Introduction to Post-Quantum Cryptography
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1 Introduction to Post-Quantum Cryptography
2 GMU 10 PhD students 3 MS students
3 Features Required from Today s Ciphers STRENGTH PERFORMANCE software hardware FUNCTIONALITY easy key distribution digital signatures 3
4 Secret-key (Symmetric) Ciphers key of Alice and Bob - K AB key of Alice and Bob - K AB Network Alice Encryption Decryption Bob Most Popular Standards: AES, Triple DES 4
5 Features of Secret-Key Ciphers STRENGTH PERFORMANCE software hardware Best attack: Exhaustive-key search 2 k trials for a k-bit key FUNCTIONALITY easy key distribution digital signatures Primary Application: Bulk data encryption 5
6 Public-key (Asymmetric) Ciphers Public key of Bob - K B Private key of Bob - k B Network Alice Encryption Decryption Bob Most Popular Standards: RSA, Elliptic Curve Cryptography (ECC) 6
7 Digital Signature Schemes Alice Message Signature Message Signature Bob Hash function Hash function Hash value 1 Hash value yes no Public key cipher Hash value 2 Public key cipher Alice s private key Alice s public key 7
8 Features of Public-Key Ciphers STRENGTH Best attack: Solving the underlying math problem, such as factoring of large integers: Given N=PQ, find P and Q. FUNCTIONALITY easy key distribution digital signatures PERFORMANCE software hardware Primary Applications: Exchange of keys for secret-key ciphers Digital signatures 8
9 Five security levels & corresponding key sizes allowed by American government NIST SP Level Symmetric ciphers RSA ECC I II III IV V
10 Threat of Quantum Computers Photo: Vandersypen, PQCrypto 2017 First perceived by physicists (R. Feynman, D. Deutsch) in 1980s First significant quantum algorithms (capable of running on quantum computers only) developed in 1990s First practical realization in 1998 (2 qubits) Significant technological breakthroughs during the last 20 years Quantum Artificial Intelligence lab started by Google in 2013 IBM quantum processor (16-17 qubits) in
11 Major advances during the last 20 years Timeline of Quantum Computing: Source: Vandersypen, PQCrypto
12 Effect on Secret-Key Algorithms 1996: Grover s Algorithm, reduces the time of the exhaustive-key search for secret key ciphers from 2 k to 2 k/2 operations, for a k-bit key, e.g., from to 2 64 operations, for a 128-bit key or from to operations, for a 256-bit key assuming a sufficiently powerful and reliable quantum computer available Easy Countermeasure: Double the size of a key 12
13 Effect on Public-Key Algorithms 1994: Shor s Algorithm, breaks major public key cryptosystems based on factoring: RSA discrete logarithm problem: DSA, Diffie-Hellman Elliptic Curve discrete logarithm problem: Elliptic Curve Cryptosystems independently of the key size assuming a sufficiently powerful and reliable quantum computer available No known countermeasures New algorithms and standards required 13
14 Post-Quantum Cryptography Public-key cryptographic algorithms for which there are no known attacks using quantum computers Capable of being implemented using any traditional methods, including software and hardware running efficiently on any modern computing platforms: PCs, tablets, smartphones, servers with FPGA accelerators, etc. 14
15 Post-Quantum Cryptography Efforts New public-key cryptographic families: mid-1990s-present D.J. Bernstein introduces the term post-quantum cryptography: 2003 Series of PQCrypto Conferences: 2006-present NIST Workshop on Cybersecurity in a Post-Quantum World 2015 NIST announcement of standardization plans at PQCrypto 2016, Fukuoka, Japan, Feb NIST Call for Proposals and Request for Nominations for Public-Key Post-Quantum Cryptographic Algorithms: Dec Deadline for submitting candidates: November 30,
16 Post-Quantum Cryptography NIST Project NIST Call for Proposals and Request for Nominations for Public-Key Post-Quantum Cryptographic Algorithms: Dec Deadline for submitting candidates: November 30, 2017 Source: Moody, NIST
17 Promising PQC Families Family Encryption Signature Key Agreement Hash-based XX Code-based XX X Lattice-based XX X Multivariate X XX Supersingular Elliptic Curve Isogeny XX XX high-confidence candidates, X medium-confidence candidates 17
18 Promising PQC Algorithms Family Encryption & Key Exchange Signature Hash-based XMSS (2011), SPHINCS (2015) Code-based McEliece (1978), Niederreiter (1986) Lattice-based NTRUEncrypt (1996), Ring-LWE (2010), NewHope (2016), Kyber (2017) CFS (2001) pqntrusign ( ), BLISS (2013), Dilithium (2017) Multivariate PMI+ (2004), SRP (2015) Unbalanced Oil and Vinegar (1999), HFEv-, QUARTZ (2001), Rainbow (2005) 18
19 Algorithms Selected for a Pilot Study 1. NTRUEncrypt Short Vector Encryption Scheme (SVES) fully compliant with IEEE Standard Specification for Public Key Cryptographic Techniques Based on Hard Problems over Lattices Parameter sets: Optimized for speed 192-bit security: ees1087ep1: p=3, q=2048, N=1087, df=dr= bit security: ees1499ep1: p=3, q=2048, N=1499, df=dr=79 2. Multivariate Rainbow Signature Scheme Parameter set: (17,12)(1,12) 80-bit security level 19
20 Our Objectives Paving the way for the future comprehensive, fair, and efficient hardware benchmarking of PQC candidates through 1. Uniform Hardware API 2. Uniform & Efficient Development Process 20
21 Proposed Uniform Hardware API Minimum Compliance Criteria Communication Protocol Encryption & decryption, or Signature generation & verification External key generation (e.g., in software) Permitted data port widths, etc. Interface Timing Characteristics 21
22 Comparative Analysis of Implementation Difficulties Feature NTRUEncrypt Rainbow SS High-security levels Easy to implement Challenging to implement Key sizes Small Very Large Support for multiple parameter sets swapped at run time Component operations Dependence of the execution time on message size Relatively easy to implement Standard: variable rotator, hash function Strong Challenging to implement Complex: System of Linear Equation Solver Weak 22
23 Outcomes of Our Pilot Study First hardware implementation of the full NTRUEncrypt- SVES scheme Hardware optimization for speed revealed the hash function bottleneck Changes in the NTRUEncrypt standards recommended to overcome this bottleneck State of the art implementation of the Rainbow Signature Scheme comparable to the earlier results by Tang et al. from PQCrypto 2011 New PQC Hardware API, paving the way for the fair evaluation of candidates in the NIST standardization process 23
24 Challenges of PQC Benchmarking Complex mathematical descriptions Large public and private keys Security vs. feasibility & cost trade-offs Quickly evolving algorithms and algorithm variants Uncertainty about parameter values corresponding to a given security level 24
25 See Quantum Computing & Post-Quantum Cryptography Projects
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