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Designing Identification Schemes with Keys of Short Size
 Advances in Cryptology  proceedings of CRYPTO '94
, 1994
"... In the last few years, there have been several attempts to build identification protocols that do not rely on arithmetical operations with large numbers but only use simple operations (see [10, 8]). One was presented at the CRYPTO 89 rump session ([8]) and depends on the socalled Permuted Kerne ..."
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Cited by 25 (4 self)
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In the last few years, there have been several attempts to build identification protocols that do not rely on arithmetical operations with large numbers but only use simple operations (see [10, 8]). One was presented at the CRYPTO 89 rump session ([8]) and depends on the socalled Permuted Kernel problem (PKP). Another appeared in the CRYPTO 93 proceedings and is based on the syndrome decoding problem (SD) form the theory of error correcting codes ([11]). In this paper, we introduce a new scheme of the same family with the distinctive character that both the secret key and the public identification key can be taken to be of short length. By short, we basically mean the usual size of conventional symmetric cryptosystems. As is known, the possibility of using short keys has been a challenge in public key cryptography and has practical applications. Our scheme relies on a combinatorial problem which we call Constrained Linear Equations (CLE in short) and which consists of solving a set of linear equations modulo some small prime q, the unknowns being subject to belong to a specific subset of the integers mod q. Thus, we enlarge the set of tools that can be used in cryptography.
How to Exploit the Intractability of Exact TSP for Cryptography
, 1994
"... We outline constructions for both pseudorandom generators and oneway hash functions. These constructions are based on the exact TSP (XTSP), a special variant of the well known traveling salesperson problem. We prove that these constructions are secure if the XTSP is infeasible. Our constructions a ..."
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Cited by 2 (1 self)
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We outline constructions for both pseudorandom generators and oneway hash functions. These constructions are based on the exact TSP (XTSP), a special variant of the well known traveling salesperson problem. We prove that these constructions are secure if the XTSP is infeasible. Our constructions are easy to implement, appear to be fast, but require a large amount of memory.
Analysis of some natural variants of the PKP Algorithm
"... In 1989, Adi Shamir [15] proposed a new zeroknowledge identi cation scheme based on a NPcomplete problem called PKP for Permuted Kernel Problem. For a given prime p, a given matrix A and a given vector V, the problem is to nd a permutation π such that the permuted vector Vπ veri es A · Vπ = 0 mod ..."
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Cited by 2 (0 self)
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In 1989, Adi Shamir [15] proposed a new zeroknowledge identi cation scheme based on a NPcomplete problem called PKP for Permuted Kernel Problem. For a given prime p, a given matrix A and a given vector V, the problem is to nd a permutation π such that the permuted vector Vπ veri es A · Vπ = 0 mod p. This scheme is still in 2011 known as one of the most e cient identi cation scheme based on a combinatorial problem. However, we will see in this paper that it is possible to improve this scheme signi cantly by combining new ideas in order to reduce the total number of computations to be performed and to improve very e ciently the security against side channel attacks using precomputations. We will obtain like this a new scheme that we have called SPKP. Moreover, if we use precomputed values in the scheme SPKP, then the prover will need to perform no computations (i.e. only selection and transmission of precomputed values). This is very interesting for security against side channel attacks because our scheme is zeroknowledge and we don't perform any computations using the key during the identi cation so we prove that any attacker (even using side channel attacks) being successfully identi ed implies that he has a solution to the NPcomplete problem PKP. 1
How Traveling Salespersons Prove Their Identity
"... . In this paper a new identification protocol is proposed. Its security is based on the Exact Traveling Salesperson Problem (XTSP). The XTSP is a close relative of the famous TSP and consists of finding a Hamiltonian circuit of a given length, given a complete directed graph and the distances betwee ..."
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. In this paper a new identification protocol is proposed. Its security is based on the Exact Traveling Salesperson Problem (XTSP). The XTSP is a close relative of the famous TSP and consists of finding a Hamiltonian circuit of a given length, given a complete directed graph and the distances between all vertices. Thus, the set of tools for use in publickey cryptography is enlarged. 1 Introduction In publickey cryptography it is common to base the security of a cryptosystem on the hardness of number theoretical problems. This remains true for zeroknowledge identification schemes. Motivations to consider other problems are:  Cryptosystems based on number theory tend to be only moderately efficient, since they typically depend on multiplying large numbers.  It is dangerous to have all eggs in one basket, i.e. to depend completely on the same source of problems. In 1989 Shamir [10] published an identification scheme based on an NPhard algebraic problem, the Permuted Kernel Proble...