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市場調查報告書
商品編碼
1623915

安全多方運算 (SMPC) 的全球市場:產業分析、規模、佔有率、成長、趨勢和預測 (2024-2031)

Secure Multiparty Computation (SMPC) Market: Global Industry Analysis, Size, Share, Growth, Trends, and Forecast, 2024 - 2031

出版日期: | 出版商: Persistence Market Research | 英文 190 Pages | 商品交期: 2-5個工作天內

價格
簡介目錄

重要見解

  • 安全多方運算 (SMPC) 市場規模(2024 年):9 億美元
  • 市場規模預測(2031年):17億美元
  • 全球市場成長率(2024-2031):複合年增長率9%

市場成長動力:

安全多方運算 (SMPC) 市場的推動因素包括對高階資料安全解決方案不斷增長的需求、資料隱私方面不斷增長的監管要求以及網路威脅的擴散。當組織跨分散式系統處理敏感資訊時,SMPC 為安全協作提供了強大的框架。區塊鏈技術和保護隱私的機器學習的日益普及也進一步加速了市場需求。此外,增加對安全資料分析和協作工具的投資也是推動市場成長的關鍵因素。

市場阻礙因素:

儘管潛力巨大,SMPC 市場仍面臨運算成本高、實施複雜性和技術意識低等課題。SMPC 協議的複雜性以及實施該協議所需的專業知識也會阻礙實施。此外,大規模應用程式中的可擴展性問題和遺留系統的變革阻力也阻礙了市場的擴張。克服這些障礙需要 SMPC 演算法的進步和加強用戶教育。

市場機會:

由於技術創新和用例擴展,SMPC 市場擁有巨大的成長機會。雲端運算和邊緣技術的進步正在為將 SMPC 整合到分散式環境中創造途徑。人工智慧和大數據分析等以數據為中心的行業的興起,為 SMPC 應用開闢了新途徑。技術提供者、學術機構和監管機構之間的合作將加速採用和標準化。由於對數位轉型和網路安全的需求不斷增長,新興國家的潛力尚未開發。

該報告調查了全球安全多方計算(SMPC)市場,並提供了市場定義和概述、市場促進和阻礙因素、各種趨勢、市場機會、課題和市場規模(數量和部分數量),詳細總結了趨勢和預測。

目錄

第1章執行概要

第2章 市場概況

  • 市場範圍和定義
  • 市場動態
    • 推動因素
    • 阻礙因素
    • 機會
    • 任務
    • 主要趨勢
  • 宏觀經濟因素
  • COVID-19 影響分析
  • 預測因素:相關性和影響
  • 監管狀況
  • 供應鏈分析
  • PESTLE分析
  • 波特五力分析

第3章價格走勢分析

  • 主要亮點
  • 影響產品價格的主要因素
  • 價格分析(按報價)
  • 區域價格以及過去和未來的成長趨勢

第 4 章 全球安全多方運算 (SMPC) 市場展望:趨勢與預測

  • 主要亮點
  • 市場規模分析與預測
  • 全球市場展望:依產品類別劃分
  • 市場吸引力分析:按產品類別
  • 全球市場前景:按發展劃分
  • 市場吸引力分析:按發展狀況
  • 全球市場前景:按產業劃分
  • 市場吸引力分析:按產業

第5章按地區劃分的全球安全多方計算 (SMPC) 市場展望

  • 主要亮點
  • 市場規模趨勢
  • 市場規模預測
    • 北美
    • 歐洲
    • 東亞
    • 南亞/大洋洲
    • 拉丁美洲
    • 中東/非洲
  • 市場吸引力分析:按地區

第 6 章 北美安全多方計算 (SMPC) 市場展望:趨勢與預測

  • 主要亮點
  • 價格分析
  • 市場規模趨勢
    • 按國家
    • 按規定類別
    • 展開類別
    • 行業
  • 市場規模趨勢/預測:按國家/地區劃分
    • 美國
    • 加拿大
  • 市場規模趨勢與預測:依產品類別
    • 解決方案
    • 服務
  • 市場規模趨勢與預測:按發展劃分
    • 本地
  • 市場規模趨勢與預測:按行業
    • BFSI
    • IT/IT人員
    • 政府
    • 衛生保健
    • 零售/電子商務
    • 其他
  • 市場吸引力分析

