bits in the modulus.
Before proceeding with the formal details, we discuss in general terms how such a knapsack system can be used to generate signatures. The sender chooses and publicizes a knapsack system determined by A = (a,, . . . ,a„) and m such that the system leads to apparently difficult knapsack problems but the problems can actually be solved quickly by some secret trapdoor information. The sender signs a message oc by using the trapdoor information to solve (*): the n-tuple (c,,.. ., cj constitutes the signature for a. The legal receiver who has received both a and the signature can verify the signature by checking that (*) holds. If the legal receiver or a cryptanalyst wants to forge the sender's signature for some message a', he/she has to solve the instance of the knapsack problem determined by the triple (A, n% a'). An additional requirement concerning the choice of the knapsack system is that all conceivable messages a must have a signature, that is, (*) must have a solution for all such a.