lattice-based cryptography
DESCRIPTION
Gaussian error distributions. Lattice-Based Cryptography. ( or , fast and provably secure cryptography). Why lattice-based cryptography?. FAST: Speeds approaching Symmetric Crypto primitives (e.g., AES). SECURE: Best attacks take exponential time, secure against quantum attacks. - PowerPoint PPT PresentationTRANSCRIPT
Lattice-Based Cryptography(or, fast and provably secure cryptography)
Ring-based learning with errors problem (R-LWE)
(One-time) Signatures from R-LWESecret-key Encryption from R-LWE
What is a lattice?
• : Sample uniform random , four “small” ring elements .Verification key: ,Secret key:
• : Let be the encoding of message as a “small” element of , .Signature: .
• : Check and .Output “accept” if both checks succeed, and “reject” otherwise.
Gaussian error distributions
Let be a prime, . Consider the ring of polynomials.
Given a secret element and a number of pairs
where are chosen uniformly at random, and are chosen coefficient wise according to the discrete error distribution .R-LWE problem: Find the secret (search), or distinguish whether a list of pairs was chosen as described above or whether both were chosen uniformly at random (decision).
Why lattice-based cryptography?
Short basis = Good basis Long basis = Bad basis
FAST: Speeds approaching Symmetric Crypto primitives (e.g., AES)
SECURE: Best attacks take exponential time, secure against quantum attacks
• : Sample a “small” ring element .Secret key:
• : Let be the encoding of message as a “small” element of . is uniformly random in is asmall ring element .
Encryption: .• : Output
This scheme can be turned into a fully homomorphic encryption, that can compute any function on encrypted data.
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