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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 57651 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Eghlidos, Taraneh
- Abstract:
- With the advent of quantum computers, the security of cryptographic primitives, including digital signature schemes, has been compromised. Therefore, a kind of signature scheme has been introduced to resist these computers. These schemes are based on hard problems that have so far resisted against quantum computers, known as post-quantum schemes. One group of these schemes is based on the hard problems of coding theory, which are called code-based cryptographic schemes. The first code-based cryptosystem was the McEliece encryption scheme. A number of code-based signature schemes are based on the McEliece encryption scheme. Some of these schemes use three matrices including a non-singular matrix, a parity-check matrix, and a permutation matrix as private keys, and their product as the public key. In this thesis, our focus is on the analysis of such signature schemes. For this purpose, we first prove that the linear relationships between the columns of the parity-check matrix (or generator matrix) appear in the public key matrix, and then we show that such signature schemes are vulnerable to signature forgery attacks. The proposed attack in this thesis is based on the idea that the attacker can derive a set of spurious private keys corresponding to the given public key and use these keys to forge the signature. Using the proposed method, we analyze a code-based ring signature and a code-based full-time signature scheme
- Keywords:
- Code-based Cryptosystem ; Code-based Signature ; Post-Quantum Cryptography ; Parity Check ; Permutation Matrix ; Scrambler Matrix ; Generator Matrix
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