Results 11  20
of
28
Hidden Field Equations HFE and Isomorphisms of Polynomials IP: two new Families of Asymmetric Algorithms
, 1996
"... In #11# T. Matsumoto and H. Imai described a new asymmetric algorithm based on multivariate polynomials of degree twoover a #nite #eld. Then in #14# this algorithm was broken. The aim of this paper is to show that despite this result it is probably possible to use multivariate polynomials of degree ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
In #11# T. Matsumoto and H. Imai described a new asymmetric algorithm based on multivariate polynomials of degree twoover a #nite #eld. Then in #14# this algorithm was broken. The aim of this paper is to show that despite this result it is probably possible to use multivariate polynomials of degree two in carefully designed algorithms for asymmetric cryptography. In this paper we will give some examples of suchschemes. All the examples that we will give, belong to two large family of schemes: HFE and IP. With HFE we will be able to do encryption, signatures or authentication in an asymmetric way. Moreover HFE #with properly chosen parameters# resist to all known attacks and can be used in order to givevery short asymmetric signatures or very short encrypted messages #of length 128 bits or 64 bits for example#. IP can be used for asymmetric authentications or signatures. IP authentications are zero knowledge. Note 1 : Another title for this paper could be #How to repair MatsumotoImai algorithm with the same kind of public polynomials". Note 2 : This paper is the extended version of the paper with the same title published at Eurocrypt '96. 1
Combinatorially Based Cryptography for Children (and Adults)
, 2000
"... In this paper we show how certain notions of modern cryptography can be presented to youngsters using combinatorial constructions. Among the topics discussed are the use of Boolean circuits for bit commitment protocols and hash functions, and the construction of a public key message transmission sys ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
In this paper we show how certain notions of modern cryptography can be presented to youngsters using combinatorial constructions. Among the topics discussed are the use of Boolean circuits for bit commitment protocols and hash functions, and the construction of a public key message transmission system using perfect codes in a graph. We also discuss how efforts such as this in popularizing mathematics for children are related to mathematics education reform.
Enforcing and defying associativity, commutativity, totality, and strong noninvertibility for oneway functions in complexity theory
 In ICTCS
, 2005
"... Rabi and Sherman [RS97,RS93] proved that the hardness of factoring is a sufficient condition for there to exist oneway functions (i.e., ptime computable, honest, ptime noninvertible functions) that are total, commutative, and associative but not strongly noninvertible. In this paper we improve th ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Rabi and Sherman [RS97,RS93] proved that the hardness of factoring is a sufficient condition for there to exist oneway functions (i.e., ptime computable, honest, ptime noninvertible functions) that are total, commutative, and associative but not strongly noninvertible. In this paper we improve the sufficient condition to P = NP. More generally, in this paper we completely characterize which types of oneway functions stand or fall together with (plain) oneway functions—equivalently, stand or fall together with P = NP. We look at the four attributes used in Rabi and Sherman’s seminal work on algebraic properties of oneway functions (see [RS97,RS93]) and subsequent papers—strongness (of noninvertibility), totality, commutativity, and associativity—and for each attribute, we allow it to be required to hold, required to fail, or “don’t care. ” In this categorization there are 3 4 = 81 potential types of oneway functions. We prove that each of these 81 featureladen types stand or fall together with the existence of (plain) oneway functions. Key words: computational complexity, complexitytheoretic oneway functions, associativity, 1.1
A Status Report on the P versus NP Question
"... We survey some of the history of the most famous open question in computing: the P versus NP question. We summarize some of the progress that has been made to date, and assess the current situation. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We survey some of the history of the most famous open question in computing: the P versus NP question. We summarize some of the progress that has been made to date, and assess the current situation.
PostQuantum Signatures
, 2004
"... Digital signatures have become a key technology for making the Internet and other IT infrastructures secure. But in 1994 Peter Shor showed that quantum computers can break all digital signature schemes that are used today and in 2001 Chuang and his coworkers implemented Shor’s algorithm for the firs ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Digital signatures have become a key technology for making the Internet and other IT infrastructures secure. But in 1994 Peter Shor showed that quantum computers can break all digital signature schemes that are used today and in 2001 Chuang and his coworkers implemented Shor’s algorithm for the first time on a 7qubit NMR quantum computer. This paper studies the question: What kind of digital signature algorithms are still secure in the age of quantum computers? 1 1
Cryptography from tensor problems
, 2012
"... We describe a new proposal for a trapdoor oneway function. The new proposal belongs to the “multivariate quadratic” family but the trapdoor is different from existing methods, and is simpler. Known quantum algorithms do not appear to help an adversary attack this trapdoor. (Beyond the asymptotic ..."
Abstract
 Add to MetaCart
(Show Context)
We describe a new proposal for a trapdoor oneway function. The new proposal belongs to the “multivariate quadratic” family but the trapdoor is different from existing methods, and is simpler. Known quantum algorithms do not appear to help an adversary attack this trapdoor. (Beyond the asymptotic squarerootspeedup which applies to all oracle search problems.)
Keywords Negative Databases · Immuneinspired Algorithms · Privacy · Information Hiding · Data Representations
"... Information Abstract In a negative representation a set of elements (the positive representation) is depicted by its complement set (the negative representation). That is, the elements in the positive representation are not explicitly stored, and those in the negative representation are. The concept ..."
Abstract
 Add to MetaCart
(Show Context)
Information Abstract In a negative representation a set of elements (the positive representation) is depicted by its complement set (the negative representation). That is, the elements in the positive representation are not explicitly stored, and those in the negative representation are. The concept, feasibility, and properties of negative representations are explored in the paper, in particular, properties related to privacy concerns. It is shown that a positive representation consisting of n lbit strings can be represented negatively using only O(ln) strings, through the use of an additional symbol. It is also shown that membership queries for the positive representation can be processed against the negative representation in time no worse than linear in its size, while reconstructing the original positive set from its negative representation is an N Phard problem. The paper introduces algorithms for constructing negative representations as well as operations for updating and maintaining them.