第 7 章歐洲安全多方計算 (SMPC) 市場展望:趨勢與預測

  • 主要亮點
  • 價格分析
  • 市場規模趨勢
  • 市場規模趨勢/預測:按國家/地區劃分
    • 德國
    • 法國
    • 英國
    • 義大利
    • 西班牙
    • 俄羅斯
    • 土耳其
    • 其他
  • 市場規模趨勢與預測:依產品類別
  • 市場規模趨勢與預測:按發展劃分
  • 市場規模趨勢與預測:按行業
  • 市場吸引力分析

第 8 章東亞安全多方計算 (SMPC) 市場展望:趨勢與預測

  • 主要亮點
  • 價格分析
  • 市場規模趨勢
  • 市場規模趨勢/預測:按國家/地區劃分
    • 中國
    • 日本
    • 韓國
  • 市場規模趨勢與預測:依產品類別
  • 市場規模趨勢與預測:按發展劃分
  • 市場規模趨勢與預測:按行業
  • 市場吸引力分析

第 9 章南亞和大洋洲安全多方計算 (SMPC) 市場前景:趨勢和預測

  • 主要亮點
  • 價格分析
  • 市場規模趨勢
  • 市場規模趨勢/預測:按國家/地區劃分
    • 印度
    • 東南亞
    • 澳洲
    • 其他
  • 市場規模趨勢與預測:依產品類別
  • 市場規模趨勢與預測:按發展劃分
  • 市場規模趨勢與預測:按行業
  • 市場吸引力分析

第 10 章拉丁美洲安全多方計算 (SMPC) 市場展望:趨勢與預測

  • 主要亮點
  • 價格分析
  • 市場規模趨勢
  • 市場規模趨勢/預測:按國家/地區劃分
    • 巴西
    • 墨西哥
    • 其他
  • 市場規模趨勢與預測:依產品類別
  • 市場規模趨勢與預測:按發展劃分
  • 市場規模趨勢與預測:按行業
  • 市場吸引力分析

第11章中東和非洲安全多方計算 (SMPC) 市場前景:趨勢與預測

  • 主要亮點
  • 價格分析
  • 市場規模趨勢
  • 市場規模趨勢/預測:按國家/地區劃分
    • 海灣合作委員會國家
    • 埃及
    • 南非
    • 北非
    • 其他
  • 市場規模趨勢與預測:依產品類別
  • 市場規模趨勢與預測:按發展劃分
  • 市場規模趨勢與預測:按行業
  • 市場吸引力分析

第12章 競爭格局

  • 市場佔有率分析
  • 市場結構
  • 公司簡介(詳細資訊 - 概述、財務、策略、近期發展)
    • Microsoft Corporation
    • IBM Corporation
    • Google LLC
    • Fireblocks
    • Blockdaemon
    • Penta Security Inc.
    • Qredo Services Ltd.
    • Zengo Ltd.
    • Inpher
    • CYBAVO Pte. Ltd.
    • Liminal Custody

第13章附錄

簡介目錄
Product Code: PMRREP35000

Persistence Market Research has recently released a comprehensive report on the global Secure Multiparty Computation (SMPC) Market, providing an in-depth analysis of key market dynamics, including driving forces, emerging trends, opportunities, and challenges. This report offers a detailed understanding of the market landscape, empowering stakeholders to make strategic decisions.

Key Insights:

  • SMPC Market Size (2024E): US$ 0.9 Bn
  • Projected Market Value (2031F): US$ 1.7 Bn
  • Global Market Growth Rate (CAGR 2024 to 2031): 9%

Secure Multiparty Computation (SMPC) Market - Report Scope:

Secure Multiparty Computation (SMPC) is a cryptographic technique that allows multiple parties to jointly compute a function over their inputs while keeping those inputs private. The technology is gaining traction across industries such as finance, healthcare, and government due to its potential to enhance data security and privacy in distributed computing environments. SMPC ensures compliance with stringent data privacy regulations and is increasingly used in applications like fraud detection, secure voting systems, and privacy-preserving AI.

Market Growth Drivers:

The SMPC market is driven by the rising need for advanced data security solutions, increasing regulatory requirements for data privacy, and the proliferation of cyber threats. As organizations handle sensitive information across distributed systems, SMPC provides a robust framework for secure collaboration. The growing adoption of blockchain technology and privacy-preserving machine learning further accelerates market demand. Additionally, increased investments in secure data analytics and collaboration tools are key factors fueling market growth.

