What Happened with Knapsack Cryptographic Schemes

The knapsack problem originates from the economic world. Suppose one wants to transport some goods which have a given economical value and a given size (e.g. volume). The transport medium, e.g. a car, is however limited in size. The question then is to maximize the total economical value to transport, given the size limitations of the car.

[1]  Martin E. Hellman,et al.  A cryptanalytic time-memory trade-off , 1980, IEEE Trans. Inf. Theory.

[2]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[3]  A. J. McAuley,et al.  New trapdoor-knapsack public-key cryptosystem , 1985 .

[4]  M.E. Hellman,et al.  Privacy and authentication: An introduction to cryptography , 1979, Proceedings of the IEEE.

[5]  Ravi Kannan,et al.  Improved algorithms for integer programming and related lattice problems , 1983, STOC.

[6]  James L. Massey,et al.  Fast Authentication in a Trapdoor - Knapsack Public Key Cryptosystem , 1982, EUROCRYPT.

[7]  Ingemar Ingemarsson,et al.  A new Algorithm for the Solution of the Knapsack Problem , 1982, EUROCRYPT.

[8]  Martin E. Hellman,et al.  An improved algorithm for computing logarithms over GF(p) and its cryptographic significance (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[9]  C. A. Rogers,et al.  An Introduction to the Geometry of Numbers , 1959 .

[10]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  Jeffrey C. Lagarias The Computational Complexity of Simultaneous Diophantine Approximation Problems , 1985, SIAM J. Comput..

[13]  Joos Vandewalle,et al.  A general public key cryptographic Knapsack algorithm based on linear algebra , 1983 .

[14]  Michael Willett Trapdoor Knapsacks Without Superincreasing Structure , 1983, Inf. Process. Lett..

[15]  Claus-Peter Schnorr,et al.  A More Efficient Algorithm for Lattice Basis Reduction , 1988, J. Algorithms.

[16]  Jeffrey C. Lagarias,et al.  Performance Analysis of Shamir's Attack on the Basic Merkle-Hellman Knapsack Cryptosystem , 1984, ICALP.

[17]  Adi Shamir,et al.  A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[18]  Adi Shamir,et al.  On the security of the Merkle- Hellman cryptographic scheme (Corresp.) , 1980, IEEE Trans. Inf. Theory.

[19]  Ronald L. Rivest,et al.  A knapsack-type public key cryptosystem based on arithmetic in finite fields , 1988, IEEE Trans. Inf. Theory.

[20]  Ehud D. Karnin,et al.  A Parallel Algorithm for the Knapsack Problem , 1984, IEEE Transactions on Computers.

[21]  Tore Herlestam Critical remarks on some public-key cryptosystems , 1978 .

[22]  Andrew M. Odlyzko,et al.  Cryptanalytic attacks on the multiplicative knapsack cryptosystem and on Shamir's fast signature scheme , 1984, IEEE Trans. Inf. Theory.

[23]  Hendrik W. Lenstra,et al.  Integer Programming with a Fixed Number of Variables , 1983, Math. Oper. Res..

[24]  Ernest F. Brickell,et al.  Breaking Iterated Knapsacks , 1985, CRYPTO.

[25]  Jeffrey C. Lagarias,et al.  Evaluation of the Adleman Attack on Multiply Iterated Knapsack Cryptosystems , 1983, CRYPTO.

[26]  Joos Vandewalle,et al.  A critical analysis of the security of knapsack public-key algorithms , 1984, IEEE Trans. Inf. Theory.

[27]  Ian F. Blake,et al.  Complexity Issues for Public Key Cryptography , 1988 .

[28]  Ralph Howard,et al.  Data encryption standard , 1987 .

[29]  Jeffrey C. Lagarias,et al.  Knapsack Public Key Cryptosystems and Diophantine Approximation , 1983, CRYPTO.

[30]  Andrew M. Odlyzko,et al.  Discrete Logarithms in Finite Fields and Their Cryptographic Significance , 1985, EUROCRYPT.

[31]  Adi Shamir A Fast Signature Scheme , 1978 .

[32]  Garrett Birkhoff,et al.  A survey of modern algebra , 1942 .

[33]  P. S. Henry,et al.  B.S.T.J. BRIEF fast decryption algorithm for the knapsack cryptographic system , 1981, The Bell System Technical Journal.

[34]  Joos Vandewalle,et al.  Linear algebra and extended mappings generalise public key cryptographic Knapsack algorithms , 1983 .

[35]  Ralph C. Merkle,et al.  Secure communications over insecure channels , 1978, CACM.

[36]  Whitfield Diffie,et al.  Special Feature Exhaustive Cryptanalysis of the NBS Data Encryption Standard , 1977, Computer.

[37]  Joos Vandewalle,et al.  How iterative transformations can help to crack the Merkle-Hellman cryptographic scheme , 1982 .

[38]  Jeffrey C. Lagarias,et al.  Solving low density subset sum problems , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[39]  Benjamin Arazi A trapdoor multiple mapping (Corresp.) , 1980, IEEE Trans. Inf. Theory.

[40]  Joos Vandewalle,et al.  FAST AUTHENTICATION USING PUBLIC KEY SCHEMES. , 1984 .

[41]  Adi Shamir,et al.  On the cryptocomplexity of knapsack systems , 1979, STOC.

[42]  Leonard M. Adleman,et al.  On breaking generalized knapsack public key cryptosystems , 1983, STOC.

[43]  A. Diporto,et al.  A public-key cryptosystem based on a generalization of the knapsack problem , 1985 .

[44]  Fred Piper,et al.  Recent Developments in Cryptography , 1988 .

[45]  Anthony J. McAuley,et al.  A New Trapdoor Knapsack Public-Key Cryptosystem , 1985, EUROCRYPT.

[46]  Joos Vandewalle,et al.  A highly secure cryptographic algorithm for high speed transmission , 1982 .

[47]  Ehud D. Karnin,et al.  The largest super-increasing subset of a random set , 1983, IEEE Trans. Inf. Theory.

[48]  Martin E. Hellman,et al.  Hiding information and signatures in trapdoor knapsacks , 1978, IEEE Trans. Inf. Theory.

[49]  Ernest F. Brickell,et al.  Solving Low Density Knapsacks , 1983, CRYPTO.