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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Semantically Secure Public-Key Cryptosystems Based on the Decoding Problem of Linear Codes

Kazukuni Kobara

Published Jan 1, 2004• 0 citations
OpenAlex

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A Quantum Public-Key Cryptosystem and Message Authentication Scheme Based on Quantum CSS Error Correcting Codes

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This paper presents a quantum public-key cryptosystem by using quantum Calderbank-Shor-Steane(CSS) error correcting codes and the NPC problem related with decoding general linear codes. It uses classical key to encrypt quantum message, and its security relies on the fact that NPC problem can not be solved on quantum Turing machines. Based on this public-key cryptosystem, this paper also gives a message authentication scheme and proves its security.

JOURNAL OF ELECTRONICS INFORMATION TECHNOLOGY•Jan 1, 2006•0 citations

On lattices, learning with errors, random linear codes, and cryptography

Oded Regev

Our main result is a reduction from worst-case lattice problems such as GapSVP and SIVP to a certain learning problem. This learning problem is a natural extension of the “learning from parity with error” problem to higher moduli. It can also be viewed as the problem of decoding from a random linear code. This, we believe, gives a strong indication that these problems are hard. Our reduction, however, is quantum. Hence, an efficient solution to the learning problem implies a quantum algorithm for GapSVP and SIVP. A main open question is whether this reduction can be made classical (i.e., nonquantum). We also present a (classical) public-key cryptosystem whose security is based on the hardness of the learning problem. By the main result, its security is also based on the worst-case quantum hardness of GapSVP and SIVP. The new cryptosystem is much more efficient than previous lattice-based cryptosystems: the public key is of size Õ( n 2 ) and encrypting a message increases its size by a factor of Õ( n ) (in previous cryptosystems these values are Õ( n 4 ) and Õ( n 2 ), respectively). In fact, under the assumption that all parties share a random bit string of length Õ( n 2 ), the size of the public key can be reduced to Õ( n ).

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Securities of lattice-based public-key cryptosystems

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•Jan 1, 2007•0 citations

Unconditionally Secure Public-key Cryptosystem using Entangled Quantum States

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On Lattices, Learning with Errors, Random Linear Codes, and Cryptography

Oded Regev

Our main result is a reduction from worst-case lattice problems such as GapSVP and SIVP to a certain learning problem. This learning problem is a natural extension of the `learning from parity with error' problem to higher moduli. It can also be viewed as the problem of decoding from a random linear code. This, we believe, gives a strong indication that these problems are hard. Our reduction, however, is quantum. Hence, an efficient solution to the learning problem implies a quantum algorithm for GapSVP and SIVP. A main open question is whether this reduction can be made classical (i.e., non-quantum). We also present a (classical) public-key cryptosystem whose security is based on the hardness of the learning problem. By the main result, its security is also based on the worst-case quantum hardness of GapSVP and SIVP. The new cryptosystem is much more efficient than previous lattice-based cryptosystems: the public key is of size $\tilde{O}(n^2)$ and encrypting a message increases its size by a factor of $\tilde{O}(n)$ (in previous cryptosystems these values are $\tilde{O}(n^4)$ and $\tilde{O}(n^2)$, respectively). In fact, under the assumption that all parties share a random bit string of length $\tilde{O}(n^2)$, the size of the public key can be reduced to $\tilde{O}(n)$.

arXiv:2401.03703•Jan 8, 2024•4 citations
Our main result is a reduction from worst-case lattice problems such as GapSVP and SIVP to a certain learning problem. This learning problem is a natural extension of the “learning from parity with error” problem to higher moduli. It can also be viewed as the problem of decoding from a random linear code. This, we believe, gives a strong indication that these problems are hard. Our reduction, however, is quantum. Hence, an efficient solution to the learning problem implies a quantum algorithm for GapSVP and SIVP. A main open question is whether this reduction can be made classical (i.e., nonquantum). We also present a (classical) public-key cryptosystem whose security is based on the hardness of the learning problem. By the main result, its security is also based on the worst-case quantum hardness of GapSVP and SIVP. The new cryptosystem is much more efficient than previous lattice-based cryptosystems: the public key is of size Õ( n 2 ) and encrypting a message increases its size by a factor of Õ( n ) (in previous cryptosystems these values are Õ( n 4 ) and Õ( n 2 ), respectively). In fact, under the assumption that all parties share a random bit string of length Õ( n 2 ), the size of the public key can be reduced to Õ( n ).
Our main result is a reduction from worst-case lattice problems such as GapSVP and SIVP to a certain learning problem. This learning problem is a natural extension of the `learning from parity with error' problem to higher moduli. It can also be viewed as the problem of decoding from a random linear code. This, we believe, gives a strong indication that these problems are hard. Our reduction, however, is quantum. Hence, an efficient solution to the learning problem implies a quantum algorithm for GapSVP and SIVP. A main open question is whether this reduction can be made classical (i.e., non-quantum). We also present a (classical) public-key cryptosystem whose security is based on the hardness of the learning problem. By the main result, its security is also based on the worst-case quantum hardness of GapSVP and SIVP. The new cryptosystem is much more efficient than previous lattice-based cryptosystems: the public key is of size O~(n2)\tilde{O}(n^2)O~(n2) and encrypting a message increases its size by a factor of O~(n)\tilde{O}(n)O~(n) (in previous cryptosystems these values are O~(n4)\tilde{O}(n^4)O~(n4) and O~(n2)\tilde{O}(n^2)O~(n2), respectively). In fact, under the assumption that all parties share a random bit string of length O~(n2)\tilde{O}(n^2)O~(n2), the size of the public key can be reduced to O~(n)\tilde{O}(n)O~(n).