The knowledge complexity of interactive proof-systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Zero knowledge proofs of identity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
An alternative to the Fiat-Shamir protocol
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
A new identification scheme based on syndrome decoding
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Improved algorithms for the permuted kernel problem
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
An Efficient Identification Scheme Based on Permuted Kernels (Extended Abstract)
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
The MD4 Message Digest Algorithm
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
On the Security of the Permuted Kernel Identification Scheme
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
A new public key cryptosystem based on higher residues
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
Communication-efficient anonymous group identification
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
A New \mathcal{NP}-Complete Problem and Public-Key Identification
Designs, Codes and Cryptography
NSS: An NTRU Lattice-Based Signature Scheme
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Fault Injection and a Timing Channel on an Analysis Technique
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Efficient Zero-Knowledge Authentication Based on a Linear Algebra Problem MinRank
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
MiniPASS: Authentication and Digital Signatures in a Constrained Environment
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
A Digital Signature Scheme Based on NP-Complete Lattice Problems
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Efficient zero-knowledge identification schemes which respect privacy
Proceedings of the 4th International Symposium on Information, Computer, and Communications Security
Security proofs for signature schemes
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
A new identification scheme based on the perceptrons problem
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Cryptanalysis of an identification scheme based on the permuted perceptron problem
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
A zero-knowledge identification scheme based on the q-ary syndrome decoding problem
SAC'10 Proceedings of the 17th international conference on Selected areas in cryptography
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Public-key identification schemes based on multivariate quadratic polynomials
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Zero-knowledge proof of generalized compact knapsacks (or a novel identification/signature scheme)
ATC'06 Proceedings of the Third international conference on Autonomic and Trusted Computing
Full cryptanalysis of the chen identification protocol
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Feasibility of position-based multivariate cryptosystems for WSN
International Journal of Internet Technology and Secured Transactions
Public-Key identification schemes based on multivariate cubic polynomials
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Extended security arguments for signature schemes
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
Zero-Knowledge for multivariate polynomials
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
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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 so-called 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.