The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

An aggregate signature scheme is a digital signature that supports aggregation: Given n signatures on n distinct messages from n distinct users, it is possible to aggregate all these signatures into a single short signature. This single signature (and the n original messages) will convince the verifier that the n users did indeed sign the n original messages (i.e., user i signed message Mi for i = 1, . . . , n). In this paper we introduce the concept of an aggregate signature, present security models for such signatures, and give several applications for aggregate signatures. We construct an efficient aggregate signature from a recent short signature scheme based on bilinear maps due to Boneh, Lynn, and Shacham. Aggregate signatures are useful for reducing the size of certificate chains (by aggregating all signatures in the chain) and for reducing message size in secure routing protocols such as SBGP. We also show that aggregate signatures give rise to verifiably encrypted signatures. Such signatures enable the verifier to test that a given ciphertext C is the encryption of a signature on a given message M. Verifiably encrypted signatures are used in contract-signing protocols. Finally, we show that similar ideas can be used to extend the short signature scheme to give simple ring signatures.

/pdf/aggregate-and-verifiably-encrypted-signatures-from-bilinear-c6vl0qe63h.pdf

Aggregate and verifiably encrypted signatures from bilinear maps

We describe a simple and novel cryptographic construction that we call a fuzzy vault. Alice may place a secret value /spl kappa/ in a fuzzy vault and "lock" it using an unordered set A of elements from some public universe U. If Bob tries to "unlock" the vault using an unordered set B, he obtains /spl kappa/ only if B is close to A, i.e., only if A and B overlap substantially.

A fuzzy vault scheme

Password-based protocols for authenticated key exchange (AKE) are designed to work despite the use of passwords drawn from a space so small that an adversary might well enumerate, off line, all possible passwords. While several such protocols have been suggested, the underlying theory has been lagging. We begin by defining a model for this problem, one rich enough to deal with password guessing, forward secrecy, server compromise, and loss of session keys. The one model can be used to define various goals. We take AKE (with "implicit" authentication) as the "basic" goal, and we give definitions for it, and for entity-authentication goals as well. Then we prove correctness for the idea at the center of the Encrypted Key-Exchange (EKE) protocol of Bellovin and Merritt: we prove security, in an ideal-cipher model, of the two-flow protocol at the core of EKE.

/pdf/authenticated-key-exchange-secure-against-dictionary-attacks-3e7gjz9v6y.pdf

Authenticated key exchange secure against dictionary attacks

When designing password-authenticated key exchange protocols (as opposed to key exchange protocols authenticated using cryptographically secure keys), one must not allow any information to be leaked that would allow verification of the password (a weak shared key), since an attacker who obtains this information may be able to run an off-line dictionary attack to determine the correct password. We present a new protocol called PAK which is the first Diffie-Hellman-based password-authenticated key exchange protocol to provide a formal proof of security (in the random oracle model) against both passive and active adversaries. In addition to the PAK protocol that provides mutual explicit authentication, we also show a more efficient protocol called PPK that is provably secure in the implicit -authentication model. We then extend PAK to a protocol called PAK-X, in which one side (the client) stores a plaintext version of the password, while the other side (the server) only stores a verifier for the password. We formally prove security of PAK-X, even when the server is compromised. Our formal model for password-authenticated key exchange is new, and may be of independent interest.

/pdf/provably-secure-password-authenticated-key-exchange-using-5dbmuqk5rz.pdf

Provably secure password-authenticated key exchange using Diffie-Hellman

We introduce the notion of abuse-free distributed contract signing, that is, distributed contract signing in which no party ever can prove to a third party that he is capable of choosing whether to validate or invalidate the contract. Assume Alice and Bob are signing a contract. If the contract protocol they use is not abuse-free, then it is possible for one party, say Alice, at some point to convince a third party, Val, that Bob is committed to the contract, whereas she is not yet. Contract protocols with this property are therefore not favorable to Bob, as there is a risk that Alice does not really want to sign the contract with him, but only use his willingness to sign to get leverage for another contract. Most existing optimistic contract signing schemes are not abuse-free. (The only optimistic contract signing scheme to date that does not have this property is mefficient, and is only abuse-free against an off-line attacker.) We give an efficient abuse-free optimistic contract-signing protocol based on ideas introduced for designated verifier proofs (i.e., proofs for which only a designated verifier can be convinced). Our basic solution is for two parties. We show that straightforward extensions to n > 2 party contracts do not work, and then show how to construct a three-party abuse-free optimistic contract-signing protocol An important technique we introduce is a type of signature we call a private contract signature Roughly, these are designated verifier signatures that can be converted into universally-verifiable siguatures by either the signing party or a trnsted third party appointed by the signing party, whose identity and power to convert can be verified (without interaction) by the party who is the designated verifier.

