RSA+: An RSA Variant Combining RSA and Rabin Cryptosystems

핵심 개념

RSA+ combines RSA and Rabin schemes for improved security and efficiency.

초록

The content introduces the RSA+ cryptosystem, combining elements of RSA and Rabin schemes. It explores the motivation behind creating RSA+, comparing it to traditional RSA and Rabin systems in terms of security, performance, and practicality. The runtime analysis reveals that breaking RSA+ is as difficult as breaking RSA, with implications for factoring large moduli. The decryption process of RSA+ is discussed in detail, highlighting advantages over Rabin's scheme in producing at most two possible decrypted messages. Security implications are explored, suggesting that breaking RSA+ may be equivalent to factoring the modulus n. The article concludes by discussing the number of possible clear texts output during decryption and acknowledges contributions from various authors.
Introduction:

Introducing a new probabilistic public-key cryptosystem called RSA+
Combines elements of well-known RSA and Rabin cryptosystems
Motivation for Creating RSA+:

Aimed to create a more practical system than Rabin's while maintaining high security levels
Runtime Analysis:

Breaking RSA+ is as challenging as breaking traditional RSA
Implications for factoring large moduli
Decryption Process:

Advantages of producing at most two possible decrypted messages compared to Rabin's four
Security Implications:

Breaking RSA+ may be equivalent to factoring the modulus n
Conclusion:

Discussion on the number of possible clear texts output during decryption
Acknowledgment section recognizing contributions from various authors

통계

"Bob’s public key is (n, e) where e is 2020 Mathematics Subject Classification."
"Let p and q be two large distinct prime numbers of size at least 1500 bits each."
"In our tests, we observed an accuracy of formula (4.1) of roughly 99%."

인용구

"It seems reasonable to expect that breaking our new algorithm is equivalent to factoring the large modulus n."
"The runtime analysis reveals that breaking RSA+ is as difficult as breaking traditional RSA."

핵심 통찰 요약

RSA+

by Soeren Klein... 게시일 arxiv.org 03-26-2024

https://arxiv.org/pdf/2301.01282.pdf

더 깊은 질문

How does the choice of x impact the security level of the proposed cryptosystem

提案された暗号システムのセキュリティレベルに対するxの選択肢は重要です。xが選ばれる方法によって、RSA+の安全性が大きく影響を受けます。例えば、xがnと互いに素であることを確認する必要があります。もし攻撃者が逆数を見つけ出すことができれば、これは暗号解読への脅威となり得ます。

What are the potential implications if an attacker manages to find an inverse modulo ϕ(n)

攻撃者がϕ(n)モジュロで逆数を見つけ出した場合、それは深刻な問題を引き起こす可能性があります。この知識を利用して平文mから復号化指数d（RSA+では˜
x）を計算することで、攻撃者は簡単にクリアテキストmを取得できるかもしれません。しかし、この行動は通常ファクタリングnへの道筋となります。

How can the concept of semantic security be applied to evaluate the effectiveness of the proposed cryptosystem

提案された暗号システムの有効性評価において意味的セキュリティ概念をどう活用するか考える必要があります。意味的セキュリティはパッシブ攻撃に対する保護水準です。具体的に言うと、「オスカー」という敵対勢力から「ボブ」へ送られたメッセージm0やm1（平文）からciphertext c（暗号文）作成後、「オスカー」はciphertext cから正しい平文 m0 または m1 を推測しなければならないゲーム形式です。
この概念ではRSA+の効果的性能評価や強度分析等行われるべきです。