Bounded-Storage Encryption with Short Keys and Perfect Secrecy
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Solution Overview
Problem
Existing cryptographic protocols for secure data transmission and storage, such as the one-time pad scheme, require impractically large key sizes, and current practical cryptosystems lack everlasting security due to reliance on unproven computational assumptions, making them vulnerable to future technological breakthroughs.
Innovation Solution
A new cryptosystem based on the bounded storage model, using a short secret key and a short public random string, independent of message length, ensures perfect cryptographic secrecy by employing finite group operations and XOR encryption, even if the key is revealed to the adversary.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the one-time pad scheme is used to achieve provably secure encryption, then security is improved, but key size becomes impractically large
Solution Approach 1:
The encryption scheme is segmented into multiple passes, where each pass uses a shorter key derived from the previous pass. This divides the single large key requirement into multiple smaller key generation steps, making the system practical while maintaining security through the bounded storage model.
Solution Approach 2:
The system performs preliminary key derivation in advance using a short seed and pseudorandom generation. Instead of requiring a large pre-shared key, the key material is generated beforehand through computational processes that leverage the adversary's bounded storage constraint, reducing the initial key size requirement.
2Ease of operation
If practical cryptosystems are used for secure data transmission, then ease of operation is improved, but everlasting security is lost due to reliance on computational assumptions
Solution Approach 1:
The system uses short-lived pseudorandom keys that are generated and discarded in each encryption pass. These disposable key materials are derived from short seeds and used only temporarily, eliminating the need for long-term computational assumptions while maintaining practical operability through efficient XOR operations.
Solution Approach 2:
The system changes the fundamental parameter from computational hardness assumptions to information-theoretic security based on bounded storage. By shifting from computational complexity parameters to physical storage constraints, the system achieves both practicality and everlasting security simultaneously.
3Device complexity
If a short secret key and public random string are used, then device complexity is reduced, but achieving perfect secrecy becomes more difficult
Solution Approach 1:
The system introduces pseudorandom generation as an intermediary mechanism between the short seed and the encryption keys. This intermediary process expands the short key material into sufficient encryption material while maintaining security through the bounded storage model, resolving the conflict between short keys and perfect secrecy.
Solution Approach 2:
The system employs dynamic key derivation where keys are generated on-the-fly from short seeds through pseudorandom processes. This dynamic approach allows the system to maintain perfect secrecy with short static seeds, as the actual encryption keys change dynamically based on the bounded storage constraints and message context.
Data Source
AI summary
Techniques for secure remote digital storage or transmission of a ciphertext message include determining a maximum storage capacity of an adversary, determining a security parameter k, wherein 1<<k<<m, and determining a prime number n, such that ≤0.3kn. A current public portion of random string α, comprising n random elements, is read from a public site. A secret key z, wherein z has 2k elements, comprising k additive co-primes of n and k multiplicative co-primes of n is shared with a receiving site. An encryption key X, based on the secret key and the current public string, is determined and applied to a plaintext message M of length ≤m to encrypt the plaintext message as Y=M⊕X, thereby creating the ciphertext message Y, which can be placed on a public forum for receiving by a receiving node.