Annotated Bibliography for Zero Knowledge proof
presentation.
Md. Sadekur Rahman
Computer Science Department
Lamar University.
Buchmann, Johannes. Introduction to cryptography. New York: Springer, 2003.
This book deals with how number systems are relate to cryptography. To understand
cryptography we need better understanding of algorithms relate to number system. Here we get
how computation time and storage capacity plays important role in designing cryptographic
algorithms, and this introduces big O and Ω notation for the complexity measurement of
cryptographic algorithms. Multiprecision integers also widely used in cryptography, for analyzing
algorithms we must count their “polynomial running time”. Prime factorization is the basis of
RSA cryptography system and other cryptographic schemas. This book also describes how
computing discrete algorithms are frequently study in cryptography.
Davis,Tom."RSAEncryption."Geometer.org.October10,2003.
http://www.geometer.org/mathcircles (accessed march 19, 2011).
This electronic resource mainly discuss about RSA encryption. Key distribution is big challenge
in public key encryption. “One way chippers” deals with the technique –many can encode a
message but only one can decode it and it’s done by using key for both encoding and decoding.
It’s easy to make key for encoding but almost impossible for decoding. This paper talks about
basic problem relates to public key encryption –someone can misinterpret the original message.
Encoding text for certification can solve above problem. Here we get a full description of RSA
encryption algorithm. How to generate prime number p and q , relative prime (e) considering
formula : (p-1)(q-1). And techniques use by receiver to decode message using formula –Cd(mod
N).
Jean-Jacques Quisquater, Louis C. Guillou, Thomas A. Berson. "How to Explain Zero-Knowledge
Protocols to Your Children." Advances in Cryptology - CRYPTO '89. 1990. 628-631
This paper mainly discusses about well known story “Ali-baba and forty thieves” and how this
story relates with ZKP. Using Al-baba’s experiment to discover the secret message writers
gradually diverted our mind from story to complex cryptic system. Ali-baba wrote a manuscript
describing the whole story but hiding the secret message and this is the basic concept of ZKP.
Here writers introduce Mick Ali’s story, and his way to hide the magic word to give a clear view
how knowledge hiding is done in ZKP. A modified version of the previous one also explained to
add more complex arithmetic schemas.
Mohr, Austin. "A Survey of Zero-Knowledge Proofs with." www.austinmohr.com/. April 24, 2007.
www.austinmohr.com/Home_files/zkp.pdf (accessed March 21, 2011)
Austin Mohr in this paper described a modified version of Ali-Baba’s story. In this paper writer
showed how probability and randomization can be applied to ZKP. If we advance inside the paper
we will be able to know how ZKP can be safely used to graph isomorphism. In the isomorphic
theory only few jargons (like π or π-Ф etc) and other important information’s are kept secret. This
paper also describes how we can apply ZKP in NP problems. The most preliminary uses of ZKP
is “entity authentication”. Fiad-Shamir protocol is the basis of ZKP though it has no practical
usages.
Pope, J.W. "Zero Knowledge Proofs." infohost.nmt.edu. May 2004. (accessed march 18, 2011)
In this electronic resource by J.W. Pope from new mexico tech describes ZKP in a chronological
order , starts with Ali-baba and gradully moves to some complex cryptographic theorems. Here
writer has mentioned some important properties of ZKP like completeness, soundness etc. This
paper also describes how ZKP can be use to Hamiltonian cycle, and NP and NP-completeness are
related to ZKP. “Bit commitment” concept also well studied in terms of ZKP. A well defined list
of ZKP applications (example: smart card, key authentication etc. ) can be found here. This paper
mentioned some well known problems that can’t be handled by ZKP.
Song, Fang, Sean Hallgren, and Adam Smith. Classical cryptographic protocols in a qunatum world .
Singapore, January 9, 2011.
This paper describes usages of ZKP in quantum world, and talks about ways to hide information
from prover, using “Peggy and Victor” example. This paper vastly describes about possible
attacks in quantum protocols, though it’s not our point of concern. A key based cryptography
called “rewinding” has been well studied in this paper. If underlying encryption schemas is well
resistive against attack then large scale of classical security analysis remain valid. “Simple
hybrid” mechanism has been introduced to proof – that there is always exists a classical protocol
under any vulnerable condition.
Wikipedia, The free encyclopedia. january 15, 2001. http://en.wikipedia.org/wiki/Zero-knowledge_proof
(accessed march 21, 2011).
This web resource has a clear description of what actually ZKP means. Pictorial representation of
well known “Peggy and Victor” story and uses of probability in the schema has made the concept
more precise and clear. A formal description of ZKP in terms of turing machine also adopted
here. Variations of ZKP’s has been enlisted and depicted in this paper. All important properties
of ZKP has been mentioned and clarified. “Secure Multiparty Computation” a more practical
example of ZKP has well studied here. Most convincing history of ZKP has been mentioned
based on chronology.