In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of...In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of reference, accommodating multiple object-oriented durations in a dynamical system. The novelty of building temporal space using finite geometry is rooted in recent advancements in the theory of relationalism which utilizes Euclidean geometry, set theory, dimensional analysis, and a causal signal system. Multiple independent and co-existing cyclic durations are measurable as a network of finite one-dimensional timelines. The work aligns with Leibniz’s comments on relational measures of duration with the addition of using discrete cyclic relational events that define these finite temporal spaces, applicable to quantum and classical physics. Ancient formulas have symmetry along with divisional and subdivisional orders of operations that create discrete and ordered temporal geometric elements. Elements have cyclically conserved symmetry but unique cyclic dimensional quantities applicable for anchoring temporal equivalence relations in linear time. We present both fixed equivalences and expanded periods of temporal space offering a non-Greek calendar methodology consistent with ancient global timekeeping descriptions. Novel applications of Euclid’s division algorithm and Cantor’s pairing function introduce a novel paired function equation. The mathematical description of finite temporal space within relationalism theory offers an alternative discrete geometric methodology for examining ancient timekeeping with new hypotheses for Egyptian calendars.展开更多
函数加密作为一种多功能的新型公钥加密原语,因其能实现细粒度的密文计算,在云存储中有着广阔的应用前景,受到研究者们的广泛研究.因此,将数据的访问权限控制有机地融合到加解密算法中,实现“部分加解密可控、按需安全计算”是一个非常...函数加密作为一种多功能的新型公钥加密原语,因其能实现细粒度的密文计算,在云存储中有着广阔的应用前景,受到研究者们的广泛研究.因此,将数据的访问权限控制有机地融合到加解密算法中,实现“部分加解密可控、按需安全计算”是一个非常有意义的探索方向.但现有函数加密方案无法精细控制发送者权限且使用了较复杂的理论工具(如不可区分性混淆、多线性映射等),难以满足一些特定应用场合需求.面对量子攻击挑战,如何设计抗量子攻击的特殊、高效的函数加密方案成为一个研究热点.内积函数加密是函数加密的特殊形式,不仅能够实现更复杂的访问控制策略和策略隐藏,而且可以有效地控制数据的“部分访问”,提供更细粒度的查询,在满足数据机密性的同时提高隐私保护.针对更加灵活可控按需安全计算的难点,该文基于格上Learning with errors困难问题提出一种基于身份的细粒度访问控制内积函数加密方案.该方案首先将内积函数与通过原像抽样算法产生的向量相关联,生成函数私钥以此控制接收方的计算能力.其次,引入一个第三方(访问控制中心)充当访问控制功能实施者,通过剩余哈希引理及矩阵的秩检验密文的随机性,完成对密文的重随机化以实现控制发送者权限的目的.最后,接收者将转换后的密文通过内积函数私钥解密,仅计算得到关于原始消息的内积值.理论分析与实验评估表明,所提方案在性能上有明显优势,不仅可以抵御量子攻击,而且能够控制接收者的计算权限与发送者的发送权限,在保护用户数据机密性的同时,有效实现开放环境下数据可用不可见、数据可算不可识的细粒度权限可控密文计算的目标.展开更多
文摘In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of reference, accommodating multiple object-oriented durations in a dynamical system. The novelty of building temporal space using finite geometry is rooted in recent advancements in the theory of relationalism which utilizes Euclidean geometry, set theory, dimensional analysis, and a causal signal system. Multiple independent and co-existing cyclic durations are measurable as a network of finite one-dimensional timelines. The work aligns with Leibniz’s comments on relational measures of duration with the addition of using discrete cyclic relational events that define these finite temporal spaces, applicable to quantum and classical physics. Ancient formulas have symmetry along with divisional and subdivisional orders of operations that create discrete and ordered temporal geometric elements. Elements have cyclically conserved symmetry but unique cyclic dimensional quantities applicable for anchoring temporal equivalence relations in linear time. We present both fixed equivalences and expanded periods of temporal space offering a non-Greek calendar methodology consistent with ancient global timekeeping descriptions. Novel applications of Euclid’s division algorithm and Cantor’s pairing function introduce a novel paired function equation. The mathematical description of finite temporal space within relationalism theory offers an alternative discrete geometric methodology for examining ancient timekeeping with new hypotheses for Egyptian calendars.
文摘函数加密作为一种多功能的新型公钥加密原语,因其能实现细粒度的密文计算,在云存储中有着广阔的应用前景,受到研究者们的广泛研究.因此,将数据的访问权限控制有机地融合到加解密算法中,实现“部分加解密可控、按需安全计算”是一个非常有意义的探索方向.但现有函数加密方案无法精细控制发送者权限且使用了较复杂的理论工具(如不可区分性混淆、多线性映射等),难以满足一些特定应用场合需求.面对量子攻击挑战,如何设计抗量子攻击的特殊、高效的函数加密方案成为一个研究热点.内积函数加密是函数加密的特殊形式,不仅能够实现更复杂的访问控制策略和策略隐藏,而且可以有效地控制数据的“部分访问”,提供更细粒度的查询,在满足数据机密性的同时提高隐私保护.针对更加灵活可控按需安全计算的难点,该文基于格上Learning with errors困难问题提出一种基于身份的细粒度访问控制内积函数加密方案.该方案首先将内积函数与通过原像抽样算法产生的向量相关联,生成函数私钥以此控制接收方的计算能力.其次,引入一个第三方(访问控制中心)充当访问控制功能实施者,通过剩余哈希引理及矩阵的秩检验密文的随机性,完成对密文的重随机化以实现控制发送者权限的目的.最后,接收者将转换后的密文通过内积函数私钥解密,仅计算得到关于原始消息的内积值.理论分析与实验评估表明,所提方案在性能上有明显优势,不仅可以抵御量子攻击,而且能够控制接收者的计算权限与发送者的发送权限,在保护用户数据机密性的同时,有效实现开放环境下数据可用不可见、数据可算不可识的细粒度权限可控密文计算的目标.