Market Restraints:

Despite its potential, the SMPC market faces challenges such as high computational costs, complexity in implementation, and limited awareness about the technology. The intricate nature of SMPC protocols and the need for specialized knowledge for deployment can deter adoption. Furthermore, scalability issues in large-scale applications and resistance to change in legacy systems hinder market expansion. Overcoming these barriers will require advancements in SMPC algorithms and enhanced user education.

Market Opportunities:

The SMPC market presents significant opportunities for growth through innovation and expanding use cases. Advancements in cloud computing and edge technologies are creating pathways for the integration of SMPC in decentralized environments. The rise of data-centric industries, such as AI and big data analytics, opens up new avenues for SMPC application. Partnerships between technology providers, academic institutions, and regulatory bodies can accelerate adoption and standardization. Emerging economies represent untapped potential, driven by increasing digital transformation and cybersecurity needs.

Key Questions Answered in the Report:

  • What are the primary factors driving the growth of the Secure Multiparty Computation (SMPC) market?
  • Which industries are leading in the adoption of SMPC solutions?
  • How are advancements in cryptographic techniques shaping the SMPC landscape?
  • Who are the major players in the SMPC market, and what strategies are they employing to maintain their competitive edge?
  • What are the emerging trends and future prospects for the global SMPC market?

Competitive Intelligence and Business Strategy:

Key players in the global SMPC market, such as IBM, Intel Corporation, and Microsoft Corporation, are driving innovation through R&D investments and strategic partnerships. These companies focus on enhancing SMPC protocols for scalability, efficiency, and usability to meet diverse industry demands. Collaborations with industry verticals, cloud service providers, and academic institutions are critical for fostering technology adoption. Efforts to simplify deployment and integration while ensuring regulatory compliance are helping these firms gain a competitive edge in the evolving SMPC market.

Key Companies Profiled:

  • Microsoft Corporation
  • IBM Corporation
  • Google LLC
  • Fireblocks
  • Blockdaemon
  • Penta Security Inc.
  • Qredo Services Ltd.
  • Zengo Ltd.
  • Inpher
  • CYBAVO Pte. Ltd.
  • Liminal Custody

Secure Multiparty Computation (SMPC) Industry Research by Category:

By Offering

  • Solutions
  • Services

By Deployment

  • Cloud
  • On-premises

By Vertical

  • BFSI
  • IT and ITes
  • Government
  • Healthcare
  • Retail and E-commerce
  • Others

By Region

  • North America
  • Latin America
  • Europe
  • East Asia
  • South Asia
  • Oceania
  • The Middle East & Africa

Table of Contents

1. Executive Summary

  • 1.1. Global Secure Multiparty Computation (SMPC) Market Snapshot, 2024 and 2031
  • 1.2. Market Opportunity Assessment, 2024 - 2031, US$ Bn
  • 1.3. Key Market Trends
  • 1.4. Future Market Projections
  • 1.5. Premium Market Insights
  • 1.6. Industry Developments and Key Market Events
  • 1.7. PMR Analysis and Recommendations

2. Market Overview

  • 2.1. Market Scope and Definition
  • 2.2. Market Dynamics
    • 2.2.1. Drivers
    • 2.2.2. Restraints
    • 2.2.3. Opportunity
    • 2.2.4. Challenges
    • 2.2.5. Key Trends
  • 2.3. Macro-Economic Factors
    • 2.3.1. Global Sectorial Outlook
    • 2.3.2. Global GDP Growth Outlook
    • 2.3.3. Other Macro-economic Factors
  • 2.4. COVID-19 Impact Analysis
  • 2.5. Forecast Factors - Relevance and Impact
  • 2.6. Regulatory Landscape
  • 2.7. Supply Chain Analysis
  • 2.8. PESTLE Analysis
  • 2.9. Porter's Five Force Analysis

3. Price Trend Analysis, 2019 - 2031

  • 3.1. Key Highlights
  • 3.2. Key Factors Impacting Product Prices
  • 3.3. Pricing Analysis, By Offering
  • 3.4. Regional Prices and Historical and Future Growth Trends

