Compact Ciphertext Proof for Mixnet Communication Complexity
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Solution Overview
Problem
Current plaintext equivalence proof techniques for mixnets are inefficient due to their finite group size limitations, particularly with Elgamal encryption algorithms, which require splitting longer plaintexts into shorter ones, leading to increased communication complexity in zero-knowledge proofs.
Innovation Solution
A method that compactifies ciphertexts by dividing them into partial ciphertexts, encrypting each with an asymmetric key scheme, and using hash exponents to create compacted and re-encrypted ciphertexts, allowing for proof communication complexity independent of plaintext size, using cryptographic hash functions like random oracles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If plaintexts are split into shorter sequences to meet encryption algorithm limits, then encryption security is maintained, but communication complexity increases linearly with the number of plaintext elements
Solution Approach 1:
The patent combines multiple individual plaintext equivalence proofs into a single aggregated proof. Instead of performing separate zero-knowledge proofs for each plaintext element in the sequence, the invention merges them into one proof that verifies all elements simultaneously, reducing communication complexity from linear O(n) to constant O(1) while maintaining the security guarantees of individual proofs
2Manufacturing precision
If standard plaintext equivalence proof techniques are used for each ciphertext element, then correctness of individual encryptions is verified, but total proof size and communication overhead grow with sequence length
Solution Approach 1:
The patent aggregates multiple individual proofs into a single compact proof structure. By combining the verification of all ciphertext elements into one unified proof, the total proof size remains constant regardless of the number of elements, while still ensuring each element's correctness through the aggregated verification process
3Reliability
If finite group size encryption algorithms like ElGamal are used, then cryptographic security is achieved, but maximum plaintext length is limited requiring sequence splitting
Solution Approach 1:
The patent enables handling of arbitrarily long plaintext sequences by merging multiple short ciphertexts into a single aggregated proof. This allows the system to maintain the security properties of fixed-size group encryption algorithms while effectively supporting unlimited plaintext lengths through the aggregation technique, eliminating the need for sequence splitting in the proof process
Data Source
AI summary
Methods aiding in proving shuffles of re-encryptions of ciphertexts and a mixnet employing such methods. A method for compacting ciphertexts includes encrypting a plaintext using an asymmetric key encryption scheme for a ciphertext, dividing the ciphertext into partial ciphertexts, encrypting each of the partial ciphertexts using the asymmetric key encryption scheme to obtain re-encrypted partial ciphertexts, creating hash exponents from a digest of a cryptographic hash function taking the partial ciphertexts, the re-encrypted partial ciphertexts and arbitrary salt values as argument of the cryptographic hash function, calculating a compacted ciphertext by multiplying all of the partial ciphertexts exponentiated by a respective one of the plurality of hash exponents, and calculating a compacted re-encrypted ciphertext by multiplying all of the re-encrypted partial ciphertexts exponentiated by a respective one of the hash exponents.