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Όλ¬Έ(λ°μ¬) -- μμΈλνκ΅λνμ : μμ°κ³Όνλν μ리과νλΆ, 2022. 8. μ΄νν¬.The advent of a quantum mechanical computer presents a clear threat to existing cryptography. On the other hand, the quantum computer also suggests the possibility of a new cryptographic protocol through the properties of quantum mechanics. These two perspectives, respectively, gave rise to a new field called post-quantum cryptography as a countermeasure against quantum attacks and quantum cryptography as a new cryptographic technology using quantum mechanics, which are the subject of this thesis.
In this thesis, we reconsider the security of the current post-quantum cryptography through a new quantum attack, model, and security proof. We present the fine-grained quantum security of hash functions as cryptographic primitives against preprocessing adversaries. We also bring recent quantum information theoretic research into cryptography, creating new quantum public key encryption and quantum commitment. Along the way, we resolve various open problems such as limitations of quantum algorithms with preprocessing computation, oracle separation problems in quantum complexity theory, and public key encryption using group action.μμμνμ μ΄μ©ν μ»΄ν¨ν°μ λ±μ₯μ μΌμ΄μ μκ³ λ¦¬μ¦ λ±μ ν΅ν΄ κΈ°μ‘΄ μνΈνμ λͺ
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ν¨μΌλ‘μ¨ μλ‘μ΄ μμ 곡κ°ν€μνΈμ μμ 컀λ°λ¨ΌνΈ λ±μ μλ‘μ΄ λ°κ²¬μ μ μνλ€. μ΄ κ³Όμ μμ μ μ²λ¦¬ κ³μ°μ ν¬ν¨ν μμμκ³ λ¦¬μ¦μ νκ³, μμ 볡μ‘κ³λ€μ μ€λΌν΄λΆλ¦¬ λ¬Έμ , κ΅°μ μμ©μ μ΄μ©ν 곡κ°ν€ μνΈ λ±μ μ¬λ¬ μ΄λ¦°λ¬Έμ λ€μ ν΄κ²°μ μ μνλ€.1 Introduction 1
1.1 Contributions 3
1.2 Related Works 11
1.3 Research Papers 13
2 Preliminaries 14
2.1 Quantum Computations 15
2.2 Quantum Algorithms 20
2.3 Cryptographic Primitives 21
I Post-Quantum Cryptography: Attacks, New Models, and Proofs 24
3 Quantum Cryptanalysis 25
3.1 Introduction 25
3.2 QROM-AI Algorithm for Function Inversion 26
3.3 Quantum Multiple Discrete Logarithm Problem 34
3.4 Discussion and Open problems 39
4 Quantum Random Oracle Model with Classical Advice 42
4.1 Quantum ROM with Auxiliary Input 44
4.2 Function Inversion 46
4.3 Pseudorandom Generators 56
4.4 Post-quantum Primitives 58
4.5 Discussion and Open Problems 59
5 Quantum Random Permutations with Quantum Advice 62
5.1 Bound for Inverting Random Permutations 64
5.2 Preparation 64
5.3 Proof of Theorem 68
5.4 Implication in Complexity Theory 74
5.5 Discussion and Open Problems 77
II Quantum Cryptography: Public-key Encryptions and Bit Commitments 79
6 Equivalence Theorem 80
6.1 Equivalence Theorem 81
6.2 Non-uniform Equivalence Theorem 83
6.3 Proof of Equivalence Theorem 86
7 Quantum Public Key Encryption 89
7.1 Swap-trapdoor Function Pairs 90
7.2 Quantum-Ciphertext Public Key Encryption 94
7.3 Group Action based Construction 99
7.4 Lattice based Construction 107
7.5 Discussion and Open Problems 113
7.6 Deferred Proof 114
8 Quantum Bit Commitment 119
8.1 Quantum Commitments 120
8.2 Efficient Conversion 123
8.3 Applications of Conversion 126
8.4 Discussion and Open Problems 137λ°