4. Global Secure Multiparty Computation (SMPC) Market Outlook: Historical (2019 - 2023) and Forecast (2024 - 2031)

  • 4.1. Key Highlights
  • 4.2. Market Size (US$ Bn ) Analysis and Forecast
    • 4.2.1. Historical Market Size (US$ Bn ) Analysis, 2019 - 2023
    • 4.2.2. Current Market Size (US$ Bn ) Analysis and Forecast, 2024 - 2031
  • 4.3. Global Secure Multiparty Computation (SMPC) Market Outlook: Offering
    • 4.3.1. Introduction / Key Findings
    • 4.3.2. Historical Market Size (US$ Bn ) Analysis, By Offering, 2019 - 2023
    • 4.3.3. Current Market Size (US$ Bn ) Analysis and Forecast, By Offering, 2024 - 2031
      • 4.3.3.1. Solutions
      • 4.3.3.2. Services
  • 4.4. Market Attractiveness Analysis: Offering
  • 4.5. Global Secure Multiparty Computation (SMPC) Market Outlook: Deployment
    • 4.5.1. Introduction / Key Findings
    • 4.5.2. Historical Market Size (US$ Bn ) Analysis, By Deployment, 2019 - 2023
    • 4.5.3. Current Market Size (US$ Bn ) Analysis and Forecast, By Deployment, 2024 - 2031
      • 4.5.3.1. Cloud
      • 4.5.3.2. On-premises
  • 4.6. Market Attractiveness Analysis: Deployment
  • 4.7. Global Secure Multiparty Computation (SMPC) Market Outlook: Vertical
    • 4.7.1. Introduction / Key Findings
    • 4.7.2. Historical Market Size (US$ Bn ) Analysis, By Vertical, 2019 - 2023
    • 4.7.3. Current Market Size (US$ Bn ) Analysis and Forecast, By Vertical, 2024 - 2031
      • 4.7.3.1. BFSI
      • 4.7.3.2. IT & ITes
      • 4.7.3.3. Government
      • 4.7.3.4. Healthcare
      • 4.7.3.5. Retail & e-Commerce
      • 4.7.3.6. Others
  • 4.8. Market Attractiveness Analysis: Vertical

5. Global Secure Multiparty Computation (SMPC) Market Outlook: Region

  • 5.1. Key Highlights
  • 5.2. Historical Market Size (US$ Bn ) Analysis, By Region, 2019 - 2023
  • 5.3. Current Market Size (US$ Bn ) Analysis and Forecast, By Region, 2024 - 2031
    • 5.3.1. North America
    • 5.3.2. Europe
    • 5.3.3. East Asia
    • 5.3.4. South Asia and Oceania
    • 5.3.5. Latin America
    • 5.3.6. Middle East & Africa
  • 5.4. Market Attractiveness Analysis: Region

6. North America Secure Multiparty Computation (SMPC) Market Outlook: Historical (2019 - 2023) and Forecast (2024 - 2031)

  • 6.1. Key Highlights
  • 6.2. Pricing Analysis
  • 6.3. Historical Market Size (US$ Bn ) Analysis, By Market, 2019 - 2023
    • 6.3.1. By Country
    • 6.3.2. By Offering
    • 6.3.3. By Deployment
    • 6.3.4. By Vertical
  • 6.4. Current Market Size (US$ Bn ) Analysis and Forecast, By Country, 2024 - 2031
    • 6.4.1. U.S.
    • 6.4.2. Canada
  • 6.5. Current Market Size (US$ Bn ) Analysis and Forecast, By Offering, 2024 - 2031
    • 6.5.1. Solutions
    • 6.5.2. Services
  • 6.6. Current Market Size (US$ Bn ) Analysis and Forecast, By Deployment, 2024 - 2031
    • 6.6.1. Cloud
    • 6.6.2. On-premises
  • 6.7. Current Market Size (US$ Bn ) Analysis and Forecast, By Vertical, 2024 - 2031
    • 6.7.1. BFSI
    • 6.7.2. IT & ITes
    • 6.7.3. Government
    • 6.7.4. Healthcare
    • 6.7.5. Retail & e-Commerce
    • 6.7.6. Others
  • 6.8. Market Attractiveness Analysis