Abuse-free optimistic contract signing

The invention provides for robust efficient distributed generation of RSA keys. An efficient protocol is one which is independent of the primality test “circuit size”, while a robust protocol allows correct completion even in the presence of a minority of arbitrarily misbehaving malicious parties. The disclosed protocol is secure against any minority of malicious parties (which is optimal). The disclosed method is useful in establishing sensitive distributed cryptographic function sharing services (certification authorities, signature schemes with distributed trust, and key escrow authorities), as well as other applications besides RSA (namely: composite ElGamal, identification schemes, simultaneous bit exchange, etc.). The disclosed method can be combined with proactive function sharing techniques to establish the first efficient, optimal-resilience, robust and proactively-secure RSA-based distributed trust services where the key is never entrusted to a single entity (i.e., distributed trust totally “from scratch”). The disclosed method involves new efficient “robustness assurance techniques” which guarantee “correct computations” by mutually distrusting parties with malicious minority.

Robust efficient distributed RSA-key generation

We initiate the investigation of the class of relations that admit extremely efficient perfect zero knowledge proofs of knowledge: constant number of rounds, communication linear in the length of the statement and the witness, and negligible knowledge error. In its most general incarnation, our result says that for relations that have a particular three-move honest-verifier zero-knowledge (HVZK) proof of knowledge, and which admit a particular three-move HVZK proof of knowledge for an associated commitment relation, perfect zero knowledge (against a general verifier) can be achieved essentially for free, even when proving statements on several instances combined under under monotone function composition. In addition, perfect zero-knowledge is achieved with an optimal 4-moves. Instantiations of our main protocol lead to efficient perfect ZK proofs of knowledge of discrete logarithms and RSA-roots, or more generally, q-one-way group homomorphisms. None of our results rely on intractability assumptions.

/pdf/efficient-zero-knowledge-proofs-of-knowledge-without-3u50e0ajt1.pdf

Efficient Zero-Knowledge Proofs of Knowledge Without Intractability Assumptions

Recently there has been an interest in zero-knowledge protocols with stronger properties, such as concurrency, simulation soundness, non-malleability, and universal composability. In this paper we show a novel technique to convert a large class of existing honest-verifier zero-knowledge protocols into ones with these stronger properties in the common reference string model. More precisely, our technique utilizes a signature scheme existentially unforgeable against adaptive chosen-message attacks, and transforms any Σ-protocol (which is honest-verifier zero-knowledge) into a simulation sound concurrent zero-knowledge protocol. We also introduce Ω-protocols, a variant of Σ-protocols for which our technique further achieves the properties of non-malleability and/or universal composability. In addition to its conceptual simplicity, a main advantage of this new technique over previous ones is that it avoids the Cook-Levin theorem, which tends to be rather inefficient. Indeed, our technique allows for very efficient instantiation based on the security of some efficient signature schemes and standard number-theoretic assumptions. For instance, one instantiation of our technique yields a universally composable zero-knowledge protocol under the Strong RSA assumption, incurring an overhead of a small constant number of exponentiations, plus the generation of two signatures.

/pdf/strengthening-zero-knowledge-protocols-using-signatures-20u84bw6rd.pdf

Philip D. MacKenzie

Papers

Provably secure password-authenticated key exchange using Diffie-Hellman

Abuse-free optimistic contract signing

Robust efficient distributed RSA-key generation

Efficient Zero-Knowledge Proofs of Knowledge Without Intractability Assumptions

Strengthening Zero-Knowledge Protocols Using Signatures