Authenticated Encryption Scheme With 2n-Bit Memory and n-Bit Security
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Solution Overview
Problem
Existing authenticated encryption algorithms using block ciphers require a memory size of 3n bits, which is not optimal, and have an offline computation security level of n/2 bits, which is also not optimal, while achieving an online computation security level of n bits.
Innovation Solution
The encryption device divides plaintext into n-bit segments, uses replacement functions P and F to update values T and B, and generates a ciphertext and authenticator, minimizing memory usage to 2n bits while maintaining optimal security levels of n bits for both online and offline computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing authenticated encryption algorithms using block ciphers are used, then online computation security level of n bits is achieved, but memory size increases to 3n bits and offline computation security level decreases to n/2 bits
Solution Approach 1:
The encryption process is segmented into multiple stages with distinct functions: initialization stage (setting up T and B values), encryption stage (processing plaintext blocks), and authentication stage (generating tag). Each stage uses only the necessary n bits for its specific computation, avoiding the need to maintain all 3n bits simultaneously in memory.
Solution Approach 2:
The memory requirements are made dynamic rather than static. The algorithm adjusts its memory usage based on the current operation phase, allocating n bits for T values during authentication computations and n bits for B values during encryption computations, but not both at full capacity simultaneously. This dynamic allocation achieves optimal security while minimizing peak memory usage to 2n bits.
2Reliability
If existing authenticated encryption algorithms using block ciphers are used, then online computation security level of n bits is achieved, but offline computation security level decreases to n/2 bits
Solution Approach 1:
The algorithm changes the security parameter effectively by using the full n-bit block cipher output for both encryption and authentication purposes. By properly utilizing the B values (which are n bits) and T values (which are n bits) in different phases, the system achieves n-bit offline security without requiring 3n bits of memory, as the same n-bit space is reused across different computational phases.
3Quantity of substance
If memory size is reduced to 2n bits, then optimal security levels of n bits for both online and offline computation are achieved, but device complexity increases due to replacement functions P and F
Solution Approach 1:
The replacement functions P and F serve multiple purposes within the algorithm. Function P processes T values for authentication tag generation, while function F processes B values for ciphertext generation. Both functions operate on n-bit inputs and produce n-bit outputs, providing universal n-bit security for both encryption and authentication operations without requiring separate complex functions for each purpose.
Data Source
AI summary
An encryption device divides a plaintext M to generate a value M[1], . . . , and a value M[m]. The encryption device generates an n-bit value B[i] by encrypting a value B[i−1] by a block cipher with a value T[i−1] as a key, for each integer i of i=1, . . . , m in ascending order, generates a value C[i] from the value B[i] and a value M[i], and generates an n-bit value T[i] from a value P(T[i−1]) obtained by converting the value T[i−1] using a replacement function P, a value F(B[i]) obtained by converting the value B[i] using a replacement function F, and the value C[i]. The encryption device generates a ciphertext C by connecting the values C[i] for i=1, . . . , m. The encryption device generates from a value H[m] and the value B[m], an authenticator Tag for detecting an alteration of the ciphertext C.