7. Europe Secure Multiparty Computation (SMPC) Market Outlook: Historical (2019 - 2023) and Forecast (2024 - 2031)

  • 7.1. Key Highlights
  • 7.2. Pricing Analysis
  • 7.3. Historical Market Size (US$ Bn ) Analysis, By Market, 2019 - 2023
    • 7.3.1. By Country
    • 7.3.2. By Offering
    • 7.3.3. By Deployment
    • 7.3.4. By Vertical
  • 7.4. Current Market Size (US$ Bn ) Analysis and Forecast, By Country, 2024 - 2031
    • 7.4.1. Germany
    • 7.4.2. France
    • 7.4.3. U.K.
    • 7.4.4. Italy
    • 7.4.5. Spain
    • 7.4.6. Russia
    • 7.4.7. Turkey
    • 7.4.8. Rest of Europe
  • 7.5. Current Market Size (US$ Bn ) Analysis and Forecast, By Offering, 2024 - 2031
    • 7.5.1. Solutions
    • 7.5.2. Services
  • 7.6. Current Market Size (US$ Bn ) Analysis and Forecast, By Deployment, 2024 - 2031
    • 7.6.1. Cloud
    • 7.6.2. On-premises
  • 7.7. Current Market Size (US$ Bn ) Analysis and Forecast, By Vertical, 2024 - 2031
    • 7.7.1. BFSI
    • 7.7.2. IT & ITes
    • 7.7.3. Government
    • 7.7.4. Healthcare
    • 7.7.5. Retail & e-Commerce
    • 7.7.6. Others
  • 7.8. Market Attractiveness Analysis

8. East Asia Secure Multiparty Computation (SMPC) Market Outlook: Historical (2019 - 2023) and Forecast (2024 - 2031)

  • 8.1. Key Highlights
  • 8.2. Pricing Analysis
  • 8.3. Historical Market Size (US$ Bn ) Analysis, By Market, 2019 - 2023
    • 8.3.1. By Country
    • 8.3.2. By Offering
    • 8.3.3. By Deployment
    • 8.3.4. By Vertical
  • 8.4. Current Market Size (US$ Bn ) Analysis and Forecast, By Country, 2024 - 2031
    • 8.4.1. China
    • 8.4.2. Japan
    • 8.4.3. South Korea
  • 8.5. Current Market Size (US$ Bn ) Analysis and Forecast, By Offering, 2024 - 2031
    • 8.5.1. Solutions
    • 8.5.2. Services
  • 8.6. Current Market Size (US$ Bn ) Analysis and Forecast, By Deployment, 2024 - 2031
    • 8.6.1. Cloud
    • 8.6.2. On-premises
  • 8.7. Current Market Size (US$ Bn ) Analysis and Forecast, By Vertical, 2024 - 2031
    • 8.7.1. BFSI
    • 8.7.2. IT & ITes
    • 8.7.3. Government
    • 8.7.4. Healthcare
    • 8.7.5. Retail & e-Commerce
    • 8.7.6. Others
  • 8.8. Market Attractiveness Analysis

9. South Asia & Oceania Secure Multiparty Computation (SMPC) Market Outlook: Historical (2019 - 2023) and Forecast (2024 - 2031)

  • 9.1. Key Highlights
  • 9.2. Pricing Analysis
  • 9.3. Historical Market Size (US$ Bn ) Analysis, By Market, 2019 - 2023
    • 9.3.1. By Country
    • 9.3.2. By Offering
    • 9.3.3. By Deployment
    • 9.3.4. By Vertical
  • 9.4. Current Market Size (US$ Bn ) Analysis and Forecast, By Country, 2024 - 2031
    • 9.4.1. India
    • 9.4.2. Southeast Asia
    • 9.4.3. ANZ
    • 9.4.4. Rest of South Asia & Oceania
  • 9.5. Current Market Size (US$ Bn ) Analysis and Forecast, By Offering, 2024 - 2031
    • 9.5.1. Solutions
    • 9.5.2. Services
  • 9.6. Current Market Size (US$ Bn ) Analysis and Forecast, By Deployment, 2024 - 2031
    • 9.6.1. Cloud
    • 9.6.2. On-premises
  • 9.7. Current Market Size (US$ Bn ) Analysis and Forecast, By Vertical, 2024 - 2031
    • 9.7.1. BFSI
    • 9.7.2. IT & ITes
    • 9.7.3. Government
    • 9.7.4. Healthcare
    • 9.7.5. Retail & e-Commerce
    • 9.7.6. Others
  • 9.8. Market Attractiveness Analysis

10. Latin America Secure Multiparty Computation (SMPC) Market Outlook: Historical (2019 - 2023) and Forecast (2024 - 2031)

  • 10.1. Key Highlights
  • 10.2. Pricing Analysis
  • 10.3. Historical Market Size (US$ Bn ) Analysis, By Market, 2019 - 2023
    • 10.3.1. By Country
    • 10.3.2. By Offering
    • 10.3.3. By Deployment
    • 10.3.4. By Vertical
  • 10.4. Current Market Size (US$ Bn ) Analysis and Forecast, By Country, 2024 - 2031
    • 10.4.1. Brazil
    • 10.4.2. Mexico
    • 10.4.3. Rest of Latin America
  • 10.5. Current Market Size (US$ Bn ) Analysis and Forecast, By Offering, 2024 - 2031
    • 10.5.1. Solutions
    • 10.5.2. Services
  • 10.6. Current Market Size (US$ Bn ) Analysis and Forecast, By Deployment, 2024 - 2031
    • 10.6.1. Cloud
    • 10.6.2. On-premises
  • 10.7. Current Market Size (US$ Bn ) Analysis and Forecast, By Vertical, 2024 - 2031
    • 10.7.1. BFSI
    • 10.7.2. IT & ITes
    • 10.7.3. Government
    • 10.7.4. Healthcare
    • 10.7.5. Retail & e-Commerce
    • 10.7.6. Others
  • 10.8. Market Attractiveness Analysis

11. Middle East & Africa Secure Multiparty Computation (SMPC) Market Outlook: Historical (2019 - 2023) and Forecast (2024 - 2031)

  • 11.1. Key Highlights
  • 11.2. Pricing Analysis
  • 11.3. Historical Market Size (US$ Bn ) Analysis, By Market, 2019 - 2023
    • 11.3.1. By Country
    • 11.3.2. By Offering
    • 11.3.3. By Deployment
    • 11.3.4. By Vertical
  • 11.4. Current Market Size (US$ Bn ) Analysis and Forecast, By Country, 2024 - 2031
    • 11.4.1. GCC Countries
    • 11.4.2. Egypt
    • 11.4.3. South Africa
    • 11.4.4. Northern Africa
    • 11.4.5. Rest of Middle East & Africa
  • 11.5. Current Market Size (US$ Bn ) Analysis and Forecast, By Offering, 2024 - 2031
    • 11.5.1. Solutions
    • 11.5.2. Services
  • 11.6. Current Market Size (US$ Bn ) Analysis and Forecast, By Deployment, 2024 - 2031
    • 11.6.1. Cloud
    • 11.6.2. On-premises
  • 11.7. Current Market Size (US$ Bn ) Analysis and Forecast, By Vertical, 2024 - 2031
    • 11.7.1. BFSI
    • 11.7.2. IT & ITes
    • 11.7.3. Government
    • 11.7.4. Healthcare
    • 11.7.5. Retail & e-Commerce
    • 11.7.6. Others
  • 11.8. Market Attractiveness Analysis

12. Competition Landscape

  • 12.1. Market Share Analysis, 2023
  • 12.2. Market Structure
    • 12.2.1. Competition Intensity Mapping By Market
    • 12.2.2. Competition Dashboard
  • 12.3. Company Profiles (Details - Overview, Financials, Strategy, Recent Developments)
    • 12.3.1. Microsoft Corporation
      • 12.3.1.1. Overview
      • 12.3.1.2. Segments and Products
      • 12.3.1.3. Key Financials
      • 12.3.1.4. Market Developments
      • 12.3.1.5. Market Strategy
    • 12.3.2. IBM Corporation
    • 12.3.3. Google LLC
    • 12.3.4. Fireblocks
    • 12.3.5. Blockdaemon
    • 12.3.6. Penta Security Inc.
    • 12.3.7. Qredo Services Ltd.
    • 12.3.8. Zengo Ltd.
    • 12.3.9. Inpher
    • 12.3.10. CYBAVO Pte. Ltd.
    • 12.3.11. Liminal Custody

13. Appendix

  • 13.1. Research Methodology
  • 13.2. Research Assumptions
  • 13.3. Acronyms and Abbreviations